Unit 2 Revision - mrvahora



Unit 2 Revision

Number

1. 600 ÷ 30

2. 777 ÷ 37

3. 27.6 x 23

4. 36.2 ÷ 0.2

5. -2 + -4

6. 365 x 54

7. 753 ÷ 36

8. 3 x -5

9. -3 x -5

10. 10 ÷ -5

11. -10 ÷ -5

12. 5.36 + 7.8

13. 13.76 – 5.21

14. 356 x 100

15. 356 ÷ 100

16. 3 x 0.4

17. 0.7 ÷ 1000

18. 8.8 x 10

19. pens cost £0.45, how many can you buy for £18

20. 5 + -7

21. 13 x -5

22. write a fraction between ¼ and ½

23. why is ¾ the same as 6/8?

24. write in order: 3/8, 1/4 , 3/10

25. order: 0.39, 0.4, 0.049, 0.49, 0.409

26. write the first 10 primes

27. write 30 in prime factor form

28. write 18 as a product of its primes

29. write 252 as a product of its primes

30. list all the common factors of 24 & 36

31. find the HCF of 24 & 36

32. find the LCM of 15 & 20

33. write 12 up to 152

34. write 13, 23, 33, 43 & 53

35. 103 =

36. work out root 100

37. Find the length of a square with area 81cm2

38. Why is 2 cubed not 6?

39. Why does root 9 have two answers?

40. work out 70

41. 106 =

42. which is larger: 23 or 32?

43. 57 ÷ 53 =

44. 33 x 34 =

45. (42)3 =

46. simplify 16/24 & 28/35

47. write 27/10 as a mixed number

48. 1½ + 2¾ =

49. 2/3 – ¼

50. 21/3 + 1¾

51. give the value of 6 in 3.476

52. write 0.30 as a fraction

53. write 0.3 as a fraction

54. write 0.37 as a fraction

55. write 0.65 as a fraction

56. convert to decimals: ½, ¼, 1/5, 1/10, 1/100, 1/8

57. write 3/8 as a decimal

58. write 1.25 as a mixed number

59. write 1/3 as a decimal

60. show 0.33333 = 1/3

61. find ¾ of 48

62. find ¾ of 6

63. find 3/5 of £3.50

64. find 10% of £60

65. find 5% of £60

66. find 2.5% of £60

67. find 17.5% of £60

68. increase 60 by 20%

69. decrease 60 by 20%

70. multiply 60 by 1.05

71. increase 60 by 5%

72. compare answers to Q70 and Q71

73. simplify the ratio 20:12

BODMAS

74. insert brackets: 20 – 3 x 2 = 34

75. insert brackets: 14.5 – 2.6 × 4.5 – 3.6 = 49.95

76. 5 x 2 + 3 =

77. 5 x (2 + 3) =

78. 3(2 + 5)2 =

79. estimate √90 =

80. Work out the value of 2 + [pic]

Ratio

81. share £15 in the ratio 3:2

82. share 20m in the ratio 11:6:3

83. Bill & Mary share £P in the ratio 3:5, Bill gets £12, how much does Mary get?

84. Adapt a recipe for 6 people to serve 8 people

85. round 54327 to the nearest ten, hundred and thousand

86. round 37451 to 1sf, 2sf, 3sf

87. round 1.257 to 1.d.p, 2.d.p and 3.d.p

88. round 0.0007269 to 1sf

89. estimate [pic]

90. estimate [pic]

91. using: 17 × 19 = 323, work out: 0.17 × 1.9 and 323 ÷ 0.019

92. find the cost of 1 litre if 50 litres cost £45

Algebra

93. if n is even, what is 2n?

94. if n is even, what is n – 1?

95. 2a = a x a, true/false?

96. find the area of a square of length b

97. find the area of a rectangle length 4 and width (b + 2)

98. simplify: 3a + 2c – a – 3c + 2

99. simplify: x + 5 – 2x – 1 + 4 – x

100. simplify: a x b x 2

101. 2(x + 4)

102. 2a(a + 5)

103. 3p(2q – 7)

104. 3(2x – 1) -2(2x – 3)

105. factorise: 10x = 5

106. factorise: 9x – 3

107. x2 + 3x

108. 6x2 – 9x

109. 2ab2 – 4ab

110. Bhavna uses this formula to work out her Electricity bill:

Cost = Number of units used × Cost for each unit + Meter hire

Bhavna uses 350 units. The cost for each unit is 7.5p. The Meter hire is £15.50.

Work out the cost of her bill

Sequences

111. find the next term: 2, 7, 12, 17, …

112. find the nth term: 2, 7, 12, 17, …

113. find the nth term: 4, 10, 16, 22, …

114. find the 10th term if rule is 3n

115. find the 10th and 20th terms if the rule is 3n – 4

116. find the next term: 1, 2, 4, 8, …

117. find the next term: 1,3,6,10, …

118. find the next term: 1,4,5,8,…

119. plot the points: (3,4), (3,-4), (0,6), (-2,4)

120. find the 4th coordinate of a parallelogram with vertices: (2,1),(-7,3) & (5,6)

121. find the midpoint of A(1,7) & B(5,3)

122. draw graphs of: y = 4, x = 3, y = 2x + 3, x + y = 7, y = ½x -1

123. plot x + y = 6 without a table

Geometry

124. [pic]

125. [pic]

126. [pic]

127. [pic]

128. [pic]

find the exterior angle

129. [pic] find the exterior angle

130. [pic]

find x if this is a regular Octagon

131. [pic]

132. [pic]

133. Name these shapes.

[pic]

134. Which shapes have rotational symmetry?

[pic]

135. Write down the order of rotational symmetry for:

i rectangle ii parallelogram iii. Rhombus

136. Find the area of:

[pic]

Metric & Imperial Units

a. 3metres = ____cm

b. 4 litres = _____ ml

c. 2 gallons = ___ litres

d. 5½ km = ____ m

e. 1 kg = _______ pounds

f. 1 litre = ______ pints

g. 1 gallon = ____ pints

h. 5miles = _____ km

i. 1 foot = ______ inches

j. 1 foot = ______ cm

k. 22 pounds = ___ kilograms

l. 28 miles = ___ kilometres

m. Fred went on holiday to France.

He changed £475 to Euros.

Given that £1 = 1.57 Euros

Change £475 to Euros.

n. How many miles has a car travelled in 3hours at 40mph?

o. How long does it take to travel 200km at 60km/h?

p. change 45km/h to m/s

HIGHER TIER ONLY

Fractional indices:

1. 31/3 x 22/5

2. 15/8 ÷ ¾

3. ¾ x 36

4. 106 =

5. 100 =

6. 9-1=

7. Evaluate:

a Write down the value of

i 50

ii 4-2

b Simplify:

i[pic][pic]

ii [pic]

iii[pic][pic][pic]

iv 80

v 5–2

vi [pic]

vii [pic]

Recurring decimals to fractions:

Change 0.4444444444 to a fraction

Change 0.3777777777 to a fraction

Change 0.4545454545 to a fraction

Change 0.3453453453 to a fraction

Change 1.2323232323 to a fraction

Surds:

√5 x √5 =

√3 x √12 =

√50 ÷ √2 =

√50 = k√2 find k

√8 = 2√m find m

(√5 + 4)(√5 – 4)

(3 – √3)2 = a + b√3

Expanding brackets:

(x+2)(x+5) =

(x+2)(x-5) =

(x+3)(x-3)=

(n+m)(n-m)=

(x+7)2 =

(p + q)2 =

(a – b)2 =

(3x+2)(2x-5) =

Factorising expressions

X2 + 5x + 6

X2 + 2x – 15

X2 – 8x + 12

6x2 + x – 2

6x2 – 11x – 10

6(x+y)2 – 4(x+y)

X2 – 49

X2 – 81

X2 – 169

4x2 – 9y2

81p2 – 25q2

(xy)2 – (ab)2

Simplify these expressions:

[pic]

[pic]

[pic]

[pic]

[pic] + [pic]

Substitution

a. Tayub said, “When x = 3, then 4x2 is 144”. Bryani said, “When x = 3, then 4x2 is 36”. Who was right? Explain why.

b. Work out the value of 4(x + 1)2 when

x = –3.

Straight lines & y=mx+c

a. Write down the equation of a line parallel to y = [pic]x + 1

b. Draw the lines: x = 3 , y =5, x = -4 and y = -6, y = x and y = -x

c. The diagram shows 4 lines, P, Q, R and S.

[pic]

The equations of the straight lines are:

A: y = 2x

B: y = 3 - 2x

C: y = 2x + 3

D: y = 3

Match each straight line, P, Q, R and S to its equation.

d. The diagram shows three points A [pic], B [pic] and C [pic].

A line L is parallel to AB and passes through C.

Find the equation of the line L.

[pic]

e. Find the equation of the straight line which passes through the point (0, 3) and is perpendicular to the straight line with equation y = 2x.

Upper & Lower Bounds

x = 40, correct to the nearest 10.

y = 60, correct to the nearest 10.

a i Write down the lower bound of x & y.

ii Write down the upper bound of x & y.

b Calculate the greatest possible value of xy.

c Calculate the least possible value of xy.

d Calculate the greatest possible value of x/y.

Standard Form

a. [pic]

If p = 4 × 105 & q = 1.25 × 104

Calculate the value of x.

Give your answer in standard form

b. Write 0.000 000 03 in standard form.

c. Express 0.327 ( 105 in standard form.

d. Write 2.5 ( 105 as an ordinary number.

e. The mass of 5 m3 of copper is 44 800 kg.

i. Work out the density of copper.

The density of zinc is 7130 kg/m3.

ii. work out the mass of 5 m3 of zinc

f.

[pic]

The volume this solid cuboid is 140 cm3.

(a) Work out the height of the cuboid.

The cuboid is made from wood.

The wood has a density of 1.2 grams per cm3.

(b) Work out the mass of the cuboid.

[pic]

g. This triangular prism is made of wood with density 0.85 g/cm3. Work out its mass.

Other

[pic]

1. Work out the size of angle SOB.

[pic]

2. Work out the size of angle BAO.

[pic]

3. What are the coordinates of the midpoint of the line segment PQ

4. There are 960 litres of water in a tank. A workman empties the tank. The water flows out of the tank at a constant rate of 0.4 litres per second. How long, in minutes does it tale the workman to empty the tank completely?

END OF QUESTIONS

[pic]

[pic] [pic][pic]

1.

(a) Write the following numbers in order of size.

Start with the smallest number.

5 17 2 25 8

(1)

(b) Write the following numbers in order of size.

Start with the smallest number.

–3 0 6 –10 –7

(1)

2. (a) What time does the clock show?

(1)

(b) On the clock below, show the time half past two.

(1)

Claire leaves home at 3.30 p.m. She arrives at the station at 4.20 p.m.

(c) How long did her journey from home to the station take? (2)

3. The table shows some temperatures at midnight in Canada.

|Town |Temperature at midnight |

|Banff | 2 °C |

|Norquay |–4 °C |

|Revelstoke |–6 °C |

|Calgary | 5 °C |

(a) What is the difference in temperatures

(i) between Norquay and Revelstoke,

(ii) between Calgary and Revelstoke? (2)

In Revelstoke, the temperature drops by 11 °C from midnight to 6 a.m.

(b) What is the temperature in Revelstoke at 6 a.m? (1)

4. (a) Simplify d + d + d + d (1)

(b) Simplify 3f + 4 – 2f + 6 (2)

5. Draw accurately a circle of radius 5 cm. (2)

6. The shape below is made from a rectangle and a triangle.

(a) Mark with arrows (>>) a pair of parallel lines. (1)

(b) Mark with the letter A an acute angle. (1)

7. A ticket for a football match costs £38. Ahmed has £120. He buys as many tickets as possible.

(a) How many tickets does he buy? (2)

(b) How much money has he got left? (1)

8. Here is a list of numbers.

2 3 10 12 15 16 24

From the list write down

(a) an odd number (1)

(b) a multiple of 6 (1)

(c) a factor of 18 (1)

9. (a) Write [pic] as a decimal. (1)

(b) Write 0.8 as a percentage. (1)

(c) Write the ratio 2 : 6 in its simplest form. (1)

10. (a)

Work out the size of the angle marked x.

(2)

(b) ABCD is a quadrilateral.

Work out the size of the angle marked y.

(2)

11. Here is a bill for a dishwasher repair. Complete the bill.

| Dishwasher Repair |

|Description |Number |Cost of each item |Total |

|Filter |1 |£28.95 |£28.95 |

|Basket wheel |8 |£1.50 |£................................. |

|Spray arm |2 |£................................. |£20.90 |

|Labour charge 1[pic]hours at £18.00 an hour |£................................. |

|Total cost |£................................. |

(4 marks)

12. Fran is decorating her bedroom. She is going to put a border all around the bedroom.

This diagram shows a plan of the bedroom.

Border rolls are sold in 4 m lengths. Work out the number of border rolls Fran will need to buy.

(Total for Question 12 is 4 marks)

13. (a) Write down the value of 72 (1)

(b) Write down the value of [pic] (1)

(c) Write down the value of 23 (1)

14. Here are the first four terms of a number sequence.

4 7 10 13

(a) (i) What is the next term in the sequence?

(ii) Explain how you found your answer. (2)

(b) What is the 8th term in the sequence? (1)

Alexi says 34 is in the sequence.

(c) Is Alexi correct? You must give a reason for your answer. (1)

*15. The diagram shows the plan of the floor of Mrs. Phillips’ living room.

Mrs. Phillips is going to cover the floor with floor boards.

One pack of floor boards will cover 2.5 m2.

How many packs of floor boards does she need? You must show your working. (4 marks)

16. Buses to Exeter leave a bus station every 20 minutes.

Buses to Plymouth leave the bus station every 16 minutes.

A bus to Exeter and a bus to Plymouth both leave the bus station at 8 a.m.

When will buses to Exeter and Plymouth next leave the bus station at the same time?

(3 marks)

17. Given x = 4;

Work out the value of 2x2 + 7 (2 marks)

18. On the grid, draw the graph of y = 4x + 2 from x = –1 to x = 3

(3 marks)

*19. Mr Smith drives 24 miles to work. On Monday his journey to work takes 30 minutes. On Tuesday the average speed of his journey to work is 56 km/h. Did Mr Smith drive more quickly to work on Monday or Tuesday?

You must show all your working.

(4 marks)

[pic]

TOTAL FOR PAPER 60 MARKS

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