Download Unit 2 Revision

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 +
100
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
7.8  5.3
10.3
6.2  3.92
90. estimate
1.25
89. estimate
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
129.
find the exterior angle
x
130.
Diagram NOT
accurately drawn
find x if this is a regular Octagon
yº
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
108º
xº
37º
xº
131.
B
A
C
56º
x
D
E
F
y
132.
133.
G
Name these shapes.
134. Which shapes have rotational
symmetry?
Geometry
124.
81º
yº
43º
A
Diagram NOT
accurately drawn
125.
62°
x
B
C
Diagram NOT
accurately drawn
D
126.
D
135. Write down the order of rotational
symmetry for:
i rectangle ii parallelogram iii. Rhombus
E
y°
62°
64°
F
136. Find the area of:
G
Diagram NOT
accurately drawn
A
100°
D
2x°
127.
47°
x°
C
B
Diagram NOT
accurately drawn
128.
find the exterior angle
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 16

3
4
1
8 3
ii 27 3
 3
 
 2
iv 8
v
–2
vi 27
vii

Simplify these expressions:
4k  8
k 8
2
n2 – 1
2

n 1 n – 2
2
0
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
6x 2  7 x  3
9x 2  6x  1
2
iii
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) =
1
3
1
25 2
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
4x 2 – 6x
4x 2 – 9
2
3
+
x 1
x –1
Substitution
2
a. Tayub said, “When x = 3, then 4x is
2
144”. Bryani said, “When x = 3, then 4x
is 36”. Who was right? Explain why.
2
b. Work out the value of 4(x + 1) when
x = –3.
Straight lines & y=mx+c
a. Write down the equation of a line
parallel to y =
1
x+1
2
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.
P
i.
Work out the density of copper.
3
The density of zinc is 7130 kg/m .
3
ii. work out the mass of 5 m of zinc
y
Q
f.
O
R
x
5 cm
S
8 cm
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.
3
The volume this solid cuboid is 140 cm .
(a) Work out the height of the cuboid.
The cuboid is made from wood.
The wood has a density of 1.2 grams per
3
cm .
(b) Work out the mass of the cuboid.
The diagram shows three points A
(1, 5) , B (2,  1) and C (0, 5) .
A line L is parallel to AB and passes
through C.
Find the equation of the line L.
g. This triangular prism is made of wood with
density 0.85 g/cm3. Work out its mass.
Other
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.
1. Work out the size of angle SOB.
2. Work out the size of angle BAO.
Standard Form
a.
x
pq
pq
5 &
4
If p = 4 × 10
q = 1.25 × 10
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.
3
e. The mass of 5 m of copper is 44 800
kg.
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
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?
3.
The table shows some temperatures at midnight in Canada.
Town
Temperature at
midnight
Banff
2 °C
Norquay
–4 °C
Revelstoke
–6 °C
Calgary
4.
(b)
5.
6.
(2)
5 °C
(a)
(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)
Simplify d + d + d + d
(1)
Simplify 3f + 4 – 2f + 6
(2)
Draw accurately a circle of radius 5 cm.
(2)
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.
8.
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)
Here is a list of numbers.
2
3
10
12
15
16
24
From the list write down
9.
(a)
an odd number
(1)
(b)
a multiple of 6
(1)
(c)
a factor of 18
(1)
(a)
Write
1
as a decimal.
4
(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.
Description
Filter
Dishwasher Repair
Number
Cost of each item
1
£28.95
Basket wheel
8
£1.50
Spray arm
2
£...........................
......
Total
£28.95
£...........................
......
£20.90
1
hours at £18.00 an hour
2
£...........................
......
£...........................
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.
Labour charge 1
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
(b)
Write down the value of 25
(1)
(c)
Write down the value of 23
(1)
(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.
(b) What is the 8th term in the sequence?
(2)
(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)
TOTAL FOR PAPER 60 MARKS