Master Maths Year 7

Master Maths 7 Worksheet 1 Measuring Angles

1

Name: 2. For the following angles, first estimate their size, then use a protractor to measure them.

1. Without measuring, circle the best estimate of each angle drawn below. (a)

o

30

80

150o

300o

(b)

B

O o

L

A

o

o

60

90

180o

100o

M J

K

(c)

40o

140o

240o

340o

N S L

(d)

(e)

45o

200o

225o

135o R

o

T

o

30

330

230o

130o

Angle

Estimate

Measure

ÐAOB ÐLMN (f)

45o

65o

ÐJKL

75o

85o

ÐRST

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Master Maths 7 Worksheet 2 Drawing Angles

2

Name: 1. Complete these angles using your protractor. (a)

30o

2. Follow these directions: o (a) At A draw a line at an angle of 40 . (b) Make this line 2 cm long. (c) At B draw a line at an angle of 140o. (d) Make this line 2 cm long. (e) Connect the ends of these two lines.

(b)

70o 40o

140o

B

A

(c)

The shape you have constructed o

100

is called a

3. Follow the directions below. (a) Find point C such that ABC is 90o and the length of BC is the same as AB. (b) Find point D such that BAD and o BCD are 105 . (c) What is the name of this shape?

(d)

300o B

(e)

A

55o

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Master Maths 7 Worksheet 3 Types of Angles

3

Name: 1. From the list below choose the correct name for the following angle sizes. REFLEX ACUTE OBTUSE RIGHT ANGLE STRAIGHT ANGLE Size of Angle 90

3. From the list below choose the correct name for each of the following angles and write the correct name under each angle. ABC

CAB P

Name

0 - 90 o

RPQ

QRP

A B

C

C

R

o

PQR B

A

Q

o

BCA

o

90 - 180 180

180o - 360o

A

P

2. In the boxes under the following angles state if each angle is: A - an acute angle B - a right angle C - an obtuse angle D - a straight angle E - a reflex angle (a)

R

Q

o

B

P

C

R

4. In the diagram below there are 5 acute angles, 5 obtuse angles and 10 reflex angles. Under the diagram list the names (eg AOB) of all of these angles. B

(c)

(b)

Q

C A

O D

Acute Angles (d)

(e)

(g) 300o

o

(k) 195

Reflex Angles

(f)

o

(h) 58

o

(l) 96

o

o

(i) 139

(j) 180

o

(m) 289

E

Obtuse Angles

o

(n) 23

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Master Maths 7 Worksheet 4 Calculating Angles

4

Name: 1. Calculate the unknown angles. (a)

2. (a) Find the obtuse angle formed by the hands of a clock at 8:00.

(b)

11

b

1 2 3

9

40o

60o

12

10

4

8 7

a

6

5

(b) Find the reflex angle formed by the hands of a clock at 8:00. a=

b=

(c)

(d)

o

30 d

c

o

110

3. The blades of a windmill complete one revolution every minute. What angle would the blades turn through in the following times? (a) One second

40o (b) Ten seconds

c=

d= 4. How many degrees are in the following angles?

(e)

(a) 15 of a circle

(f) 127 o

o

f

32

e

(b) 3 of a circle 5

e=

f= 5. (a) Find x.

(g)

(h)

o

281 g

2x

34

o

x

h 43o

3x

(b) Find y. y + 10o

y

o

y + 20 y + 30o g=

h=

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Master Maths 7 Worksheet 5 Angles in Triangles

5

Name: 1. Calculate the unknown angles. (a)

b

(b)

a

o

30

35

o o

40

2. Two hikers walk in a direction of north 30o east from their camp and then change their direction to north 55o west until they are directly north of their camp. See the diagram below. Find angles x and y from this diagram.

65

o

x a=

y

b=

o 35

(c)

o

55

30o

(d)

x=

o

52

c

c=

d

d=

(e)

f

(f) 100

f

o

e

58

e

o

y=

Camp

3. Two cables are used to support a pole as shown in this diagram. The cable closest to the pole makes an angle o o of 62 with the ground. 8 The angle between the o cables is 8 . Find the angle (q) that the other cable makes 62o q with the ground.

f=

e=

q= (g)

35o

(h) h

g

4. In this diagram the length of line BD is the same as the length of DC.

B

o

D

50o o

70

g=

66

o

h=

72o

Find

ABD.

30 100

o

C

25o

A ABD =

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Master Maths 7 Worksheet 6 The Compass 1

6

Name: Your task is to draw a larger version of the compass diagram shown on the right by following the directions below. Use a pencil to allow for corrections. 1. On the W line, mark a point 2 cm from the centre. 2. Mark points 2 cm from the centre on the N, E and S lines. 3. From the 2 cm mark on the W line, draw lines to the ends of the N and S lines. 4. From the 2 cm mark on the N line, draw lines to the ends of the E and W lines. 5. Repeat this procedure for the other two 2 cm marks. 6. Draw a line 5 cm long from the centre, at an angle of 45o between N and E. 7. Draw similar lines between N & W, W & S and S & E. 8. Connect the end of these lines to the two closest 2 cm marks. 9. Colour your diagram similar to the diagram provided.

N

E

W

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Master Maths 7 Worksheet 7 The Compass 2

7

Name: 1. Find the angle between the compass points below, always moving in a clockwise direction when finding the angle. Examples: The angle between N & E is 90o The angle between N & W is 270o

3. You are at the centre of the grid below. Follow the directions and find the animal at which you finish.

Directions: South 4 units West 3 units North 3 units East 5 units North 5 units

Compass Points

E

S

E

W

SE

SW

SW

SE

NW

S

NE

N

SE

NW

SW

W

Angle Between

J

2. A person is facing East. He turns left 90o. He then about faces. He turns right 90o. He then about faces again. What direction does he now face?

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Master Maths 7 Worksheet 8 Polygons

8

Name: X 1. Choose which of the angles below is the right-angle in this shape. A XYZ B ZXY Z C YZX D XZY 2. Choose which of the lines below is parallel to PQ. A QR B RS C SQ D SP

6. Draw a polygon that has three vertex o angles greater than 180 . Y

P

S

Q

R

7. (a) Unscramble these letters to find the name of the shape below. ROUGH PETAL EARRING

3. Colour in the shapes below that are polygons.

(b) Using a ruler, draw all possible diagonals in this shape. (c) How many diagonals are there? 4. Circle the shape/s from question 3 that are regular polygons. 5. In the space below draw a concave hexagon and a convex hexagon.

Concave hexagon

8. Research different polygons and find the names of three polygons that have more than 10 sides. State how many sides they have.

Convex hexagon

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Master Maths 7 Worksheet 9 Triangles and Quadrilaterals

9

Name: 1. Study the triangles below and colour in red the scalene triangles and colour in blue the isosceles triangles. 30o

8m

4. Find the unknown angles in the following quadrilaterals. o (a) 110 130o

8m

o

80

a

60o 60o

100o

60o 40o

45o

85o

(b)

17 m

105o

105o

76o

11 m 3m

a=

10 m 52o

b=

b

4m

2. What is the name given to the triangles not coloured in from question 1?

o

64

(c)

238o 3. Write the name of each of the following quadrilaterals.

c

c

2d

(d)

c=

o

2d + 30

o

d + 30 d

d=

5. How many rectangles are in the drawing below? (The answer is not 6!)

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Master Maths 7 Worksheet 10 Symmetry

10

Name: 1. Complete these symmetrical shapes by drawing the other half. Colour in the shapes.

3. (a) Complete the other half of the symmetrical letters below. The completed letters will spell words.

DECODED CHOICE DIOXIDE (b) Do these words have a horizontal or vertical axis of symmetry?

(c) Write two other words that have the same axis of symmetry.

2. Complete and colour in the symmetrical shape below. 4. (a) Complete the other half of the symmetrical letters below. The completed letters will spell words.

M U M

H O T

W A Y

(b) Do these words have a horizontal or vertical axis of symmetry?

(c) Write two other words that have the same axis of symmetry.

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Master Maths 7 Worksheet 11 Rotations

11

Name: 1. Rotate the following shapes 90o clockwise about O and redraw them. Colour in the resultant shapes.

2. Colour in the shapes below that would appear the same after being rotated 90o in a clockwise direction about O? O

O

O

O O O O

O

O

O 3. For those shapes in question 2 that are not coloured in, write under them the minimum clockwise rotation needed for them to appear the same. 4. Use the guide lines on the diagram below to redraw the shaded shape after it is rotated 30o about the centre of the circles. Continue rotating and redrawing this shape until the pattern is complete. Creatively colour it in.

O

O O

O

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Master Maths 7 Worksheet 12 Tessellations

12

Name: On the grids below create several tessellations. Be creative with shapes and colours.

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Master Maths 7 Worksheet 13 Constructions 1

13

Name: 1. Using the line AB below, a compass and a ruler, construct an equilateral triangle.

A

4. Use a compass and ruler to construct a regular hexagon of sides 4 cm. Start with a circle of radius 4 cm and use the compass to scribe 4 cm marks around its circumference.

B

2. Using the line CD below, a compass and a ruler, construct an isosceles triangle with the two equal sides of length 5 cm.

5. Use a compass and ruler to construct a perpendicular bisector of the line PQ below.

C

D

P

3. Use a compass and a ruler to construct a triangle with sides of length 5 cm, 4 cm and 3 cm.

Q

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Master Maths 7 Worksheet 14 Constructions 2

14

Name: 3. Complete this sequence by drawing the last two diagrams.

1. Use a compass to bisect ÐABC.

A

B

C

2. Use a compass to construct this shape on the larger grid below.

4. Without using a ruler, sketch these two diagrams and colour them in.

V

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Master Maths 7 Worksheet 15 3 Dimensional Objects 1

15

Name: 1. Sketch these objects in the spaces provided.

2. This object has: * 8 vertices * 6 faces * 12 side edges

(a)

Complete the following table. Object

Vertices

Faces

Edges

(b)

3. Find the names of the following objects. (c)

Name

(d)

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Master Maths 7 Worksheet 16 3 Dimensional Objects 2

16

Name: 4. Three different views are shown of the same die. Fill in the missing dots on the blank face.

1. There are 8 small cubes in this object.

How many small cubes are in the two objects below? (a)

cubes

(b) 5. Suppose the shape below was cut out and folded on the dotted lines to form a solid object.

cubes

2. If the object in question 1(a) was to be painted black, how many of the small cubes would have: (a) 3 black faces?

What is the name of the solid object that would be formed?

(b) 2 black faces? (c) 1 black face? Complete: 3. Unscramble to find words from this worksheet:

CAFES

It would have

faces.

It would have

edges.

It would have

vertices.

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Master Maths 7 Worksheet 17 Isometric Drawings 1

17

Name: 1. (c)

1. Redraw the following objects on the isometric dots provided. (a)

. . . . . .

. . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . . . .

. . . . . .

. . . . .

. . . . . .

. . . . . .

. . . . .

. . . . .

. . . . . .

. . . . .

2. The front, side and top views of an object are drawn below. Draw the object on the isometric dots provided.

(b) Front view

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . .

. . . . .

. . . . . . de *

Si w vie

. . . . . . .

Side view

. . . . . .

. . . . . . .

Top view

. . . . . .

. . . . . . .

. . . . . . * Front view

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Master Maths 7 Worksheet 18 Isometric Drawings 2

18

Name: 1. An object is drawn on the isometric dots below.

. . . . . . .* Side

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

. . . . . . .

*

. . . . . . .

Side view

Top view

. . . . . . .

Front

Sketch the front, side and top views of this object in the spaces below.

Front view

2. The letter T is drawn on the dots below.

. . . . . . . .

. . . . . . .

. . . . . . . .

. . . . . . .

. . . . . . . .

. . . . . . .

On the dots provided below draw the letters F and H.

. . . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . .

. . . . . . . . . . . . .

. . . . . . . . . . . .

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Master Maths 7 Worksheet 19 Maps 1

19

Name: This is part of a street directory of the suburb of Myrtle Grove. SWIMMING POOL CHURCH

8

TOWN HALL

KURRAJONG ST

5

GOANNA ST

WOMBAT RESERVE

WATTLE RD

6

FLAMINGO ST

KANGAROO ST

7

POLICE STATION

ROSELLA ST

4 POST OFFICE

3

SCHOOL

BILBY AV

2 1

SUPER MARKET

A

B

C

D

E

F

G

H

I

J

K

1. Find the compass directions of the following locations from the school. (a) Swimming Pool

(b) Post Office

(c) Church

(d) Supermarket

2. What features are located at the following grid reference points? (a) H8

(b) K7

(c) J3

(d) C3

3. Find the grid reference points for the following features. (a) Wombat reserve

(b) Swimming pool

(c) Town hall

(d) Supermarket

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Master Maths 7 Worksheet 20 Maps 2

20

Name: This is part of a street directory of the suburb of Myrtle Grove. SWIMMING POOL CHURCH

8

TOWN HALL

KURRAJONG ST

5

GOANNA ST

WOMBAT RESERVE

WATTLE RD

6

FLAMINGO ST

KANGAROO ST

7

POLICE STATION

ROSELLA ST

4 POST OFFICE

3

SCHOOL

BILBY AV

2 1

SUPER MARKET

A

B

C

D

E

F

G

H

I

J

K

Scale: 1 cm = 200 m 1. State the locality at which you would arrive at if you followed the directions below starting at the school entrance. Note the scale on the map is 1 cm = 200 m. (a) North 800 metres then East 1700 metres. (b) North 400 metres then West 300 metres. 2. Find the distance between the following pairs of localities. Choose the shortest path along the streets. (a) School and Town Hall

(b) Supermarket and Swimming Pool

(d) Church and Wombat Reserve

(e) Police Station and Post Office

(c) Church and Post Office

(f) Church and School

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Master Maths 7 Worksheet 21 Networks 1

21

Name: A family visited a zoo. The exhibits they wanted to see were the pandas, reptiles, monkeys and birds. A map showing these exhibits, the entrance and the distances between them is shown below.

List all the possible orders that the exhibits could be seen, find the total distance walked for each and hence find the order that would lead to the least amount of walking. (Some orders will be the reverse of others).

145 m

101 m

93 m

87 m 73 m

78 m

92 m

137 m

Entrance/Exit

The family wanted to find the order of seeing these exhibits that would mean the shortest distance. One possible order would be, after entering(E) the zoo, to see the pandas(P), reptiles(R), monkeys(M) and birds(B), then walk to the exit(E). This could be shown simply as: E - P - R - M - B - E The distances between exhibits in this order are shown below: E

137 m

P 87 m

R

93 m

M

-

B

145 m

-

E

92 m

The total distance walked while seeing the exhibits in this order is: 137 + 87 + 93 + 145 + 92 = 554 m

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Master Maths 7 Worksheet 22 Networks 2

22

Name: 1. Colour in the shapes below that could be drawn without lifting your pen and without drawing any line more than once. Clearly show below how these can be drawn.

2. This diagram shows the major towns between Adelaide and Darwin. The distances, in kilometres, from the two capital cities are also shown. (a) What is the distance from Adelaide to: (i) Woomera?

0

Ù

3051

119 2932

Ù

Ú

320 2731

Ù

Ú

997 2054

Ù

Ú

Katherine

Tennant Creek Alice Springs

2193 858

Coober Pedy

(ii) Katherine? Ù

Ú

2560 491

Ù

3051

Ù

Woomera

Ú

2733 318

Ù (ii) Coober Pedy?

Adelaide River

1548

Ú

(b) What is the distance from Darwin to: (i) Tennant Creek?

Darwin

Ú

Ú 0

Port Augusta

Adelaide

Ú

(c) What is the distance from Woomera to Katherine? (d) What is the distance from Tennant Creek to Coober Pedy? (e) What is the distance from Port Augusta to Katherine? (f) The distance from Alice Springs to Darwin is missing from the diagram. Find this distance.

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Master Maths 7 Worksheet 23 Whole Numbers 1

23

Name: 1. Write the following numbers in numeral form. (a) seven hundred and forty-three

5. Write the correct symbol (< or >) between the following pairs of numbers. (a)

(b) thirteen thousand, eight hundred and nine (c) six hundred and fifty-three thousand and twenty (d) seven million, seventeen thousand, eight hundred and fifty-four

57

(c) 1092

68

(b) 394

389

1029

(d) 660

671

6. Write the number shown by the dot on the number lines below. (a) 0

100

200

500

1000

1000

2000

(b) 2. Write the following numbers in words. (a) 956

0

(c) (b) 47 180

(c) 8 203 914

0

7. The divisions on this thermometer are 5oC. (a)Write the temperature next to each mark on o the scale. (0 is shown) (b) What temperature is this thermometer reading?

o

C

0

3. Using all the digits 6, 8, 1 and 3 write: (a) the largest number possible (b) the smallest number possible 4. Arrange the following numbers in order from the smallest to the largest. 3452 3542 3425 2345 2543

8. (a) List all the odd numbers that can be formed using the digits 5, 7 and 4.

(b) List all the even numbers that can be formed using these digits.

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Master Maths 7 Worksheet 24 Whole Numbers 2 - Place Value

24

Name: 1. Write the whole number represented on each spike abacus below. (a)

5. Add 100 to the following numbers. (a) 9

(b) 1075

(c) 12 970

(b)

6. Subtract 100 to the following numbers. (a) 3781

(b) 4062

(c) 32 504

2. Write each of the following as one number. 7. Round the following numbers to the nearest 10. (c) 6797 (a) 37 (b) 852

(a) 4000 + 900 + 70 + 2 (b) 5000 + 300 + 6

8. Round the following numbers to the nearest 100. (c) 5896 (a) 739 (b) 3463

(c) 8000 + 10 (d) 60 000 + 400 + 50 (e) 700 + 3000 + 9 (f) 20 + 7000 + 80 000 3. Add 10 to the following numbers. (a) 79

(d) 95

(b) 349

(e) 2350

9. Find the following numbers. (a) This four digit odd number has seven thousands and twice as many hundreds as it has tens. The sum of the three digits is 28.

(c) 703

(f) 8993

(b) The sum of the four digits of this number is 20. It has one more unit than it has thousands. It has three more hundreds than it has units. It is larger than 5000.

4. Subtract 10 to the following numbers. (a) 81

(b) 497

(c) 501

10. Rearrange the letters of the following phrases to spell numbers. (a) SHIVERY TENT

(d) 1003

(e) 2675

(f) 7002 (b) NEW TOY NET

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Master Maths 7 Worksheet 25 Addition and Subtraction

25

Name: 1. Complete this addition table without using a calculator.

+

31

36 58

4. Jay and Mitchell bought a 10 kg box of small chocolates. They each guessed how many chocolates were in the box. Jay guessed 258. Mitchell guessed 316. They counted 284 chocolates in the box. (a) Who was closest with their guess?

52 63

70 15

41 86

39

(b) They roughly divided the chocolates into two piles. Jay had 161 in his pile. How many does he need to give Mitchell so they have the same number each?

50 61 2. Find the answers to the following problems. (a)

(c)

568 +927

(b)

823 17

-4

2069 157 4385 671 + 1304

3. Four containers were to be loaded onto a truck. The weights of the containers are shown below.

1256 kg 985 kg

5. Find the missing digits in the following calculations.

28 5 6 + 17 1000

(a)

(b)

8 -

5

9 228

6. Write numbers in the circles in the diagram below so that the numbers in the squares are the sum of the numbers in the two adjoining circles.

842 kg 1397 kg

(a) Find the total weight of the four containers. Do not use a calculator.

(b) The maximum weight that can be carried by the truck is 4250 kg. How many kilograms will need to be removed to make this load limit?

55

56

57

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Master Maths 7 Worksheet 26 Multiplication, Factors and Multiples

26

Name: 1. Complete this multiplication table without using a calculator.

´

8

4. What is the highest common factor of the following pairs of numbers. (a) 15, 40 (b) 42, 40 (c) 40, 120

10

21 4

24 48 40 48

9 7

18 49

2. (a) Dali's chooks laid 6 eggs every day. How many eggs does he get each week? (b) Dali sells 3 dozen of his eggs each week to friends. How many eggs does he keep for himself each week? (c) Mez bought 9 tubes of paint. She received $16 change from $70. How much did each tube of paint cost?

3. Write all the factors of the following numbers. (a) 15

5. A carpenter had two lengths of wood. One was 120 cm and the other was 72 cm long He wanted to cut them into small pieces. (a) What is the largest length that these small pieces could be and have no waste?

(b) How many of these small pieces would there be?

6. Find the lowest common multiple of the following pairs of numbers. (a) 9, 12 (b) 6, 9 (c) 12, 10

7. There are three bus services from the Abbey bus station. Every second day a bus leaves for Berton. Every third day a bus leaves for Claire. Every fifth day a bus leaves for Darley. st On January 1 all three buses services run. (a) What are the next three dates when two buses will run?

(b) 40 (c) 42

(b) What is the next date that all three buses will run?

(d) 120 Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 27 Divisibility and Prime Numbers

27

Name: 1. Use the tests for divisibility to complete the table below by ticking the boxes to indicate which of the numbers at the top are factors of the numbers shown. One row is completed as an example.

2

3

4

5

6

8

10

9

8880 3942 32 160 44 280 51 840 2136 36 720 2. From the numbers below, circle the two that are prime numbers.

352 387

349 531

571

505

0 0 3

45 9

3. Complete the factor tree for each of the following numbers.

1764

9000

4. Write the two numbers from question 3 as products of their prime factors. (a) 1764 = (b) 9000 =

5. (a) Unscramble the letters of the phrase below to spell the name given to a number that is not a prime number. MICE UP TROMBONES

(b) Unscramble the letters of the phrases below to find terms from this worksheet. NUMB PREMIER

CARROT FEET

VIII TIDY LIBS

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Master Maths 7 Worksheet 28 Powers and Square Roots

28

Name: 1. Write the following terms in index form. (a) 2 ´ 2 ´ 2 ´ 2 (b) 5 ´ 5 ´ 5

4. Use a calculator to evaluate the following. 4

(a) 3 ´ 53 (b) 23 ´ 54 ´ 72

2. (a) Complete the factor tree for each of the following numbers.

8100

5488

(c) 74 + 11

3

3 (d) (6.8)

(e)

4624

(f)

6625.96

5. Write the following numbers in scientific notation. (a) 7000 (b) Write these numbers as products of their prime factors.

(c) 5 000 000

8100 =

(d) 800 000 000

5488 = (c) Write these numbers as products of their prime factors in index form. 8100 =

(e) three thousand million

6. Research the population of three major cities in the world. Round the population off and write the population in scientific notation.

5488 = 3. Find the numbers represented by the products of prime numbers shown below. (a) 23 ´ 32 ´ 7

(b) 20 000

2

City

Population (Rounded)

Population (Sci. Notation)

3 2 3 (b) 3 ´ 5 ´ 7

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Master Maths 7 Worksheet 29 Multiplication and Division

29

Name: 1. Complete the following multiplication problems. (a)

(c)

68 ´ 7

(b)

27 ´18

(d)

´

359 4

´

569 87

6. Complete the following table. One line is completed as an example. Problem Answer Difference Answer with Using Between Using Problem Rounded Rounded the Calculator Numbers Numbers Answers

23 ´ 57

1311

20 ´ 60

1200

111

57 ´ 8 83 ´ 29 43 ´ 78 92 ´ 49 7. Without using a calculator evaluate the following. (a) 348 ¸ 6

2. Find the product of 73 and 96. Clearly show workings.

(b) 2036 ¸ 4 (c) 16 030 ¸ 5 3. Without using a calculator evaluate the following. (a) 40 ´ 100

(d) 2506 ¸ 7 (e) 6000 ¸ 20 (f) 80 000 ¸ 400

(b) 30 ´ 60 (c) 50 ´ 700

8. Complete the following table. One line is completed as an example.

(d) 800 ´ 900 4. Round the following numbers to the nearest 10. (a) 48

(b) 94

(c) 51

(d) 27

Problem Answer Difference Answer with Using Between Using Problem Rounded Rounded the Calculator Numbers Numbers Answers

924 ¸ 28

33

900 ¸ 30

30

3

609 ¸ 21 5. Round the following numbers to the nearest 100. (a) 371

(b) 847

(c) 209

(d) 780

899 ¸ 29 1536 ¸ 48 792 ¸ 18

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Master Maths 7 Worksheet 30 Problem Solving

30

Name: 1. The lowest temperature overnight was 7oC. o The highest temperature the next day was 25 C. By how many degrees did the temperature rise that day? 2. A truck weighs 2350 kg. 22 containers each weighing 75 kg are loaded onto the truck. What will be the total weight of the truck and its load?

3. Tim makes picture frames. It takes him 40 minutes to make each frame. (a) How many minutes will it take him to make 15 frames?

(b) How many hours is this?

(c) Tim has calculated that the material for each frame costs $25. Tim charges $20 per hour for his labour. What will be the total charge (materials and labour) for Tim to make the 15 frames?

4. Chloe is starting a job earning $18 per hour. If she works for 14 hours, how much will she earn?

5. Jason works for 12 hours and earns $192. How much did he earn each hour?

6. There are 52 people who want to play in a badminton competition. Each team is to have four players. How many teams can be formed?

7. A sporting club is going to conduct a ride-a-thon to raise money. One bike is to be ridden non-stop for two days. There are 24 riders. For how many hours will each rider need to ride?

8. Bales of horse feed are being sold at a special price of $8 per bale for a minimum of 30 bales. Four friends decide to equally share the cost of buying 30 bales. How much will they each need to pay?

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Master Maths 7 Worksheet 31 BODMAS

31

Name: 1. Write the word represented by each letter in the acronym BODMAS.

3. Solve the following problems. (a) 8 ´ (4 + 2) - 6 ¸ 3 + 12 of (16 - 4)

B O D

(b) 12 + 8 ¸ 4 ´ 3 - 12 of 6 ´ 4 - 12 ¸ 2

M A S 2. Solve the following problems. (a) 6 + 3 ´ 4 (b) (6 + 3) ´ 4

(c)

1 2

of 8 + 6

(e) 9 ´ (4 + 6) ¸ 3

(d)

1 2

of (8 + 6)

(f) 9 ´ 4 + 6 ¸ 3

4. In the spaces provided write one of the operations (+, -, ´, ¸) to make each equation correct (a) 6

4

(b) 8

12

(c) 9

3

(d) 10

8 = 16 4 = 11 3 = 10 5

4

2 = 10

5. Include brackets in the following equations to make them correct. (a) 4 + 3 ´ 3 + 2 = 19 (b) 4 ´ 2 + 8 ¸ 2 + 2 = 10 6. Complete the following equations by adding brackets and/or the operation symbols.

(e) 4 ´ 12 ¸ 6 ´ 5

(f) 8 + 9 - 3 + 7 - 5

(a) 2

2

2

2=6

(b) 2

2

2

2=4

(c) 2

2

2

2 = 12

(d) 2

2

2

2=2

(e) 2

2

2

2=5

(f) 2

2

2

2=1

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Master Maths 7 Worksheet 32 Fractions 1

32

Name: 1. What fraction of these shapes is shaded? (a)

6. Write the following fractions in words. (a)

(b) (b)

4 5 3 7

7. Complete the following equivalent fractions.

2. What fraction is shown by the dot on each of these number lines? (a) 0

1

(a)

3 = 4 16

(b)

21 7 = 8

(c)

5 = 6 42

(d)

12 2 = 9

(b) 0

1

8. Write these fractions in their simplest form.

3. Write a fraction with a denominator of 8 and a numerator of 9.

(a)

6 = 9

(b)

15 = 20

4. (a) Karley's cat had a litter of five kittens. Four were male. What fraction of the litter was male?

(c)

18 = 27

(d)

64 = 72

(b) Karley's dog also had a litter. There were 3 male and 2 female puppies. What fraction of this litter was female?

9. What fraction of this shape is shaded? Write answer in its simplest form

5. Write the following fractions in numeral form. (a) seven-eighths (b) three-quarters

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Master Maths 7 Worksheet 33 Fractions 2

33

Name: 1. Find the lowest common denominator for the following pairs of fractions and change each fraction to have this denominator. (a)

5 8

3 4

(b)

3 4

5. Three blocks of chocolate are divided as shown below and the shaded sections are eaten.

4 5

A

B

C

List the blocks of chocolate in order from the one with the most remaining to the one with the least remaining.

(c)

3 5

5 8

(d)

2 3

3 8

6. Change the following to a mixed numbers. 2. Write the symbol < or > between the fractions in question 1 to indicate which fraction is larger. 3. Which of the following shapes has the larger shaded area?

(a)

8 = 3

(b)

16 = 5

(c)

26 = 7

(d)

49 = 8

7. Change the following to improper fractions. A

B

4. List four fractions that are equivalent to the ones below.

(a)

(b)

10 16 24 32

(a)

2 35 =

(b)

3 47 =

(c)

6 79 =

(d)

5 8 11 =

8. (a) How many quarters are in 3? (b) How many fifths are in 6? 2

(c) How many thirds are in 8 3 ?

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Master Maths 7 Worksheet 34 Fractions - Addition and Subtraction

34

Name: 1. Complete the following calculations. (a)

2 5

2

+ 5

(b) 79 - 59

(c)

3 7

2

+ 7

3. Complete the following calculations. Write answers as mixed numbers in their simplest form. 5

2

3

(a) 3 6 + 2 3

(d)

1 - 38

(e) 2 15 + 3 25

(f) 5 67 - 1 37

2. Complete the following calculations. Write answers in their simplest form. (a)

1 6

1

+ 3

9 - 3 (b) 10 5

9

(b) 5 4 - 2 10

4. A cake required the following ingredients.

5 1 (c) 12 + 3

3 4

kg of flour

1 2

kg of sultanas

1 4

kg of sugar

1 4

kg of butter

What is the total weight of these ingredients?

(d) 38 + 13

(e) 78 - 35

(f)

(g) 16 + 58

5 (h) 34 - 11

(i)

3 7

+ 3

1

2 9

+ 6

1

5. It is recommended to allow 4 2 hours to walk along a certain track in a national park. Two people walk for 2 34 hours before stopping for lunch. How long will it take them to complete the walk?

1

6. Jennie made a pizza. She ate one-quarter and gave one-third to her friend. What fraction of the pizza remains?

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Master Maths 7 Worksheet 35 Fractions - Multiplication and Division

35

Name: 1. Complete the following calculations. (a)

1 3

´

2 5

(b)

3 4

´

5 7

(c)

5. Find three-quarters of five-eighths. 5 6

´

7 8

6. Complete the following calculations. Write answers in their simplest form. 2. Complete the following calculations. Cancel fractions to their simplest form and write answers in their simplest form. (a)

3 5

10

´ 21

9 10 (b) 16 ´ 21

2

3

1 3

2

(b) 34 ¸ 15 16

¸ 5

3 9 (c) 10 ¸ 14

8 25 (c) 15 ´ 36

3. Complete the following calculations. Write answers as mixed numbers in their simplest form. 8

(a) 2 9 ´ 3 8

(a)

7. Complete the following calculations. Write answers in their simplest form. 5

2

(a) 3 9 ¸ 6 3

9

2

(b) 2 10 ¸ 4 5

3

(b) 3 9 ´ 310

8. Complete the following calculations. 4. Find the following. (a) 13 of 12 m

(b) 34 of 20 kg (c) 58 of $40

(d) 35 of 45 m

7 (e) 10 of 80 kg (f) 57 of $35

(a) 6 ¸ 25

(b) 8 ¸ 2 34

3 (c) 10 ¸9

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Master Maths 7 Worksheet 36 Fractions - Problem Solving

36

Name: 1. Don, Ron and Con earned $300. Don is to receive one-quarter, Ron is to receive one-fifth and Con will receive the remainder. (a) What fraction of the earnings will Con receive?

5. Friends were watching a movie that was 1 3 2 hours long. They decided to stop it three-fifths of the way through to have a snack. (a) How many hours were remaining? Give answer as a mixed number.

(b) How much will they each receive? (b) How many minutes were remaining? Don Ron Con 1

2. A water container holds 2 2 litres. How many of these containers would be needed to fill a 30 litre drum?

3. A crowd 3000 spectators watched a game of soccer between the Strikers and the Onsiders. Four-fifths of the crowd barracked for the Strikers. How many people barracked for each team? Strikers

6. A cyclist completes 30 laps of a track in in 18 minutes. (a) How many minutes did it take to complete one lap? Give answer as a fraction in its simplest form.

(b) How many minutes would it take to complete 80 laps?

(c) How many laps could be completed if the cyclist rode for one hour?

Onsiders 3

4. A brick weighs 4 kg. (a) What would be the weight of 240 bricks?

(b) How many bricks would there be in a crate that weighs 600 kg?

7. A mixture of sand and cement was such that the amount of cement was one-quarter the amount of sand. How many kilograms of each would be required to make 20 kg of the mixture? sand cement Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 37 Decimal Numbers 1

37

Name: 1. Write the following decimal numbers in words. (a) 0.8

6. Write as decimal numbers. 6 8 (a) 3 + 10 + 100

(b) 0.007

3 2 (b) 9 + 50 + 100 + 10

(c) 0.06

7 6 (c) 1 + 400 + 1000 + 10

2. Write the following decimals as fractions. (a) 0.03

(b) 0.2

(c) 0.00009

3. What number is represented on each spike abacus below? The place value of one of the spikes is given for each abacus. (a)

(b)

7. List the following numbers in order from smallest to largest. 3 19 89 0.2 0.099 10 100 1000 0.006

8. Write the correct symbol (< or >) between the following pairs of numbers. (a) 0.45

0.54

(b) 0.41

0.4095

9. Add one hundredth to the following numbers. 1 10

(a) 3.457

1 100

4. State the place value of the 6 in each of the following numbers. Write the answers in words.

(b) 16.8

(c) 2.3969

10. Find the number midway between the following pairs of numbers. (a) 2.3 and 2.4

(b) 6.81 and 6.84

(a) 2.367 (b) 369.8 11. How many hundredths are in seven tenths?

(c) 5.2016 5. Write the following numbers in decimal form. 27 (a) 1000

306 (b) 1000

(c)

97 100

375 (d) 6 1000

41 (e) 5 1000

(f)

3452 100

12. Jose drove his racing car around a track in 56.783 seconds. Alonso's time was two hundredths of a second faster than Jose's time. How long did it take Alonso to drive around the track?

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Master Maths 7 Worksheet 38 Decimal Numbers 2

38

Name: 1. Write the number shown by the dot on each number line below. (a) 0

6. Round the following numbers to two decimal places. (a) 4.5618

(b) 19.8372

(c) 5.29611

1

(b) 7. Convert the following fractions to decimal numbers.

0.1

0

2. Write the number shown on these meters. (a)

(a)

3 10

(b)

1 4

(d)

5 8

(e) 11

(c)

3 5

(b) 0.1 0. 01

0.02

0. 0

4

0

0.05

0.2

0

0.03

3. Round the amounts of money shown in table to: (a) the nearest 5 cents (b) the nearest 10 cents (c) the nearest $1 Amount

(f) 5 3

20

4

8. Convert the following fractions to decimal numbers using a dot or bar to indicate the repeating numbers. Show workings. 5

(a) 9

2

(b) 11

Nearest 5c Nearest 10c Nearest $1

$5.36 $9.72 $20.48 $12.13

4. How many decimal places are in the following numbers? (a) 2.35

(b) 10.3578

(c) 56.09701

5. Round the following numbers to one decimal place. (a) 5.673

9. (a) Find two numbers that when rounded to one decimal place would both be 8.4, but when rounded to two decimal places would differ by three hundredths.

(b) Find two numbers that add to 10 and differ by one tenth.

(b) 12.081

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Master Maths 7 Worksheet 39 Decimals - Addition and Subtraction

39

Name: 1. Find the answers to the following problems. (a)

5 6.8 4 + 2.7 0

(c)

8 2.0 - 4 2.7

(b)

+

2 0.6 9 1.5 0 4 3.8 5 6.7 0 3.0 4

4. Complete this diagram. All lines add to give the number in the centre.

3.6 4.6

1.4 0.4

2.4

9

2. Find the answers to the following problems. Show workings. (a) 34.7 + 260.82 + 7.218 + 67

2.2 3.2 5. Test your mental arithmetic. Solve the problems below using mental arithmetic then use a calculator to find the answer and the difference between your estimate and the actual answer.

(b) 679.3 - 33.756

Problem

67.89 + 4.3 + 5.721

456.37 - 9.8 - 69.38

Mental Arithmetic Calculator Answer Difference

3. (a) Kylie weighs 65.7 kg. While holding her baby sister she stood on the scales and together they weighed 72.9 kg. What is the weight of her sister?

6. A piece of timber 5.4 metres long is cut into two pieces. One piece is 0.66 metres longer than the other. How long are the two pieces of timber?

(b) If Kylie's sister gained 2.8 kg, what would she weigh?

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Master Maths 7 Worksheet 40 Decimals - Multiplication and Division

40

Name: 1. Find the answers to the following problems. (a) ´

2 5.9 6 34

(b) ´

8 1.0 7 6.3

4. Find the answers to the following problems without using a calculator. (a) 45.67 ´ 10 (b) 678.21 ¸ 10 (c) 2.7894 ´ 100 (d) 89.103 ¸ 100

2. Find the answers to the following problems. Show all workings. (a) 33 ¸ 8

(b) 27.38 ¸ 5

(e) 6.8 ´ 1000 (f) 0.0402 ´ 10 000 (g) 0.05 ¸ 10 (h) 9.3 ¸ 100 000

(c) 56.78 ¸ 0.4

(d) 9.5 ¸ 0.008

(i) 0.2 ´ 100 000 5. Complete the following conversions

3. (a) Estimate the answer to the following problem by rounding the numbers to the nearest ten before multiplying. 87.45 ´ 19.6

(b) Use a calculator to find the answer to this problem.

(c) What is the difference between these two answers?

(a) 5.3 km =

m

(b) 40 mm =

m

(c) 0.37 kg =

g

(d) 8900 cm =

m

(e) 0.0257 ML =

L

(f) 62 000 mm =

m

(g) 72.51 MW =

W

(h) 3 mm =

m

(i) 0.00507 kg =

g

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Master Maths 7 Worksheet 41 Decimal Numbers - Problem Solving

41

Name: 1. How many balls weighing 0.3 kg each would be in a box that weighs 13.5 kg?

2. Four friends go out for dinner and the bill is $51.40. If they divide the bill equally, how much should they each pay?

3. A bag contains 11 balls - some tennis balls and some cricket balls. The total weight of the 11 balls is 2 kg. Each tennis ball weighs 0.10 kg. Each cricket ball weighs 0.25 kg. Find the number of each type of ball.

tennis balls

5. What is the weight of a dozen eggs if each weighs 0.045 kilograms?

6. Danni's three long jump attempts were 4.78 m, 5.06 m and 4.95 m. Find the average of these three jumps.

7. A green grocer noticed that three mangoes weighed the same as four avocadoes. The mangoes each weighed 0.24 kg. Find the weight of an avocado.

8. Gareth took 18 minutes 45 seconds to complete 15 laps of a go-cart track. (a) Change the time taken to a decimal number of minutes.

cricket balls min 4. Jim bought a muffin, roll and juice for a total cost of $8.30. Jacqui bought a muffin and roll for $6.05. Peta bought a roll and juice for 5.85. Find the price of each item.

muffin

(b) Use this decimal time to find the average time taken per lap (as a decimal number)

min (c) Change this average lap time to minutes and seconds.

roll juice

min

sec

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Master Maths 7 Worksheet 42 Percentages

42

Name: 1. Choose which of the percentages is the best estimate of the shaded area of each shape below. (a) A 10% B 30% C 70% D 90%

(b)

A 30% B 50% C 70% D 90%

(c)

A 15% B 25% C 35% D 45%

3. 87% of the students in a school were right-handed. What percentage was left-handed? 4. Complete the following conversion table. Percentage

Fraction

5. Find the following quantities. (a) 50% of 60 kg (b) 25% of $200

(c) 10% of 300 m

(d) 20% of 50 kg

(e) 45% of $300

(f) 6% of 700 m

6. Larry earns $56 000 a year. He receives a 3% pay rise. What will be his new annual salary

7. A town has 45 000 people. In one year the population decreased by 2.5%. What was the population at the end of the year?

Decimal

20% 1 4

0.5

8. Find the discounted price of the following items. (a) A $3500 television is discounted by 20%.

2 5

32% 11 20

(b) A $850 bicycle is discounted by 10%. 0.07

3 50

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Master Maths 7 Worksheet 43 Ratio

43

Name: 1. Divide each of the following in the given ratio. (a) $30

1:2

(b) $100

1:4

4. Mortar is to be made using sand and cement in the ration 5:1. (a) How many kg of sand and cement are required to make 30 kg of mortar? sand

(c) $200

9:1

(d) $60

1:3

cement

(e) $240

5:3

(f) $180

4:5

(b) How many kg of cement are required if 10 kg of sand is used?

2. Use a ruler to measure the length of the boxes below. (a) Divide this box in the ratio 2:5 and colour in the sections red and blue.

(b) How many kg of sand are required if 3 kg of cement is used?

5. Christie and Karley receive $600 for renovating a kitchen. Christie worked for 20 hours and Karley worked for 10 hours. How much should they each get paid? (b) Divide this box in the ratio 1:2 and colour in the sections yellow and green. Christie Karley

3. A recipe for a breakfast fruit juice is orange and mango juice mixed in the ratio of 3:1. How many mL of each juice are required to make 200 mL of the breakfast juice?

6. Sam runs at a speed of 3 metres per second. Kerry runs at a speed of 4 metres per second. They both go for a run, leaving home at the same time running in different directions. They return home at the same time. Sam knows she has run 12 km. How far has Kerry run?

orange juice mango juice

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Master Maths 7 Worksheet 44 Length 1

44

Name: 1. Complete the following sentences by writing the appropriate unit in the gap. (millimetres, centimetres, metres, kilometres)

6. (a) Guess the length (in millimetres) of the following lines. Write your guesses in the Guess column of the table below.

(a) In the school high jump competition

A

Jacques jumped 1.5

G (b) At the weekend Fred and his friends rode

B

their bikes 15

C (c) Last month Kaye's hair

D E

grew 18 (d) Horacio had a pet blue-tongue lizard that was 25

F

long.

2. Write the measurements shown on these scales. (a)

0

20

40

60

100

200

300

(b)

0

(b) Measure the length of each line and write these in the Length column of the table. (c) Find the difference between your guess and the actual length of each line. Write these differences in the Error column. (d) Add all the errors and write this total at the bottom of the Error column. (e) If this total is less than 70 you have guessed well. Line

A

(c)

0

Guess (mm) Length (mm) Error (mm)

100

200

300

B C D E

(d)

0

F

50

100

150

200

G Total

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Master Maths 7 Worksheet 45 Length 2 - Conversions

45

Name: 1. Convert the following lengths to the units shown. (a) 3 m =

cm

(b) 7000 mm =

m

(c) 0.8 km =

m

(d) 850 mm =

cm

(e) 730 cm =

m

(f) 63 cm =

mm

(g) 82 000 m =

km

(h) 75 cm =

m

(i) 568 mm =

cm

(j) 0.3 m =

mm

(k) 4.7 m =

cm

(l) 0.0425 km =

m

(m) 6.5 cm =

m

3. Round the following lengths to the nearest metre. (a) 5 m 70 cm (b) 6.73 m

(c) 8 m 93 mm

(d) 3 m 9 cm

(e) 12 m 439 mm

(f) 768 cm

4. Dave is paving a walkway that is 1.8 metres wide. He has chosen a paving block that is square with a side length of 300 mm. (a) How many of the paving blocks will fit across the walkway?

(b) The walkway is 9 metres long. How many paving blocks will be needed to fully pave the walkway?

2. Convert the following lengths to the units shown. (a) 3 m 25 cm =

cm

(b) 6 cm 8 mm =

mm

(c) 12 km 350 m =

km

(d) 9 m 9 cm =

cm

(e) 10 m 60 mm =

m

5. Jack measured his pace to be 55 cm. He walked to school and counted 654 paces. How many metres is the school from Jack's house?

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Master Maths 7 Worksheet 46 Perimeter

46

Name: 1. Use a ruler to measure the lengths (in cm) of the sides of the following shapes and state the perimeter of each shape.

3. Find the perimeter of the following shapes. (a)

14 m

(a) 8m

(b)

15 m 6m

(b)

9m

7m

43 mm

(c)

(b) A rectangle with side lengths 10 m and 7 m.

48 mm

(a) A square with side length 8 cm.

4 cm

2. Find the perimeter of the following shapes.

cm 4.2

56 mm

cm 4 . 5

4. (a) The side length of a rectangular paddock is 350 metres. The perimeter is 1200 metres. What is the width of the paddock?

(c) A regular hexagon with side length 15 cm.

(d) A regular octagon with side length 2.5 m.

(b) The perimeter of a rectangle is 180 cm. The length is 6 cm longer than the width. How long is the rectangle?

Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 47 Area 1

47

Name: 1. 4m

1

3. Find the area of these shapes if each small square represents one square centimetre. a cm

2

8m

(b)

(a) b cm

(a) The perimeter of rectangle 1 is: m (b) The perimeter of rectangle 2 is: cm cm2

(c) The area of rectangle 1 is: m2

(c)

cm2 (d)

(d) The area of rectangle 2 is: cm2 2. Draw two rectangles, each with a perimeter of 14 cm.

cm2

2

cm

4. Estimate the area of this shape if each small square represents one square centimetre.

Calculate the area of each of your rectangles. Area of rectangle 1

cm2

Area of rectangle 2

cm2

Approximate area

cm2

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Master Maths 7 Worksheet 48 Area 2

48

Name: 1. Calculate the area of these shapes.

2. Calculate the area of this shaded region.

3m

2m

3.4 cm

4m

5 cm

(a)

6m

2

cm

5m

2

cm

2m

3m

5 cm

3. Calculate the area of this shaded region.

4 cm

8 cm

10 cm

2m

1m 2m

(b)

2

m

18 cm

6 cm

(c) 20 cm

2

m 4. Calculate the area of the basketball court shown below. 2

cm

5 mm

15 m

(d)

25 m 5 mm mm2

m2 Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 49 Area 3 - Problem Solving

49

Name: 1. Penny wants to make a pen for her rabbits. She has 16 metres of wire mesh that she is going to use to make a rectangular pen. (a) If the pen is 5 metres long and 3 metres wide, what is the area of the pen?

4. The cost for advertising space in a newspaper was $2 per square centimetre (cm2). Use a ruler to measure the advertisements below and calculate the cost to place them in the newspaper. 2

(a)

m (b) Find the length and width of two other pens that she could make using the 16 metres of wire mesh. Find the area of each of these pens. Length

Width

Sally’s Dog Washing Service Anyone wanting to wash Sally’s dog please contact 55682459

Area

Pen 1

(b)

Wonted

Pen 2 2. Terry is going to tile his bathroom floor. The bathroom is 3 metres long and 2 metres wide. Tiles cost $50 per square metre. Find the cost to tile Terry’s bathroom floor.

3. Anne wants to plant grass in her backyard. The yard is 40 m long and 10 m wide and there is a 10 m by 7 m garage in the corner. 2 A packet of grass seed covers 60 m . How many packets of seed will she need?

Help to do homewerk Carnt pay mutch Pleese dont tell Mum or the Teecher Corl Bart 9%67*111

(c) Think of your own advertisement. Draw it below and work out its cost.

packets

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Master Maths 7 Worksheet 50 Volume 1

50

Name: 1. How many small cubes are in each of the following objects? (a)

(b)

3. Find the volume of the following rectangular prisms. (a)

3 cm 6c m

m 5c

(b) (c)

(d)

8 cm 20

cm

10

cm

4. Find the volume of the rectangular prisms with the following dimensions. (a) 7 m long, 4 m wide, 3 m high

2. (a) How many small cubes are in this object? (b) 30 m long, 20 m wide, 15 m high

5. Find the volume of the object below.

2 cm

6c m m 2c

(b) If each of the small cubes in this object is 1 cm3, what is the volume of this object?

2 cm 2 cm

m 2c m 2c

6 cm

m 6c Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 51 Volume 2

51

Name:

3

(a) 3 litres =

cm

3

(b) 7000 cm =

litres

(c) 0.8 litres =

cm3

3

(d) 5 m =

litres

(e) 4.9 litres =

cm3

3

(f) 7.8 m =

litres

(g) 82 000 cm3 =

litres

4. (a) How many cubic metres of water are needed to fill this container? 50 cm

1. Complete the following conversions.

1.2

2m

m

(b) How many 10 litre buckets of water would be needed to fill this container?

2. Find the volume (in litres) of the following object.

30 cm 80 cm

50

cm

3. A fish tank is 90 cm long, 40 cm wide and 65 cm high. The tank is empty. How many litres of water are needed so that the water level will be 5 cm from the top of the tank?

5. A rectangular prism is to be made to have a volume of exactly one litre. The base is to be a square with side length 5 cm. Find the height of the prism.

5c m

m 5c

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Master Maths 7 Worksheet 52 Time 1

52

Name: 1. Complete the following conversions.

5. Oscar left for a camp on Tuesday the 19th of October. He returned 18 days later. What was the day and date that Oscar returned?

(a) 1 minute =

seconds

(b) 3 hours =

minutes

(c) 2 days =

hours

(d) 1 minute =

seconds

Day

(e) 15 minutes =

seconds

Date

(f) 3 weeks =

days

4

(g)

3 12

days =

hours

2. (a) How many days are in a leap year? (b) How many days are in a non-leap year? 3. How many days are in the following months? (a) April

(b) January

(c) June

th

4. Angel was born on the 5 of February 1997. (a) How old will Angel be on her birthday in 2025?

5. The Johnson family plan to drive from Castlemaine to Corryong. The details of their drive and planned times are below. Leave Castlemaine at 7:30 am Castlemaine to Benalla - 2 14 hours Stop at Benalla - 30 minutes Benalla to Wodonga - 2 hours and 20 minutes Stop at Wodonga for lunch - 45 minutes Wodonga to Corryong - 1 hour and 40 minutes

Complete the following table showing the times of arrival and departure from each town.

Event Depart Castlemaine (b) How many days after Christmas is Angel's birthday?

Time 7:30 am

Arrive Benalla Depart Benalla Arrive Wodonga

(c) In what year did Angel turn eight years old?

Depart Wodonga Arrive Corryong

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Master Maths 7 Worksheet 53 Time 2

53

Name: 1. Noela took 8 minutes to read 10 pages of a book. How many seconds did it take her to read each page?

2. Write the times shown below two different ways. Example 2:10 = ten past two (a)

11

12

(b)

1 2

10

7

6

1 2 3

9

4

8

12

10 3

9

11

Geelong Torquay Jan Juc Bells Beach Anglesea Point Roadknight Aireys Inlet Lorne

1855 1935 1940 1945 1955 2000 2010 2035

(a) How long does it take the bus to travel between the following towns? (i) Geelong and Anglesea

4

8

5

4. A bus timetable between Geelong and Lorne is shown below.

7

6

5

(ii) Torquay and Anglesea (iii) Geelong and Lorne

(c)

11

12

(d)

1 2

10

4

8 7

6

12

1 2

10 3

9

11

5

3

9 4

8 7

6

5

3. Complete the table below showing conversions between 12 hour and 24 hour time. 12 hour time

24-hour time

7:50 am

(b) Beryl wants to travel from Geelong to Lorne but she can’t leave work till 2:00 pm. How long will she need to wait before the next bus leaves?

5. Francis wants to cook a roast chicken and potatoes for dinner. He wants to plan the dinner to be ready at 7:00 pm. The roast chicken will take 2 14 hours to cook and the potatoes will take 1 34 hours. At what time should he put the chicken and the potatoes in the oven?

0355 1:25 pm

Chicken 1430

10:32 pm

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Master Maths 7 Worksheet 54 Tally Sheets

54

Name: 1. Complete the following tally sheets. (a) Height (cm)

Tally

2. Construct tally sheets for the following sets of data.

Frequency

0-

(a) The lengths (in cm) of a number of fish caught in a river are shown below. 26 38 28 36 41

10 20 -

63 41 34 42 48

54 20 51 34 36

38 48 16 27 29

16 35 37 17 24

33 52 45 34 30

40 50 35 60 43

56 38 25 33 32

62 29 37 48 39

51 37 49 53 40

30 Length (cm)

40 -

Tally

Frequency

10 -

Total

20 30 (b) 40 Colour

Tally

Frequency

Red Black

12

60 Total

Purple 16

Yellow Magenta

(c) Tally

(b) The list below shows the favourite flavour of ice-cream for a number of people. chocolate strawberry caramel peppermint strawberry chocolate chocolate caramel peppermint chocolate peppermint caramel peppermint caramel strawberry caramel strawberry chocolate strawberry strawberry chocolate chocolate chocolate chocolate

Total

Mass (kg)

50 -

Frequency

0-

21

50 100 150 200 Total

100

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Master Maths 7 Worksheet 55 Column Graphs 1

55

Name: 1. All the students in Year 7 at a school were asked who was their favourite band. The results are shown on this graph.

2. The ages of a number of people who rode on a new attraction at Luna Park are shown on the graph below. Number of People

Number of Students

35

35

30

30

25

25

10 5

15 10 Jool

15

20

The Elfmasters

20

Lead Heads

40

Sisters of Singh

40

5 0

0

Band

(a) How many students chose each of the bands? Band

-10 -20 -30 -40 -50 -60 Age

(a) How many people older than 40 went on the ride?

Number

Sisters of Singh Lead Heads

(b) How many people up to the age of 20 went on the ride?

The Elfmasters Jool (b) How many students were in Year 7 at the school?

(c) How many people older than 10 and up to the age of 40 went on the ride?

(d) How many people had their ages recorded for this graph?

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Master Maths 7 Worksheet 56 Column Graphs 2

56

Name: 1. 80 people were asked where they would like to go on their holidays. The results are given in this table. Holiday Location

Number

Beach

24

River

12

Bush Walking

9

Overseas

10

Snow

18

Other

7

2. The weight (in kg) of a number of seals in a colony was recorded and listed below. 34 28 37 73

67 58 82 34

28 71 73 48

19 60 49 57

27 73 90 25

78 84 52 17

46 92 38 59

28 54 71 82

96 25 52 62

18 14 62 50

(a) Construct a tally sheet to display this information using the group sizes of -20, -40, -60, etc.

Display this information on the column graph below. Number

(b) Construct a column graph to display this information.

25

20

15

10

5

0 Holiday

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Master Maths 7 Worksheet 57 Line Graphs

57

Name: 1. The Tooweela company makes bicycles. It has two types of bicycles: Tektra and Cykron. The graph below shows the sales of these bicycles between the years 1999 and 2006.

2. The volume of water in a farm dam was calculated at the end of each month over a one year period. The results are shown in the table below. Volume is measured in kilolitres (kL). Volume in kL

Number Sold

Tektra Sales

Cykron Sales

500

400

300

200

January

420

February

310

March

80

April

40

May

90

June

190

July

340

August

540

September

600

October

600

November

590

December

500

Represent this information on the line graph shown below. 100 Volume (kL)

06 Year

Tektra Sales Cykron Sales

Dec

2006

Nov

2002

Oct

1999

100

Sep

(a) Complete the table below showing the approximate number of each bicycle sold in the years 1999, 2002 and 2006.

Aug

05

July

04

Jun

03

May

02

Apr

01

Mar

00

Feb

99

Jan

0

Month of year

(a) During which month did the volume drop the most?

(b) In which year were the sales of the two bicycles the same? (c) In which year were the total sales of the bicycles less than the previous year?

(b) By how much did it drop? kL

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Master Maths 7 Worksheet 58 Pie Graphs

58

Name: 1. 120 people were asked to state their favourite fruit juice. The results are shown on this pie graph.

2. 100 people were asked to state their favourite pie. The table below shows the results. Favourite Pie

Number

Orange Apple

Chicken

20

Beef

28

Tomato

Vegetable

Mango

Meat and Vegetable

Pineapple (a) 30 people chose orange as their favourite juice. Complete the table below showing the number of people who chose each juice. Juice

7 45

Complete the pie graph below displaying this information. Use your own colours to represent each section of the graph and the legend.

Number

Orange

30

Apple Tomato Mango Pineapple Total

120

(b) What fraction of the pie graph is represented by each juice? Juice Orange

Fraction 1 4

Apple Tomato Mango Pineapple

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Master Maths 7 Worksheet 59 Probability 1

59

Name: 1. Rate the probability of the following events occurring using the following scale. Answers will be decimal numbers.

(a) Tossing a coin and obtaining a head. certain

very likely

1

likely

go either way

unlikely

0.5 very unlikely

impossible

0

2. Find the probability of these events. Write your answers as fractions in their simplest form.

(a) The sun will rise tomorrow.

(b) It will rain tomorrow.

(b) Rolling a three on a dice.

(c) Rolling an even number on a die.

(c) You will pass the next maths test. (d) Choosing a green ball from this box after it is shaken. (d) When you throw a dice it will be an even number.

P RYGB

P - pink R - red Y - yellow G - green B - blue

(e) Collingwood will win the grand final next year. (e) Choosing a red ball from this box after it is shaken. (f) You throwing a dart at a dart board and scoring a 'bulls-eye'.

(g) You throwing a dart at a dart board and hitting anywhere on the board. (h) You waking up before 7 o'clock tomorrow morning.

RG RYB GB R P

P - pink R - red Y - yellow G - green B - blue

(f) Choosing a yellow ball from the box in part (e) after it is shaken.

(g) Choosing a yellow ball from the box in part (e) after a yellow ball has been removed.

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Master Maths 7 Worksheet 60 Probability 2

60

Name: 1. Garry buys 10 raffle tickets. If there are 200 tickets in the draw, what is the probability that he will win the raffle? Write your answer as a fraction in its simplest form.

3. Andrew throws a dart 200 times at the dart board shown and records the results on the graph below.

$ 50

20 10

Number of hits

2. Marita is a netballer and she wants to work out the probability of scoring when she has a shot at goal. She takes 60 shots at goal and finds that 45 of them score. (a) Based on these figures, find the probability of Marita scoring a goal. (i) As a fraction in its simplest form.

100 80 60 40 20 0

10

20

50

Score

(a) What is the probability of Andrew scoring a 50? Give answer as a fraction in its simplest form. (ii) As a decimal. (b) If she had 80 shots at goal, how many goals should Marita expect to shoot? (b) If Andrew throws 20 darts, how many scores of 10 would he expect to throw?

(c) If she wanted to scored 30 goals in a game, how many shots at goal would she expect to need?

(c) If Andrew throws 20 darts, how many scores of 50 would he expect to throw?

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Master Maths 7 Worksheet 61 Probability - Listing Outcomes

61

Name: 1. List all the numbers the can be formed using the digits 6, 5 and 2.

Give the following probabilities as fractions in their simplest form. If one of these numbers is chosen at random find the probability that it: (a) is larger than 600

3. A game at a fun park involved rolling two balls into four boxes. The boxes have the numbers 1, 3, 7 and 10. 1 3 7 10 The balls fall randomly into the boxes. (a) List all the possible combinations of numbers that could be scored with the two balls. For example: (1,1) (1,3) .......... (10,10)

(b) is larger than 200

(c) is an even number

(d) is less than 550

2. Cherrie has three coloured pencils in her pencil case - yellow, green and red. She randomly picks a pencil, colours in the centre circle of this shape, replaces the pencil, then randomly picks a pencil to colour in the outer ring. (a) Use as many of the shapes below as required to show all the possible colour combinations.

(b) What is the probability that the shape is coloured in with one colour?

(b) How many combinations are there?

(c) If the two numbers are added, circle the combinations that have a total greater than 10. (d) What is the probability that the sum of the two numbers will be greater than 10? Give answer as a fraction.

(e) A person playing the game will win a prize if the sum of the two numbers is greater than 15. What is the probability of winning a prize?

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Master Maths 7 Worksheet 62 Patterns and Rules 1

62

Name: 4. The following pattern is made using matches.

1. Complete the following patterns. (a) 1, 5, 9, 13,

,

,

(b) 2, 4, 8, 16,

,

,

(c) 30, 25, 20, 15, (d) 128, 64, 32, 16,

,

Step 1

, ,

,

2. Use words and symbols to explain the patterns in each of the parts in question 1. Example: 3, 6, 12, 24, ..... Answer: multiply by 2 (´2)

Step 2

Step 3

(a) Complete this table that shows the number of matches, m, for each step number, s. (b) Complete the rule below that could be used to find the number of matches for a given step number. m=

(a)

Step 4

s 1 2 3 4 5 6

m

s 1 2 3 4 5 6

m

s 1 2 3 4 5 6

m 6 12 18 24 30 36

´s

(c) How many matches would be needed for step 12?

(b)

(d) What step number would have 40 matches?

(c) (d) 3. Find the next four numbers in the number patterns that have the following starting numbers and method of finding each number. Example: 5 (+3) Answer: 5, 8, 11, 14, 17

5. Complete this table of values for the following rule: m=s+5

(a) 1 (´2) (b) 5 (+6) (c) 25 (-4) (d) 324 (¸3)

6. Complete the rule for this table of values. m=

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Master Maths 7 Worksheet 63 Patterns and Rules 2

63

Name: 1. Complete the rules relating the symbols for each of the following tables of values. (a)

b

a

1

(b)

n

m

7

1

4

2

8

2

8

3

9

3

12

4

10

4

16

5

11

5

20

6

12

6

24

a=

3. Complete the tables of values for each of the 'number machines' below.

(a)

y

20

(d)

Q

P

15

3

1

21

16

6

2

22

17

9

3

23

18

12

4

24

19

15

5

25

20

18

6

y=

r

7 45

15

+8 2

r

r 13 52

15

(c)

i

P=

(a) y = 6 ´ x

i i

+5

´2 2

i

2. Complete the table of values for each of the following rules

22 17

r

r

25

(a) m = n + 7 y

2

n

m

(d)

i

1

5 11

¸2

+4

3 42

r

15 i

13 120

30

1

m=

x

x

r

´5

i

(b) (c)

i

30

r

2

10 5

12

42

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Master Maths 7 Worksheet 64 Patterns and Rules 3

64

Name: 1. Complete the tables of values for the flowcharts shown below. a

(a)

+1

(a)

b

1

´4

a

3. Find the rules for the following tables of values.

2

b

3 4 x

(b)

´2

x

3 4 n

(c)

´3

n

m

1

-2

3

2

5

3

7

4

9

x

y

1

1

2

4

3

7

4

10

n

m

1

6

2

8

3

10

4

12

P

Q

1

0

2

2

3

4

4

6

b=

y=

(c)

4

2. Write the rules for the following flowcharts. (a)

-2

n

3

2

m

´3

1

(b)

2

y

b

y

1

+3

a

m

m=

m= (d) (b)

´4

a b=

+3

b

Q=

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Master Maths 7 Worksheet 65 Patterns and Rules - Problem Solving

65

Name: 1. A post and rail fence is to be built as shown below. rail

post

gap

2. A ladder company has produced an extendable ladder. It is made using pieces that can be fitted together. The pieces are all the same length. The diagram below shows different lengths of the ladder. The number of rungs and pieces are listed.

There are three rails between each set of posts. (a) Complete this table. Number of gaps between posts (G)

Number of posts (P)

Number of rails (R)

1

2

3

2

3

6

3

1 rung 5 pieces

2 rungs 8 pieces

3 rungs 11 pieces

4 (a) Complete this table showing the number of pieces needed for different numbers of rungs.

10 20 (b) Find a rule connecting the number of posts, P, and the number of gaps, G.

r = number of rungs p = number of pieces

P=

r

p

1

5

2

8

3

11

4 (c) Find a rule connecting the number of rails, R, and the number of gaps, G.

5 6

R=

(d) Find a rule connecting the number of rails, R, and the number of posts, P. R=

(b) Find a rule connecting p and r. p= (c) How many pieces would be needed for a ladder that had 12 rungs?

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Master Maths 7 Worksheet 66 Writing Equations and Substitution

66

Name: 1. Write the following relationships as equations. (a) m is equal to 7 added to p.

2. Find the value of y in the following equations if x = 3. (a) y = x + 5

(b) y = 4x

(c) y = 17 - x

(d) y = 2x + 4

(e) y = 5x - 6

(f) y = 4(x + 2)

(b) P is equal to the sum of Q and R.

(c) Y is equal to X divided by 9.

(d) b is equal to the product of c and d.

(e) m is equal to 5 less than n.

3. Find the value of P in the following equations for the values given. (a) P = 3Q + 7

(Q = 4)

(b) P = 2m + 3n (m = 5, n = 1) 2. Write the following relationships as equations. (a) Power, P, of an electric motor is equal to the product of voltage, V, and current, I.

(c) P = 6(2a + 5)

(a = 3)

(d) P = 4(3x - 2y)

(x = 4, y = 2)

4. Solve the following equations given that: (b) Acceleration, a, is equal to velocity, v, divided by time, t.

(c) Magnetic force, F, on a wire is equal to the product of the magnetic field strength, B, length of the wire, L, and the current in the wire, I.

a = 2, b = 5 and c = 8 (a) y = 2a + 5b

(b) m = ab - c

(c) d = a(2b - c)

(d) R = a2 + 5b - ac

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Master Maths 7 Worksheet 67 Solving Equations - Trial and Error

67

Name: An example of the 'trial and error' method of solving equations is shown here.

3.

Guess for n

Find n in the equation 3n + 7 = 34 Guess for n 4 8 10 9

2

n + 2n - 5 = 30 Left side Right side Comment

Left side Right side Comment 3n + 7 34 19 34 Too low 34 31 Too low 37 Too high 34 34 34 Correct n=

Answer: n = 9 Use the 'trial and error' method to find the value of n in the following equations. 4. 1.

5n - 7 = 48 Guess for n

3n + 7 = 5n - 9 Guess for n

Left side Right side Comment

Left side Right side Comment

n= n=

2.

5.

6n - 5 = 85 Guess for n

Left side Right side Comment

n=

3(n + 6) = 9(n - 6) Guess for n

Left side Right side Comment

n=

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Master Maths 7 Worksheet 68 Solving Equations - Backtracking

68

Name: 1. Complete the backtracking path on each of these flowcharts to find each value of A. (a)

+7

´3

2. Complete the flowcharts for the following equations and use backtracking to solve. (a) 4m - 5 = 23

22

A

m A= m= (b)

-3

¸4

(b) 6(m - 3) = 24

4

A

m

A= (c)

m=

-5

´6

43

A

3. Use backtracking to solve the following equations. (a) 2m + 9 = 17

A= (d)

´3

¸4

+5 11

A

m= (b)

m -5=1 3

A= (e)

´2

+8

m=

¸4 5

A

A=

(c) 6(m + 7) = 72

m=

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Master Maths 7 Worksheet 69 Solving Equations

69

Name: 1. Use the most appropriate method to solve the following problems.

(f)

3m + 7 = 17 2

(a) 3m - 6 = 9

m= (b)

m +5=9 2

m=

(g)

2(m - 9) = 10 3

m= (c) 4(m + 3) = 40

m= m=

3m (d) + 7 = 16 5 (h)

7m + 8 + 9 = 25 4

m= (e) 5(2m - 7) = 45

m= (i) 3(m + 4) = 7m - 8

m= m=

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Master Maths 7 Worksheet 70 Solving Equations - Problem Solving

70

Name: 1. Write the following problems as equations using x to represent the number. Solve the equations using an appropriate method. (a) When this number is multiplied by 2 and then 8 is added to the result the answer is 26. Equation:

3. The perimeter of this triangle is 26 cm. The three side lengths are shown on the diagram. Use trial and error to find x. 2x x x+2

x= (b) When this number is divided by 4 and then 5 is added to the result the answer is 11. Equation:

x= 4. Jonas is 9 years older than his youngest brother, Jaan. In two years Jonas will be twice Jaan's age. How old is Jonas?

x= 2. Six bricks plus 5 kg weighed 23 kg. (a) Write this as an equation using b to represent the weight of a brick.

5. A 24 m long length of rope is cut into two pieces. One is 4 m longer than the other. Find the length of the two pieces of rope.

Equation: (b) Solve this equation to find the weight of a brick.

b= (c) 20 bricks weighed the same as two bags of cement. Find the weight of a bag of cement.

6. There were 60 students on a school camp. One day there were two activities - canoeing and hiking. Those who went canoeing were told to take one bottle of water each. Those who went hiking were told to take two bottles of water each. 75 bottles of water were taken. How many students went on each activity?

Canoeing Hiking

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Master Maths 7 Worksheet 71 Simplifying Algebraic Expressions

71

Name: 1. Simplify the following algebraic expressions.

2. Write an expression for the perimeter of this triangle.

(a) a + a + a + a (b) x + x + x + x + x + x

x

x+2

(c) 2m + 3m x+3 (d) 6n + 3n + n (e) 8p - 5p 3. Simplify the following algebraic expressions. (f) 9c - 8c (g) 7a + 4a - 2a - 3a (h) x + x + y + y + y + y (i) m + n + m + n + n + m + n (j) 2x + 3y + 6x + 5y (k) 5m + 6n - 2m - 4n (l) 7x + 9y + 6x - y - 5y (m) 8a - 6a + 6b - 2a - 2b (n) m + 7n + 5m - 6n - 6m - n

(a) a ´ b (b) 6 ´ m (c) 4 ´ x ´ y (d) 3 ´ n ´ 4 (e) 2m ´ n (f) 5a ´ 6b (g) 4 ´ x ´ y (h) 3 ´ n ´ 4 (i) 3m ´ 2 ´ 5n

(o) 7a + 6 + 2a + 5 (p) 6m + 8 + 2m - 3

4. (a) Find an expression for the area of this rectangle.

(q) 8x + 3x + 11 - 2x - 6 (r) 6n + 7 - n + 3n + 8 (s) 9 + 6a + 7 - 8 - 2a (t) 7m + 2n + 6m - 2n - 13m

7b 6a (b) A bag of wheat weighs w kg. Write an expression for the weight of n bags of wheat.

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Master Maths 7 Worksheet 72 Interpreting Graphs

72

Name: 1. The graph below shows the temperature over a 24 hour period for a town. Use this line graph to answer the questions below.

2. The graph below represents the distance and the time for Maree to walk to school from home. Distance from home (metres)

Temperature o C

E

300 20 18 16 14 12 10 8 6 4 2 0 12pm

C

200

100

D

A

B

4am

8am

12am

4pm

8pm 12pm Time of day

0

1

2

3

4

5

6 time taken (minutes)

(a) How far is the school from Maree’s home?

(a) What was the highest temperature reached in this period?

(b) How long did it take Maree to get to school?

(b) What was the lowest temperature reached in this period?

(c) What do you think probably happened in the following sections of the graph?

(c) What was the temperature at 4am?

(i) A to B (d) What was the temperature at 6pm? (ii) C to D o

(e) At what times was the temperature 12 C? (iii) D to E

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Master Maths 7 Worksheet 73 Cartesian Plane 1

73

Name:

Plot the following points and connect them with a smooth curve in the order they are plotted. 1

1

1

(8,5) (6,3 2 ) (5,3) (3,3) (2,4) (3,6) (32 ,6 2 ) (4,8) (5,9) (6,10) (8,10) (9,11) (11,12) (12,12) (13,14) (15,15) (14,12) (17,11) (19,9) (20,7) (21,6) (22,4) (19,5) (17,5) (18 12 ,6 12 ) (18,7) (16 12 ,7) (15,6) (16,5) (17,3) (15,3 12 ) (14,4) (11,3) (9,3) (8,2) (712 ,3 12 ) (6, 312 )

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Ó LEADING EDUCATIONAL RESOURCES

Master Maths 7 Worksheet 74 Cartesian Plane 2

74

Name: 1. Draw a pattern or diagram on the grid below. 2. Write the numbers on the axes. 3. List the coordinates of the points that would be used to draw the shape.

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