Exam 2

 

Name:

New Document 1 1  

Class: Date:

Time:

103 minutes

Marks:

94 marks

Comments:   Comments:

 

Page 1 of 45

 

1.

Circle the cube number. 3

6

9

27 (Total 1 mark)

2.

 A probability scale is shown below. The arrow marks the probability of an event.

Circle the word that describes the probability of the event. certain

likely

evens

unlikely

impossible (Total 1 mark)

3.

Circle the answer to 0.04

0.08

0.1

0.2 (Total 1 mark)

4.

Circle the order of rotational r otational symmetry of this pattern. 0

1

2

4 (Total 1 mark)

5.

Write down all the factors of 50

 Answer (Total 2 marks)

 

Page 2 of 45

 

6.

Shapes A, B, C and D are on a square grid.

Name each shape. Choose from rhombus

trapezium

right-angled triangle

kite

isosceles triangle scalene triangle

 A B C D (Total 4 marks)

 

Page 3 of 45

 

7.

Kerry has 420 beads. She puts the beads into bags.  A full bag has 18 beads. She fills as many bags as she can. She has some beads left over and one more bag to fill. How many more beads does she need to fill this bag?

 Answer (Total 3 marks)

8.

 A large square is made from two smaller squares, A and B, and two identical rectangles. Not drawn accurately

 

Page 4 of 45

 

The area of A is 36 cm2  The area of B is 64 cm2  Work out the area of the large square.

cm3 

 Answer

(Total 3 marks)

9.

Here are three expressions. 31 – x

x2 

6 x

Write the expressions in order of size when x = 5 Start with the smallest. You must show the value of each expression.

smallest

largest (Total 2 marks)

 

Page 5 of 45

 

10.

 A, B and C are three of the vertices of a parallelogram.

One possible position of the fourth vertex is (9, 2) Work out the coordinates of the other two possible positions.

 Answer (

,

) and (

,

) (Total 2 marks)

11.

(a)

Here are the first four triangular numbers. 1

3

6

10

Work out the next triangular number.  Answer (1)

 

Page 6 of 45

 

(b)

A sequence has nth term n2 – 3 Work out the first three terms of the sequence.

 Answer

(2) (Total 3 marks)

12.

Cherries cost $4.80 per kilogram. Sal paid $4.32 for some cherries. How many grams of cherries did he buy?

 Answer

grams (Total 2 marks)

13.

Here are five number cards.

(a)

All the cards are used to make a five-digit whole number. The number is a multiple of 4 What is the smallest number that can be made?

 Answer (2)

 

Page 7 of 45

 

(b)

All the cards are used to make two whole numbers. One number has three digits. The other number has two digits. The two numbers are added together to make a total.

What is the largest total that can be made?

 Answer (c)

(2)

Use all the cards to make this calculation correct.

(1) (Total 5 marks)

14.

In this number machine, x and y are positive whole numbers.

 

Page 8 of 45

 

(a)

Work out a possible pair of values for x and y.

 x =

 y = (1)

(b)

Work out a different possible pair of values for x and y.

 x =

 y = (1)

(c)

In this number machine, m and p are positive whole numbers.

Work out a possible pair of values for m and p.

m=

 p = (1) (Total 3 marks)

 

Page 9 of 45

 

15.

13.5 million people answered a question in a vote. 62% said Yes. 38% said No. How many more people said Yes than said No?

 Answer (Total 3 marks)

16.

(a)

Complete the table of values for

 x

 –1

0

 y

 y = 3 x – 4 1

2

 –1

2

3

(2)

 

Page 10 of 45

 

(b)

Draw the graph of

 y = 3 x – 4

for values of x from –1 to 3

(2) (Total 4 marks)

 

Page 11 of 45

 

17.

Shape P is translated by

Which shape is the result of the translation? Circle your answer.  A

B

C

D (Total 1 mark)

18.

Sam grows 12 tomato plants in his garden. Here are the heights of the plants in millimetres. 104 (a)

134

112

102

123

121

109

112

117

123

131

124

Work out the range of the heights. Circle your answer. 32 mm

20 mm

34 mm

29 mm (1)

(b)

Work out the median height.

 Answer

mm (2)

 

Page 12 of 45

 

(c)

Draw an ordered stem-and-leaf diagram to represent the data. Remember to complete the key.

(3) (Total 6 marks)

 x + 12) cm and width ( x  x – 3) cm 19.  A rectangle has length ( x Not drawn accurately

The length is twice the width. Work out the value of x.

 Answer (Total 3 marks)

 

Page 13 of 45

 

20.

The fuel consumption of a new model of car is measured at different speeds. The scatter graph shows the results.

(a)

Describe the relationship between speed and fuel fuel consumption shown by the graph.

(1)

(b)

Draw a line of best fit on the scatter graph. (1)

(c)

Use your line to estimate the fuel consumption of of a car travelling travelling at 46 km per hour.  Answer

km per litre (1) (Total 3 marks)

 

Page 14 of 45

 

21.

There are 3150 houses in a town. The ratio of detached houses to other houses is 1 : 4 250 new houses will be built. The ratio of detached houses to other houses will then be 1 : 3 How many new detached houses will be built?

 Answer (Total 3 marks)

22.

(a) Not drawn accurately

Circle the expression equal to tan x

(1)

 

Page 15 of 45

 

(b)

Use trigonometry to work out the value of y. Not drawn accurately

 Answer

cm (2) (Total 3 marks)

23.

Two triangles each have angles of 51°, 34° and 95° One triangle is larger than the other. Circle the word that describes the triangles. congruent

similar

corresponding

regular (Total 1 mark)

24.

The price of a watch increases from $160 to $194 Work out the percentage increase in the price.

 Answer

% (Total 3 marks)

 

Page 16 of 45

 

25.

Two villages, A and B, are connected by a road of length 9 km Sabine left B at 10.20, running towards A at a speed of 6 km/h  A distance-time graph for Sabine is shown on the grid. Nadia left A at 10.00, walking towards B at a speed of 5 km/h  After walking 4 km she stopped stopped and waited for Sabine to arrive. arrive. (a)

On the same grid, draw a distance-time graph for Nadia.

(3)

(b)

Use the two graphs graphs to work out how long Nadia waited waited for Sabine to arrive.  Answer

minutes (1) (Total 4 marks)

 

Page 17 of 45

 

26.

The table shows information about the widths of 80 picture frames. Width, w (cm)

Frequency

20 ≤ w < 30

18

30 ≤ w < 40

20

40 ≤ w < 50

33

50 ≤ w < 60

9

Midpoint

Total = 80 Work out an estimate of the mean width.

 Answer

cm (Total 3 marks)

 xc ÷ x4 = x6 × x8 

27.

Work out the value of c.

 Answer (Total 2 marks)

 

Page 18 of 45

 

28.

Simplify fully

 Answer (Total 3 marks)

29.

 ABCDE is a regular pentagon. CPD is an equilateral triangle.

 Angle CBP = x Not drawn accurately

 

Page 19 of 45

 

Work out the size of angle x.

 Answer

° (Total 5 marks)

The first four terms of a linear sequence are

30.

 –16

–9

–2

5

Circle the expression for the nth term.

n+7

7n – 16

7n – 23

–9 – 7n (Total 1 mark)

31.

Circle the ratio equivalent to

1:8

1 : 18

8:1

18 : 1 (Total 1 mark)

32.

 A is the set of single-digit even numbers. numbers. B is the set of single-digit prime numbers. Circle the value of

n (A ∩ B) 1

2

7

0 (Total 1 mark)

 

Page 20 of 45

 

33.

Two numbers are in the ratio

9 : 13

The difference between the numbers is 504 Work out the two numbers. nu mbers.

 Answer

and (Total 3 marks)

 

Page 21 of 45

 

34.

Use a ruler and compasses for this question.  X , Y and Z are points on horizontal ground.

 A ball is rolled along the ground. The ball stops 6 m from Z an equal distance from X and Y . On the scale diagram, show the point where the ball stops. Label this point B.

(Total 4 marks)

 

Page 22 of 45

 

35.

Here are sketch graphs of

 y = 2 x + c

and

 y = 2 x2 + bx + c

P (4, 5) is a point po int of intersection.

(a)

Show that

c = –3

(1)

(b)

Work out the value of b.

 Answer (3) (Total 4 marks)

 

Page 23 of 45

 

Mark schemes 1.

27 B1

[1]

2.

likely B1

[1]

3.

0.08

B1

[1]

4.

4 B1

[1]

5.

1 2 5 10 25 50 B1 6 or 5 factors correct with up to 2 incorrect or 4 factors correct with 0 or 1 incorrect or 3 factors correct with 0 incorrect B2

Additional Guidance

Use of products is B1 for all three correct i.e. 1 × 50, 2 × 25, 5 × 10 B1

Factors must be identified if given in a factor tree 1 2 5 10 25 50 seen but answer 6 B1

1 2 5 10 25 50 with answer 6 factors B2

[2]

6.

 A isosceles triangle B trapezium C scalene triangle D kite B1 for each

B4

 

Page 24 of 45

 

Additional Guidance

Condone incorrect spelling if intention clear [4]

7.

Alternative method 1

420 ÷ 18 or 23(.3...) or 24 implied by 23 × 18 M1

their 24 × 18 or 432 their 24 must be the answer to 420 ÷ 18 rounded up to the nearest integer M1dep

12 A1

Alternative method 2

420 ÷ 18 or 23(.3...) or 24 M1

their 23 × 18 or 414 their 23 must be the answer to 420 ÷ 18 rounded down to the nearest integer M1dep

12 A1

Alternative method 3

420 ÷ 18 or 23(.3...) or 24 M1

(1 – their 0.3…) × 18 or their 0.3…× 18 or 6 their 0.3… must be the decimal part of their answer to 420 ÷ 18 M1dep

12 A1

 

Page 25 of 45

 

Alternative method 4

integer [20, 30] × 18 M1

23 × 18 or 414 or 24 × 18 or 432 M1dep

12 A1

Additional Guidance

23 × 18 or 414 or 24 × 18 or 432 M1M1

20 × 18 = 360

or

21 × 18 = 378

or

22 × 18 = 396

25 × 18 = 450

or

26 × 18 = 468

or

27 × 18 = 486

28 × 18 = 504

or

29 × 18 = 522

or

30 × 18 = 540 M1

[3]

8.

Alternative method 1

or

oe may be seen in correct positions on diagram M1

M1dep

196 A1

 

Page 26 of 45

 

Alternative method 2

or

oe may be seen in correct positions on diagram M1

implied by 96 M1dep

196 A1

[3]

9.

 At least two of (31 – x =) 26 (6 x =) 30 (  x x2 =) 25 M1

 All three correct evaluations seen and smallest x2  31 – x largest 6 x allow correct values instead of expressions A1

Additional Guidance

If all three correct evaluations seen and smallest is x2 and largest is 6 x then allow a blank middle answer line to imply 31 – x for full marks Correct order with two correct evaluations and one incorrect evaluation M1A0

Correct order with two or three incorrect evaluations

M0A0

[2]

 

Page 27 of 45

 

10.

(5, –4) and (–1, 2) B1 one correct coordinate pair or both points plotted but coordinates not stated SC1 (–4, 5) and (2, –1) B2

[2]

11.

(a)

15 B1

(b)

–2

1

6 B1 one or two correct or 12  – 3

2 2  – 3

32  – 3 oe B2

[3]

12. or

oe allow 208(.33...) for M1

900 A1

Additional Guidance

Do not award A1 if premature approximation for 900 seen e.g. 208.3 × 4.32 = 900 208.3 × 4.32 = 899.856 Answer 900 M1A1 M1A0

[2]

13.

(a)

13 452 B1 any five-digit number using all of the digits 1 to 5 ending 12 or 24 or 32 or 52 B2

Additional Guidance

14 532 B1

 

Page 28 of 45

 

(b)

573 B1 542 + 31 or 541 + 32 or 531 + 42 or 532 + 41 or 546 or 555 or 564 B2

Additional Guidance

531 + 42 with no or incorrect answer B1

543 + 21 = 564 B1

543 + 21 B0

(c)

13 × 4 = 52 B1

[5]

14.

(a)  x = 2 y = 8 or x = 3 y = 7 or x = 9 y = 4 or x = 23 y = 2 or x = 51 y = 1 must be in this order B1

Additional Guidance

Including operations is B0 in this part e.g. x = +2 y = × 8

B0

 

Page 29 of 45

 

(b)

Different pair to their answer to (a) from

 x = 2  y = 8 or x = 3 y = 7 or x = 9 y = 4 or x = 23 y = 2 or x = 51 y = 1 must be in this order B1

Additional Guidance

Same pair used in (a) and (b)

(a) B1 (b) B0

Condone operations included in this part if already penalised pe nalised in part (a) e.g. (a) x = +2 y = × 8 (b) x = +3 y = × 7 (a) B0 (b) B1

(c)

m = any multiple of 5 greater than 20

must be in this order

m and p must each be evaluated B1

Additional Guidance

m = 20 p = 0 B0

 p given as negative e.g. m = 25 p = –1 B0

Some examples of correct pairs

m = 25 p = 1

m = 30 p = 2

m = 35 p = 3

m = 40 p = 4

m = 45 p = 5

m = 50 p = 6

m = 100 p = 16

m = 500 p = 96 B1

[3]

 

Page 30 of 45

 

15.

Alternative method 1

0.62 × 13.5 (million) or 8.37 (million) or 8.4 (million) or 0.38 × 13.5 (million) or 5.1(3) (million)

M1

0.62 × 13.5 (million) – 0.38 × 13.5 (million) or 3.24

M1dep

3.24 million oe e.g. 3 240 000 or 3.24 × 10 6   SC2 0.324 million oe or 32.4 million oe SC1 digits 324 A1

Alternative method 2

62(%) – 38(%) or 24(%) oe e.g. 0.62 – 0.38 M1

or 3.24 oe e.g. 0.24 × 13.5 (million) M1dep

3.24 million oe e.g. 3 240 000 or 3.24 × 10 6   SC2 0.324 million oe or 32.4 million oe SC1 digits 324 A1

 

Page 31 of 45

 

Additional Guidance

Ignore incorrect conversion after 3.24 million seen e.g. 3.24 million = 324 000 M1M1A1

[3]

16.

(a)

 x

 –1

0

1

2

3

 y

 –7

–4

–1

2

5

B1 two correct values B2

(b)

At least 3 points plotted correctly correct or ft their table in (a)

 points can can be implied by by graph graph passing passing through through them M1

Correct straight line

A1

Additional Guidance

Two points for the same x-coordinate is choice Ignore line beyond first and last points [4]

17.

D B1

18.

(a)

32 mm B1

[1]

 

Page 32 of 45

 

(b)

102 104 109 112 112 117 121 123 123 124 131 134 or 134 131 124 123 123 121 117 112 112 109 104 102 or 102 104 109 112 112 117 121 or 134 131 124 123 123 121 117 or

or 117 and 121 chosen allow one omission, extra or transcription error in a full list

M1

119 A1

Additional Guidance

 Allow the ordered list list to be s seen een by the given list even if part (b) is blank but not if the mean is calculated in (b)  Answer 119 (from (from any or no list) M1A1

Puts list into order then finds the mean

M0A0

 Answer 117.6… or 117.7 M0A0

Selects 109 and 121 M0A0

(c)

Suitable key B1

Fully correct, ordered and aligned B1 two rows correct or complete but unordered B2

 

Page 33 of 45

 

Additional Guidance

 Alignment should be considered for for the B2 for the leaves – relative row length should be correct for each row Key: 10|2 represents 102 mm (may use a different value)

B3

[6]

19.

Alternative method 1

 x + 12 = 2 × (  xx – 3) or 2 x – 6 seen M1

 x + 12 = 2 x – 6 oe M1dep

18 SC1 –27 A1

Alternative method 2

M1

oe M1dep

18 SC1 –27 A1

Additional Guidance

18 from trial and improvement method M1M1A1

[3]

 

Page 34 of 45

 

20.

(a)

Valid description e.g. the higher the speed, the lower the fuel consumption allow negative correlation B1

Additional Guidance

 At low speeds the car has has high fuel consumption B1

Fast speeds mean low fuel consumption B1

The higher the speed, the less distance per litre of fuel B1

 As the car goes faster, more litres of fuel used (per km) B1

Fuel consumption decreases as / when speed increases B1

While the fuel consumption decreases the speed increases B1

Do not allow implication that speed is dependent on fuel consumption e.g. Lower fuel consumption makes the car faster B0

e.g. Less consumption, more speed B0

Decreasing B0

(b)

Straight line line passing through (40, 28 – 35) and (110, 16 – 21) accept clear intention to draw a straight line ignore anything outside of the gates B1

(c)

Correct reading ±   square for their straight line of best fit ft straight line with negative gradient accept if clear intention to draw a straight line ignore any working lines on the graph B1ft

 

Page 35 of 45

 

Additional Guidance

No line of best fit B0ft

Line of best fit not straight B0ft

[3]

21.

3150 ÷ (1 + 4) or 3150 ÷ 5 or 630 may be seen in the ratio 630 : 2520 M1

(3150 + 250) ÷ (1 + 3) or 3400 ÷ 4 or 850 oe e.g. 3150 ÷ 4 + 250 ÷ 4 may be seen in the ratio 850 : 2550 M1

220 A1

Additional Guidance

630 or 850 M1

630 and 850 M1M1

[3]

22.

(a) B1

(b)

cos 37 = or 12 × cos 37 or sin (90 – 37) = or 12 × sin (90 – 37) oe M1

[9.58, 9.584] or 9.6 A1

 

Page 36 of 45

 

Additional Guidance

If trigonometry and Pythagoras are used it must be a fully correct method that would lead to the correct value of y  Accept cos 37 × 12 M1

 Accept adj or a for y e.g. M1

cos =

or cosθ  =

(unless recovered) M0

 Answer coming from scale scale drawing M0A0

 Answer in range seen followed by 9 or 9.5 or 10 M1A1

[3]

23.

similar B1

[1]

24.

Alternative method 1

194 – 160 or 34 M1

or 0.2125 oe M1dep

or 21.25 or 21.3 A1

Alternative method 2

or 1.2125 or 121.25 oe M1

(their 1.2125 – 1) (× 100) or 0.2125 or their 121.25 – 100 oe M1dep

or 21.25 or 21.3 A1

 

Page 37 of 45

 

Additional Guidance

 Answer only 21 M0M0A0

[3]

25.

(a)

Straight line from (10.00, 0) through (10.30, 2.5) or (11.00, 5) or 48 (minutes) seen or 10.48 mark intention for straight line may be implied by a line that stops at 10.48

M1

Correct line stopping at 10.48 mark intention for straight line

A1

Horizontal line from their (10.48, 4) intersecting Sabine’s line

B1ft

(b)

Correct value value for the time between the end of their line and Sabine’s line line must ft the horizontal time difference B1ft

Additional Guidance

22 from no line or from a line that would give a different answer B0

[4]

26.

(18 × 25) + (20 × 35) + (33 × 45) + (9 × 55) or 450 + 700 + 1485 + 495 or 3130 may be seen in table allow one error M1

 

Page 38 of 45

 

(their 450 + their 700 + their 1485 + their 495) ÷ 80 or their 3130 ÷ 80 condone bracket error if working seen e.g. 450 + 700 + 1485 + 495 ÷ 80 M1dep

39.1(25) or 39.13

A1

Additional Guidance

One error may be a consistent error in the midpoints e.g. using 24.5, 34.5, 44.5 and 54.5 Correct value seen but answer given as one of the classes M2A0

Correct products seen in the table but a different method not using their products is choice e.g. 3130 in table but mean calculated as 80 ÷ 4 = 20 M0M0A0

[3]

27.

x6 × x8 =) x6 + 8 or x14  (  x or

x6 × x8 × x 4 =) x6 + 8 + 4 or x18  (  x or

c – 4 = 6 + 8 or 6 + 8 + 4 M1

18 A1

Additional Guidance

 Allow using a value for x leading to answer 18 M1A1

[2]

 

Page 39 of 45

 

28.

or

or

or

or oe any multiple of 6 for denominator M1

or

M1dep

oe A1

Additional Guidance

Numerator only M0M0A0

M1M1A0

[3]

29.

180 × 3 or 540 or (exterior angle =) 360 ÷ 5 or 72 oe may be implied by interior angle M1

 

Page 40 of 45

 

180 × 3 ÷ 5 or 540 ÷ 5 or 180 – 360 ÷ 5 or 180 – 72 or 108 oe method for interior angle of pentagon may be seen on diagram M1dep

(BCP =) their 108 – 60 or 48 may be seen on diagram M1dep

(180 – their 48) ÷ 2 or 132 ÷ 2 their 48 must not be 60 M1dep

66 A1

Additional Guidance

Interior angle 108 seen even if not subsequently used M1M1

 Angle BCP seen as 48 even if not subsequently used M1M1M1

360 ÷ 5 = 72 180 – 72 = 108 108 – 60 = 48 180 – 48 – 72 Ans = 60 M1M1M1M0

360 ÷ 5 = 72 72 – 60 = 12 (72 is being used as the interior angle ang le of the pentagon) M0

 Angle BPC = 360 ÷ 5 with no other valid work M0

[5]

30.

7n – 23 B1

[1]

31.

1 : 18 B1

[1]

 

Page 41 of 45

 

32.

1 B1

[1]

33.

Alternative method 1

504 ÷ (13 – 9) or 504 ÷ 4 or 126 oe working to find the negative pair eg 504 ÷ (9 – 13) or  –126

M1

9 × their 126 or 1134 or 13 × their 126 or 1638 oe  –1134 or –1638 –1638 M1dep

1134 and 1638 or  –1134 and –1638 either order A1

 

Page 42 of 45

 

Alternative method 2

or

oe working to find the negative pair e.g. M1

9 × 504 ÷ 4 or 4536 ÷ 4 or 1134 or 13 × 504 ÷ 4 or 6552 ÷ 4 or 1638 oe  –1134 or –1638 –1638

M1dep

1134 and 1638 or  –1134 and –1638 either order A1

 

Page 43 of 45

 

Alternative method 3

or

oe working to find the negative pair

M1

or

oe  –1134 or –1638 –1638 M1dep

1134 and 1638 or  –1134 and –1638 either order A1

[3]

34.

Pair of intersecting arcs, equal radii > half  XY , above and below XY M1

Perpendicular bisector of XY drawn with correct construction all construction arcs required may be a dashed line A1

 Arc, centre Z, radius [5.8, [5.8, 6.2] cm B1

Correct point marked and labelled no construction arcs required

B1

 

Page 44 of 45

 

Additional Guidance

Correct point marked and labelled with no evidence of constructions M0A0B0B1

[4]

35.

(a)

5 = 2 × 4 + c and c = –3 or 5 = 8 + c and c = –3 or

or

 y = 2 × 4 – 3 and y = 5 oe equation in c and c = –3 or full substitution shown in equation of line leading to the given y-coordinate

B1

Additional Guidance

B0

(b)

5 = 2 × 42 + 4b – 3 or 5 = 29 + 4b or 2 × 42 + 4b = 2 × 4 or 32 + 4b = 8 oe M1

5 – 29 = 4b or 4b = 8 – 32 or –24 = 4b or –24 ÷ 4 must reach at least 4b = … M1dep

 –6 A1

[4]