Homework 1
1. Evaluate
8.1 – 19.4 ÷ 4
2.
3. Bacteria in a test tube increase at the rate of 0.9% per hour. At 12 noon there are 4500 bacteria.
At 3 pm, how many bacteria will be present? Give your answer to 3 significant figures.
4. The planet Mars is at a distance of 2.3 × 108 kilometres from the Sun. The speed of light is 3.0 ×
105 km per second. How long does it take light from the Sun to reach Mars? Give your answer to
the nearest minute.
5.
6.
7.
8.
9. In a tombola game, tickets from 1 to 100 are placed in a box.
five win a prize.
(a) How many winning tickets are there in the box?
Jane is the first person to pick a ticket and she won a prize.
(b) What was the probability that she won?
(c) Find the probability that the next person wins a prize.
10.
Only tickets that end in zero or
Homework 2
1. Evaluate
43 – 5.6 × 4
2.
3. In 1999, a house was valued at £70,000 and the contents were valued at £45,000. The value of the
house appreciates by 7% each year. The value of the contents depreciates by 9% each year. What
will be the total value of the house and contents in 2002?
4. Solve the equation
5.
6.
7.
5 + 3a = a −15
8.
9.
10.
Homework 3
1. Evaluate
5.7 + 3.9 × 4 2
2.
3. James bought a car last year. It has lost 12½ % of its value since then. It is now valued at £14 875.
How much did James pay for his car?
4.
5.
6.
7.
8.
9.
10.
Homework 4
1. Evaluate
31 × 4 − 27.09 ÷ 3
2. A computer is sold for £695. This price includes VAT at 15%. Calculate the price
of the computer without VAT.
3. Solve the inequality
4.
5.
6.
7.
8 – x > 3(2x + 5)
8.
9.
10.
A ship sails 9km due North and then a further distance x km due West.
The ship is now 12km from its starting point. Calculate x.
Homework 5
1. The total number of visitors to an exhibition was 2.925 × 10 7. The exhibition was
open each day from 5 June to 20 September inclusive. Calculate the average
number of visitors per day to the exhibition.
2. Solve the equation :
3.
4.
5.
6.
5 − 2(1+ 3x) = 27
7.
8.
9.
10. A cone has a base diameter of 8cm and a height of 5cm. Calculate the volume of
this cone.
Homework 6
1. The mass of the sun is 2.2 × 1030 kilograms. The mass of the earth is 5.97 × 1024
kilograms. Express the mass of the earth as a percentage of the mass of the sun.
Give your answer in scientific notation.
2. Remove the brackets and collect like terms
3.
4.
5.
(3a − b)(2a −5b)
6.
7.
8.
9.
10.
Homework 7
1. Simplify
2.
3.
4.
5.
4(3x − 2) − 5(4x +1)
6.
7.
8.
9.
10. A flat is bought for £120,000. In each of the 3 years that follows, its value
appreciates by 3.2%. Calculate the compound interest on the flat.
Homework 8
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 9
1.
2.
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7.
8.
9.
10.
Homework 10
1.
2.
3.
4.
5.
6.
7.
8.
Tangent
9.
10. Solve for x:
Homework 11
1.
2.
3.
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6.
7.
8.
9.
10.
Homework 12
1.
2.
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10.
Homework 13
1.
2.
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7.
8.
9.
10.
Homework 14
1.
2.
3.
4.
5.
6. Multiply or divide the following, giving your answer in its simplest form
7.
8.
9.
10.
Homework 15
1.
2.
3.
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5.
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7.
8.
9.
10.
Homework 16
1.
2.
3.
4.
5.
6.
7.
8. Write down the equations of each of the graphs below:
9.
10.
Homework 17
1.
2.
3.
4.
5.
6.
7.
8. Evaluate each of the following for a = 81 and x = 8
9.
10.
Homework 18
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 19
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 20
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Answers
Homework 1
1.
8.1 – 4.85 = 3.25
2.
3.
4.
5.
6.
(a)
x2 = 202 – 172 = 111
=> x = 10.53
(b) A = x 21.06 x 34 = 358.02
7.
8.
9.
(a) 20
(b)
(c)
10.
357/140 = 2.55hrs = 2 hours 33mins
=> diagonal = 21.06
Homework 2
1.
43 – 22.4 = 20.6
2.
3.
4.
2a = -20
=>
a = -10
5.
6.
7.
8.
9.
10.
(a) £4620
(b) £1478.40
(c) £86.95
(d) 27%
Homework 3
1.
5.7 + 15.6 = 21.3
2.
3.
= 4
87.5% = £ 14 875
=>
1% = £170
=>
100% = £17000
4.
5.
6.
7.
8.
9.
(a) 7.1
10.
(a) Cash = £8600 ,
(b) 15%
(b) 8.1
H.P. = £9930 , Lease = £9450
; Total saved = 9930 – 8600 = £1330
Homework 4
1.
124 - 9.03 = 114.97
2.
115% = £ 695
=>
3.
4.
5.
(a) 11.7
(b)
12.7
6.
7.
8.
9.
Converse of Pythagoras – No!
10.
Pythagoras 7.9 km
1% = £ 6.04
=>
100% = £ 604
Homework 5
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
(a)
i)
(b)
28 cm
83.7 cm3
P=4x+12
ii)
A=x2+6x+5
Homework 6
1.
2.
3.
4.
5.
6.
7.
8.
9.
(a) (x + 5) (x - 1)
10.
(a) 8
(b) 20
(b) (a -7) (a + 3)
(c) 13
(c) (t + 4)(t - 5)
(d) p2 + 4
(d) (y + 8)(y - 4)
Homework 7
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.032^3 * 120000 = 131892.57
CI = 131892.57-120000=11892.57
Homework 8
1.
2.
3.
4.
5.
6.
7.
y=a+b
8.
9.
10.
25.1m2
Homework 9
1.
2.
3.
4.
55.8cm2
5.
6.
7.
(a)
Gradient =
Y intercept = 4
Equation is m = 3h + 4
(b)
M = 3 x 8 + 4 = 28
8.
9.
(a) £80 (b) £50 (c) £143
10.
B
Homework 10
1.
2.
3.
4.
5.
6.
7.
8.
(a) 28o
(b) 40o
9.
b2 -4ac =0 Answer = D
10.
x = -3
Homework 11
1.
2.
3.
4.
5.
6.
7.
(a) SIQR 3A = 3, SIQR 3B = 3
(b)
(c)
8.
5/4
9.
B
10.
Class 3A performed better in the tests
Homework 12
1.
2.
3.
4.
5.
6.
Area Circle = 113.04
Area Square =72
Area Unshaded = 41.04
7.
8x2+2xy-15y2
8.
Copper
:
Gold
5
:
7
160
:
224 (All copper is used)
Total weight of 14 carat gold =384g
9.
10.
(a) 83.4cm (b) 150.7cm2
Homework 13
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 14
1.
2.
3.
4.
5.
6.
7.
See proof
8.
Using iteration to get root at x = -2.3
9.
10.
Area of triangle using “sine rule” = 55.1cm2
=>
Volume = 275.7 to 1d.p
Homework 15
1.
2.
3.
4.
5.
6.
x = 1.6 or x = -3.6
7.
8.
(a)
9.
10.
1.4
3(2x-3)(2x+3)
(b)
(3x+10)(2x-3)
Homework 16
1.
2.
3.
4.
5.
6.
7.
8.
y = 4 cos 3xo
y = tan xo
y= -8 cos 4xo
9.
10.
 3
 
  2
  2
b    2 , c   , d   
2 
4 
 
 
 4
1 
 
 
0
CD   2 , EF   , GH    1
 2
 
 
 
 
Homework 17
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 18
1.
2.
b+1
3.
4.
5.
6.
A (-2,0)
B (8,0) C (0,16) D (3,25)
7.
(a) 25
(b)
8.
(a)
9.
-2, ¼
10.
32
(b)
(c)
12
(c)
Homework 19
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Homework 20
1.
2.
9
3.
4.
5.
6.
7.
Proof
8.
(a)
9.
See diagrams
10.
a) 
a = -1 , b = 3 (b)
k = 2 (c) (1,-8)
 6   6  1   2   0  13   9    11   10 
 b) c) d ) e)  f )  g ) h)
i)

10    3   6  12   0  13   2  12    8 