Department of Mathematics
Name:
Class:
Date:
Year 8 First Term Revision Sheet
1. Round each of these numbers as indicated.
a 72 to the nearest 10
b 758 to the nearest 100
c 5148 to the nearest 1000
d 5148 to the nearest 10
2. Round each of the following to the number of decimal places indicated.
a
4.572 (1 dp)
b 0.085 (2 dp)
c
5.7159 (3 dp)
d 4.558 (2 dp)
e
2.099 (2 dp)
f
g
7.124 (1 dp)
h 8.903 (2 dp)
0.7629 (3 dp)
3. Round each of the following to the nearest whole number.
a
6.7
b 9.3
c
2.8
d 7.5
e
8.38
4. Round each of the following to the number of significant figures (sf) indicated.
a
46 302 (1 sf)
b 6177 (2 sf)
c
89.67 (3 sf)
d 216.7 (2 sf)
e
7.78 (1 sf)
f
g
729.9 (3 sf)
h 5821 (1 sf)
i
0.06048 (2 sf) j
1.087 (2 sf)
0.00364 (1 sf) k 7.552 (1 sf)
1
l
0.01207 (3 sf)
5. Write out the first three multiples of each number.
a 10
....................... .....................................................................................
b 6
....................... .....................................................................................
6. List all the factors of each of these numbers.
a 20 ...................................................................................................
b 32 ...................................................................................................
7. Use your calculator to find all the factors of each of these numbers.
a 160
........................................................................................................
b 225
........................................................................................................
8. Here is a list of numbers.
4
a
b
c
9
10
12
14
20
From the list, write down a multiple of 7.
From the list, write down a multiple of 6.
From the list, write down a multiple of both 4 and 5.
9. Work out the next two prime numbers after:
a 25....................................................................................................
b 80....................................................................................................
2
10. Using a method of your choice, find:
(i) the HCF
(ii) the LCM of these pairs of numbers.
a 12 and 20
b 36 and 30
.......................................................
...........................................................
.......................................................
...........................................................
.......................................................
...........................................................
11. Find the HCF and LCM of the following pairs of numbers.
a 36 and 24 .......................................................................................
b 77 and 105 .....................................................................................
c
18 and 48
3
12. Here are four numbers.
3 12
25
36
Complete the table by putting the numbers in the correct boxes.
Square
number
Factor of 24
Odd number
Multiple of 6
13.
The table shows the maximum and minimum temperatures recorded in 5 cities
during one year.
(a) In which city was the lowest temperature recorded?
...........................................................
(b) Work out the difference between the maximum temperature and the minimum
temperature recorded in New York.
........................................................... °C
In the same year, the minimum temperature recorded in Oslo was 7 °C lower than the
minimum temperature recorded in Helsinki.
(c) Work out the minimum temperature recorded in Oslo that year.
........................................................... °C
4
14.
Here are some numbers in a list.
2
−4
−8
5
−3
(a) Write the numbers in order of size.
Start with the smallest number.
...........................................................
(b) Work out
(I) −4 + 5
...........................................................
(ii) −8 − (−3)
...........................................................
(iii) −3 × 2
...........................................................
(iv) −8 ÷ (−4)
...........................................................
5
15.
Here is a thermometer in a refrigerator.
(a) What temperature is shown on the thermometer?
..........................................................°C
The temperature in a freezer is 17°C lower than the temperature in the refrigerator.
(b) Work out the temperature in the freezer.
..........................................................°C
Room temperature is 20°C.
(c) Work out the difference between room temperature and the temperature in the
freezer.
..........................................................°C
16.
Solve each problem
6
11) 6.8 x 0.00001
12) 3.78906 x 0.1
17. Write down the following in expanded form
18. Express the following numbers in standard form:
7
19.
a) Work out the value of:
i)
ii) 10 – 3 x 2
b) Insert one pair of brackets to make the following equations correct.
i) 2 × 8 − 5 − 4 = 15
ii) 7 + 2 × 9 = 81
iii) 6 + 5 × 10 – 8 = 16
20.
8
21. (a) Write 6.43 × 105 as an ordinary number.
.............................…
(b) Work out the value of 2 ×107 × 8 ×10−12
Give your answer in standard form.
22. Work out the value of (2.3 × 1012) ÷ (4.6 × 103)
Give your answer in standard form.
23. Work out the value of
3 x 10–5 x 40 000 000
Give your answer in standard form
24. Workout the value of ( 3 × 10 4) + ( 2 × 105 )
Give your answer in standard form
25. Without a calculator, determine the following, giving your answers in both
normal and standard form:
(a) ( 6 × 105 ) + ( 3 × 106 )
(b) 8 × 10 − 2 + 9 × 10 − 3
9
(c) 6 × 10 5 − 1 × 10 4
(d) ( 8 . 2 × 1011 ) ÷ ( 4 × 10-8 )
(e) ( 1 . 92 × 10 6) × ( 3 . 2 × 10-11 )
(f) ( 6 . 2 × 10 14)3
26. Simplify the following expressions:
a) 4x + 5x + 7 + x + 2
b)- 9b + 2n – 4 + 2b
c)-8 + 2d – 7 – 5d + 12
d) 2n + 3 – 5n + 6
e)-7g + 3 – 8 – 3g + 7h
f) 5b + 7 – 3b – 4
27. Simplify the following expressions:
a) 3p x 4y
b) 8p ÷ 2
c) 5w x 9z
e) 3a x 2b x 3c
d) 15 x ÷ 3y
f)
10
!"#
$
28. Expand
a) 3(x + 2)
b) 5(2y – 7)
c) -2(n + 9)
d) -3(k – 1)
e) -4(1 + a)
f) 3(d – 4)
g) -1(3x + 4)
h) -3(b – 9 + 2y)
29. Simplify the expressions below
a) 7(2x – 1)
d) 12x + 2(-4x + 1)
b) -3(3x – 5) + 8x
e) - 8y + 4(3y + 3)
c) 9x + 2 + (3x – 7)
f) 2y + 7(2y – 3)
30. Factorize:
a) 6x + 24
b) 8x2 − 4x
e) 15pq − 20q
f) 12st2 + 15st
i) 7x2y + xy
j) a2 + ab
11
c) 6xy + 10x2 y
d) m4 − 3m2
g) −18xy − 6x
h) at − at2
31. y = 5x – 3
Find the value of y when x = 9
32. h = 5t 2 + 2
(i) Work out the value of h when t = –2
(ii) Work out a value of t when h = 47
33. Fred is a builder. He charges a £10 fee for his services, plus £5 per hour. This is
shown below
Pay = £10 + (£5 x number of hours worked)
P = 10 + 5h
Work out how much Fred will be paid if he works for:
a)
1 hour?
b)
2 hours?
c)
4 hours?
12
34. Write an algebraic expression for each word phrase.
a) 12 more than m machines
b) six times the daily amount of fiber f in your diet
c) your aunt’s age a minus 25
d) the total number of seashells s divided by 10
35. A cell phone company charges $40 per month plus a $35 activation fee.
a) Write an expression for the total cost for m months.
b) Then evaluate your expression for 10 months of service.
36. A quadrilateral has sides x, 2x, y and 3y.
Write down and simplify a formula for the perimeter, p, of the quadrilateral.
37. Write an expression for the perimeter of each shape below
13
38. Write an expression for the area of each figure.
39. Fill in the missing numbers
(a) 2 7 × 2 4 = 2 ?
(g) ? 2 × 4 4 = 4 6
(j) 7 14 ÷ 7 10 = 7 ?
(b) 3 4 × 3 5 = 3 ?
(h) 5 7 ÷ 5 4 = 5 ?
(c) 3 6 × 3 7 = 3 ?
(i) 3 4 ÷ 3 2 = 3 ?
(k) 17 5 ÷ 17 ? = 17 3
40. Fill in the missing numbers
(a) 4 = 2 ?
(b) 8 = 2 ?
(d) 64 = 2 ?
(e) 27 = 3 ?
14
(c) 16 = 2 ?
41. Simplify the following, giving your answers in index form
(a) (23)2 =
(b) (32)2 =
(c) (62)3 =
(d) (53)2 =
(e) (5?)4 = 512
(f) (105)?=1015
42. Simplify each of the following, giving your answer in index notation
43. Evaluate each of the following
44. Make y the subject of each of the following
a) y + w = c
b) y − p = m
c) m + y = s
d) y − 2g = n
e) 3y = c
f) ay = w
15
%
g) =w
&
%
h) =2c
i) a = y + p
'
j) y² = s
k) y³ = x
l) √y = g
45. Make x the subject of the following formulae
a)2x + 2y = P
d)"! +2=w
b) s = x² − 3
e) !#-5=w
g) 3y = 4x + 1
j)
#()
*
=2c
f) !$%
=h
&
h) x² + a = v
k)
!"#
$
c) y = xz + s
=3z
16
i) x³ − 4 = 5y
l) A = ½bx
46.
47.
48.
49. Find missing number
50.
51. Divide the following fractions
52. Solve the following
53. Solve these equations.
a) x + 2 = 6
b) t − 3 = 7
c) 3 + m = 2
d) 3x − 2 = 16
e) 8 = 12a – 4
f) 22 = 6b − 8
54. Solve these equations.
a 12x = 2x + 10
d 9p − 4 = 10p − 5
55.
b 7x − 8 = 3x
e 4q + 6 = 3q + 2
c 6a + 3 = 2a + 7
f6−n=n–4
56.
57. What is the value of each letter? Write and solve equations to help you.
a) When x is doubled and 4 added, the result is 12.
b) When y is trebled and 6 subtracted, the result is 6.
c) When p is multiplied by 4 and 3 added, the result is 27.
d) When 2 is added to k and the answer multiplied by 5, the result is 25.
58. Work these out.
a 14 − −15
b −21 − 12
c 42 + −15
d −33 + −12
e −15 − −12 + 4
f 18 − −23 + −30
59.Work these out.
a 2 × −6
b −7 × −4
c −3 × 7
d 9 × −8
e 5 × −12
f −8 × 15
g −10 × −23
h −6 × 20
60. Work these out.
a 45 ÷ −5
b −36 ÷ −4
c −20 ÷ 2
d −30 ÷ 6
e 56 ÷ −7
f 72 ÷ −8
g −60 ÷ 4
h −96 ÷ −12
61. Calculate these without using a calculator.
a 12 − 3 × 2
b (12 − 3) × 2
c 82 − 14 ÷ 2
d (82 − 14) ÷ 2
e (15 − 5)2 × 2 + 8
f 15 − 52 × (2 + 8)
62. Insert brackets in these calculations, if necessary, to make them correct.
a 6 + 24 ÷ 6 + 4 = 14
b 6 + 24 ÷ 6 + 4 = 9
c 6 + 24 ÷ 6 + 4 = 3
d 6 + 24 ÷ 6 + 4 = 8.4
63.Write down the first five terms of the sequence which has its nth term as:
a) n + 2
b) 4n – 1
c) 4n – 3
64. Write down the 25th and 50th term for each of these sequences:
a) 7n + 1
b) 6n + 7
65. Solve each of these pairs of simultaneous equations.
a) x + y = 15
x−y=3
b) x − y = 14
x+y=2
c) x − y = 1
d) 2x + y = 19
3x − y = 21
e) 3x + 2y = 38
x − 2y = 2
f) x + 6y = 9
x + 2y = 1
g) 2x + y = 22
x−y=5
h) y = 2x – 12
x+y=3
i) 2x + y = 0
x + 2y = 12
x + y = 30
66.Check if the number 204 is in the sequence 2n+3 (Show workout)
67.A pattern of hexagons is built up from matchsticks.
a) How many matchsticks are needed for the nth set of hexagons?
b) How many matchsticks are needed to make the 60th set of hexagons?
c) If there are only 100 matchsticks, which is the largest set of hexagons that could be
made?
68.A pattern of shapes is built up from matchsticks as shown.
a Draw the fourth diagram.
b How many matchsticks are in the nth diagram?
c How many matchsticks are in the 25th diagram?
d With 200 matchsticks, which is the biggest diagram that could be made?
69. Complete the table
70. a) Write down the first 6 multiples of 12.
b) What is the 10th multiple of 12?
c) What is the 100th multiple of 12?
71. Fill in the missing numbers.
(a) 2, 4,…… , 16, 32, . . .
(b) 100, 81, 64,….. , 36, . . .
(c) 6, 9,…., 21, 30, . . .
72. a)What is the 10th term of the sequence 2n + 1 ?
b) What is the 8th term of the sequence 3n + 6 ?
c) What is the 5th term of the sequence 4n + 1 ?
73.
74.
75.Fill in the gaps using the information above.
a 155 cm = .............. m
b 95 mm = ........... cm
c 780 mm = ........... m
d 8150 g = ............ kg
e 2300 kg = ............ t
f 32 ml = ............. cl
g 1360 ml = .......... l
h 580 cl = ............ l
i 950 kg = ............ t
76. A square has a perimeter of 24 cm. What is its area?
77. Calculate the area of each shape below.
78. Calculate the area of each of these triangles.
79. The rectangle and triangle below have the same area.
Work out the length of the base of the triangle.
80. Calculate the area of each parallelogram below.
81. Calculate the perimeter and the area of each trapezium.