Maths in Focus - Margaret Grove - Pat 1

PRACTICE ASSESSMENT TASK 1

Practice Assessment Task SET 1 p-3 p+1 = 1. 5 2

1.

Solve for p:

2.

Factorise fully: 10x + 2xy - 10y - 2y 2.

3.

Write in index form 1 (a) x (b)

3

2x + 6 . 2

17. Solve 2x 2 - 3x - 1 = 0 correct to 3 significant figures. 18. The radius r of a circle with area A is A given by r = . Find r, correct to r 2 decimal places, if A = 7.59.

x4

4.

Simplify the expression 8y - 2 ^ y + 5 h .

5.

5 Rationalise the denominator of . 5- 2 Expand and simplify ] x - 3 g ^ x 2 + 5x - 1 h .

6.

16. Simplify

7.

3x 2 Solve the equation = . ^ x ! -1h x+1 3

8.

Simplify

9.

Show that TABC and TEDC are congruent triangles. Hence, or otherwise, show that TACE is an isosceles triangle.

x 2 - 2x - 3 x+1 . ' 5 10

19. Solve 5 - 2x 1 3 and sketch the solution on a number line. 20. Evaluate

3 5 1 2 + + . 20 15 3 12

21. Solve the equation x 2 - 4x + 1 = 0, giving exact solutions in simplest surd form. 22. Write 7 - 2 as a rational number. 23. Solve simultaneous equations y = 3x - 1 and y = x 2 - 5. 24. Find integers x and y such that 3 = x + y 3. 2 3+3

10. Evaluate ] 3.9 g4, correct to 1 decimal place.

25. Evaluate |-2 | 2 - | -1 | + | 4 |. 26. Find the value of x.

11. Simplify 2 3 - 27 . 12. Find the size of each interior angle in a regular octagon. 13. Evaluate 0.72 ' 9.82 in scientific notation, correct to 3 significant figures. 14. Expand and simplify

2 ^3 5 - 2 2 h.

15. Find, correct to 2 decimal places, the ] 2.14 g3 value of . 6.94 - 3.72

27. Factorise 8x 3 - 1. 28. Rationalise the denominator of 2 3 . 3 5- 2

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Maths In Focus Mathematics Preliminary Course

29. Simplify 2 | -4 | - | 3 | + | -2 |.

41. Solve x 2 $ 9.

30. Find the sale price if a discount of 8% is given on a DVD player that usually sells for $699.

o as a fraction. 42. Write 0.16

5.21 + 4.71 correct to 3.94 # 1.76 2 significant figures.

31. Evaluate 3

32. Rationalise the denominator of

5 +1

. 2 2+3 33. The price of roller skates has increased by 6.5% to $89. Find the price before the increase.

34. Find the values of all pronumerals, giving reasons for each step of your calculations.

35. Find the area of this figure.

36. Simplify

^ a - 4 h3 # b 6

a9 # ^ b-1 h

4

38. Evaluate 4

3 2

1 in index form. x+3 45. Expand and simplify ] x + 2 g3.

44. Write

46. Find the value of a 3 b - 2 in index form if 4 2 1 3 a = c m and b = c m . 5 2 47. Find the value of x, giving reasons for each step of your working out.

48. Find values of x and y.

.

37. Solve 5x - 9 2 21. -

43. Prove that the diagonals in any rhombus bisect the angles they make with the sides of the rhombus.

as a rational number.

-

49. Write ] 3x + 2 g

1 2

without an index.

50. Simplify (a) 8x - 7y - y + 4x

39. Simplify 2 ] x - 5 g -3 ] x - 1 g .

(b)

124

40. Solve 4 2x + 1 = 8.

(c)

x2 - 9 x 3 + 27

PRACTICE ASSESSMENT TASK 1

(d) (e)

1 + 2+1

55. ABCD is a parallelogram with CD produced to E so that ED = AD. Prove that +ABC = 2+DEA.

2 2-1

3 2 4 + x + 1 x2 - 1 x - 1

1 (f) x - x when x = 2 3 (g)

^ x - 2 h5 y 4 z - 3

x4 _ y3 i

-1

^ z - 4 h- 2

a+b a + 2ab + b ' 3 - 6b 5a - 20ab 2 2

(h)

2

(i) 8 5 - 3 20 + 2 45 a3 b2 ^ c4 h 1 2 2 3 c m c m , if a = , b = 2 3 ^ a 2 h2 bc 5 4 -1 and c = c m 9 2

(j)

51. Find the values of x and y, correct to 1 decimal place.

52. Evaluate x.

2 1 5 3 56. Find the exact value of . 5 16 1 1 57. Tran spent of her salary on rent, 4 3 1 1 on food, on bus and taxi fares, and 5 6 on going out. If she puts the rest of her salary into savings, what percentage of her salary is savings? 58. The speed of light is about 2.99 # 10 8 ms - 1 . If a rocket travels at one-fifth the speed of light, find its speed in kmh - 1 (in scientific notation correct to 2 significant figures). 59. Find the value of k if ] 2x + 5 g2 = 4x 2 + kx + 25. 60. Simplify

53. The volume of a sphere is given by the 4 formula V = rr 3. Find the exact radius r, 3 2 if the volume V is 10 cm 3. 3 54. Find the perimeter of the figure below, correct to 3 significant figures.

81x 2 y 3 .

61. The sum of the interior angles in a regular polygon is 1620c. Find the size of each interior angle, to the nearest minute. 62. Find the area of the shaded region in this figure, correct to 2 decimal places.

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Maths In Focus Mathematics Preliminary Course

63. Factorise (a) 5 ] a - 2 g3 + 40b 3 (b) ] 2a - b + c g2 - ] a + 5b - c g2 64. Solve -2 #

8x - 1 1 9. 5

20 m

65. ABCD and BCEF are parallelograms. Show that AFED is a parallelogram. 25 m

71. In the figure, BD is the perpendicular bisector of AC. Prove that triangle ABC is isosceles. B

66. Find the value of b correct to 2 decimal places.

A

D

C

72. The diagonals of a rhombus are x and y. Find the length of its side. 67. The diagonals of a rhombus are 6 cm and 10 cm long. Find the (a) exact length of the sides of the rhombus (b) area of the rhombus. 68. Write as a single fraction with a rational 2 1 denominator . 3 3- 2 2+ 5 69. The exterior angles of a regular polygon are 18c . How many sides has the polygon? 70. A cable is used to support a 20 m tower as shown. If the cable is placed 25 m away from the base of the tower, how long must it be, to the nearest metre?

73. Write

1 in index form. 3 ] x - 2 g5 -

5 3

-

5 2

(a) ] x - 2 g

]x - 2 g (b) 3

-

(c) 3 ] x - 2 g 1 (d) 5 ] x - 2 g3

5 2

74. Write the number 54 000 000 in scientific notation. (a) 5.4 # 108 (b) 54 # 106 (c) 5.4 # 107 (d) 54 # 10−8

PRACTICE ASSESSMENT TASK 1

75. Simplify

^ 2a 3 b h 3

] ab g

2

.

(a) 8a b (b) 8a8b (c) 2a7b (d) 2a8b 76. A computer costs $1850. If it has increased in cost by 4% since last week, how much did it cost last week? (a) $1924.00 (b) $1778.85 (c) $1867.80 (d) $1776.00

o to a fraction. 78. Convert 0.36

7

77. Evaluate 4 (a) - 8 (b)

1 8

(c)

1 6

(d) −6

-

3 2

.

(a)

9 25

(b)

12 33

(c) 3 (d) 79.

1 3

11 30

A E C

B

D

The triangles ABC and CDE can be proven congruent by using the test (a) SSS (b) SAS (c) RHS (d) AAS.

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