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Mathematics
Stonelaw High School
Home Learning
Blue Course
Homework 1 (Covering BF1.1 and BF1.2)
1.
Given that a  8 , b  12 and
(a)
2.
2a  b
c
(b)
c  4 , calculate the value of:
a 
b
c
(c)
a2  c2
A formula is defined as E  5 p  q 2
Calculate the value of E when p  4 and q  3 .
3.
What is the value of x 2  3x  5 when x  4 ?
4.
Express
5.
Evaluate
6.
simplify :
3b  a
in its simplest form given that a   7 and b  3 .
4a
h2  g 2
60
when ℎ = −3 and 𝑔 = 4.
(a)
2 x  5x
(b)
 3a + a
(c)
7x  4x
(d)
4h + (2h)
(e)
 9a + (a)
(f)
4k  (2k)
(g)
a5
(h)
6  (4p)
(i)
 2y  7
(j)
 3d  (9d)
k)
10g  5 + 3
l)
9  12y + 7y
m)
12c + 3  6
n)
12h + 4  10h
o)
ab + 2a + 2ab
Homework 2 (Covering BF1.3 and BF1.4)
Simplify each of the following by multiplying out the brackets and collecting
like terms.
a) 5(3x + 4)
b) 3x(6x – 5)
c) -6(4x – 5)
d) -3x(7x + 3)
e) (4x + 1)(5x + 2)
f) (2x – 3)2
g) (5x – 3)(2x – 5)
h) (6x – 5)(3x + 4)
i)
(2x + 1)2
j) (8x + 3)(5x – 2)
Homework 3 (Covering BF1.5, BF1.6 and BF1.7)
1.
Simplify each of the following by multiplying out the brackets and
collecting like terms.
a) (x + 4)( x2 + 3x + 2)
2.
(x – 2)( x2 + 2x + 5)
Simplify each of the following by multiplying out the brackets and
collecting like terms.
a) 56 − (5 − q)2
3.
b)
b)
(3p + 7)(5p − 2) − (p + 2)2
a) 5(2x + 1) = 55
b)
-2(3x + 4) = 4x + 2
c) 5(x – 3) = 4(x + 3)
d)
-4(2x – 3) = 4(2x – 1)
Solve the equations.
Homework 4 (Covering BF1.8, BF1.9 and BF1.10)
1.
Solve the inequalities.
a)
c)
2.
b)
d)
2b + 8 < 6b – 3
-7(x – 5) = 2(2x + 8)
b)
y 3 y  2

2
3
4
Solve algebraically the equation.
a)
3.
8 – 5a > 12
2(3x – 3) ≥ 3(5x – 8)
2x 
 3x  1  4
4
Two boys have the same amount of money and are deciding how many
bars of Willy Wonka chocolate to buy.
John buys two bars of chocolate and has £6.60 left over.
Ahmed buys 5 bars of chocolate and has £3.00 left over.
a)
Using £b for the cost of one bar of chocolate, write down an equation
to illustrate the above information.
b)
Solve the equation to find the cost of one bar of chocolate.
c)
How much did the boys have to start with.
Homework 5 (Covering BF2.1, BF2.2 and BF2.3)
1.
Consider the framework opposite.
B
(a)
Calculate the length of BD.
A
2.
3.
(b)
Hence calculate the length of BC.
(c)
Calculate the area of triangle ABC.
26cm
24cm
D
12cm
A ship sails 18km due North and then a further 34km due East.
How far is the ship from its starting point?
An aircraft flies 90 miles due North and then a further distance x miles
due West. The aircraft is now 120 miles from its starting point.
Calculate x.
Homework 6 (Covering BF2.4)
Use Pythagoras to find the distance between the points.
(1)
(12, 9) and (-2, 10).
(2)
(-3, -5) and (2, 9).
(3)
(4, -2) and (11, -3).
C
Homework 7 (Covering BF2.5 and BF2.6)
1.
Carla is making a rectangular door with a height of 2.2 metres and a
width of 80 centimetres.
She measures the diagonal of the door as 234 centimetres to the nearest
centimetre.
Use Pythagoras to show that the door is in fact rectangular.
2.
In triangle PQR:
• PQ = x centimetres
• PR = 5x centimetres
• QR = 2y centimetres.
Show that y  6 x 2
Homework 8 (Covering BF1.10, BF2.6, and BF2.7)
1.
Round each number to the given number of significant figures.
(a)
(c)
2.
23 417 (2 sig fig)
23.493 (1 sig fig)
(b)
(d)
129 034 (3 sig fig)
0.02393 (2 sig fig)
In the diagram below, apply Pythagoras Theorem to find the value of x.
Give your answer to 3 significant figures.
x
x–7
12
Homework 9 (Covering BF2.7, BF3.1 and B3.2)
Write these numbers in normal form
1.
(a) 8.41  103
(b) 5.67  104
2.
(a) 9.17  10-3
(b) 6.65  10-2
Write these numbers in scientific notation
3.
(a) Half a million
(b) 61400
4.
(a) 0.174
(b) 0.00056
5.
The total mass of argon gas in a canister is 4.23  10-2gms.
Given that the mass of a single atom is 5.67  10-22, find to 3 significant
figures the number of argon atoms in the flask.
6.
Large distances in space are measured in light years.
A camera on a space telescope photographs a galaxy, a distance of 50
million light years away. One light year is approximately 9.46 × 1012
kilometres.
Calculate the distance of the galaxy from the space telescope in
kilometres.
Give your answer in scientific notation.
7.
A cyclotron produces high speed particles.
A particle moving inside the cyclotron takes 9.7 × 10-10 seconds to
travel 2.3 × 10-1 metres.
Calculate the speed of the particle in metres per second.
Homework 10 (Covering BF1.4 and BF3.3)
Simplify the following writing the answers with positive indices only.
1.
x2  x5
2.
y 3  y 7
3.
x6  x4
4.
y 3  y 1
5.
(2a 4 ) 3
6.
( p 4 )2
7.
x3  y 5
x2  y2
8.
a 1  b 3
a 2  b
9.
5𝑥 3 × 2𝑥 −3
10.
3𝑎5 𝑏3
5
11. 3𝑝 × 2𝑝
6𝑎2 𝑏5
1
1
3
1
2
1
12. 4𝑟 8 ÷ 2𝑟 −2
14. 𝑥 3 × 𝑥 −3
2
3
15. x ( x  1)
16. a (a  a )
8 105
17.
4 102
6  10 2
18.
4  10 3
4
2
19. (3 10 )  (5 10 )
3
5
20. (2 10 )  (4 10 )
13. 𝑎−2 × 𝑎2
1
3
2
Homework 11 (Covering BF1.4, BF3.3and BF3.4)
1.
Express without root signs.
(a)
2.
a
(b)
p3
3
(c )
x5
(d )
5
r2
a
( e)
b3
Express with root signs (write with positive indices first where
necessary).
( a)
3.
4
p
1
5
(b)
w
3
4
(c)
x
1
2
(d )
a
 34
(e)
y


 15
Simplify each of the following by ….
i) changing root signs to fractional powers;
ii) moving x's onto the numerators;
iii) expanding brackets …………………… where necessary.
1
(a)
x 2 ( x 4  1)
(d )
2  2 1
x  
x
x 3 
(g)
1
x
( j)
x2  3
x

xx

1
(c )
1 12
x x
x2
(f)
 2 1
x  
x

(i )
1

x 2   3 x 
x

3
(b)
x 2 (x 2  x2 )
(e)
1 2
x  x
x

( h)
1 

x

x

(k )
x  x
x2

2
(l )
(2 x  1) 2
3
x2
2
Homework 12 (Covering BF 1.4 and BF3.6)
1.
2.
3.
4.
Express each of the following in its simplest form.
(a) 8
(b) 12
(c) 50
(d) 45
(e) 332
(f) 540
(g) 212
(h) 418
(i) 324
(a) 52 + 32
(b) 37 - 7
(c) 43 + 23 - 33
(d) 8 + 52
(e) 53 - 12
(f)
45 + 20 + 45
(g) 50 - 8
(h) 312 + 27
(i)
75 + 108 - 3
(a) 5  5
(b) 6  2
(c) 32  2
(d) 25  35
(e) 26  33
(f)
(a) (2 + 3)(2 - 1)
(c) (22 + 3)(2 + 4)
(d) (3 + 1)(3 - 1)
(e) (2 + 5)(2 - 5)
(h) (8 + 2)(8 + 1)
(n) (5 - 23)2
Simplify:
Simplify:
82  12
Expand and simplify:
Homework 13 (Covering BF 1.4 and BF3.7)
Express each of the following with a rational denominator.
(a)
1
(b)
1
2
(d )
3
20
(e)
2
5
3
( h)
3 2
4
(f)
2 5
8
(g)
1
(c )
5 2
2 3
1
(i )
3 2
50
Homework 14 (Covering BF4.1)
1.
2.
3.
For each set of numbers below, calculate : i) the range;
(a) 5
7
3
8
8
5
(b) 23
53
21
34
87
64
3
ii) the mean.
9
For each set of numbers below, establish the median and state the mode:
(a) 2
3
3
3
4
4
(b) 32
45
33
17
22
54
5
7
7
8
8
Seven women have weights of 44kg , 51kg , 57kg , 63kg , 48kg , 49kg
and 45kg.
(a) Find the mean weight of the seven women.
(b) Find the mean weight of the remaining five women after the lightest
and the heaviest women leave.
Homework 15 (Covering BF4.1)
1.
A company manufactures boxes of tacks and claims that there are ‘on
average’ 60 tacks per box. This claim is tested by counting the number of
tacks in a sample of 100 boxes. The results are shown in the table below.
Number of
tacks
Frequency
57
7
58
13
59
21
60
24
61
19
62
12
63
4
Total
100
Number of tacks x
Frequency
(a) Copy and complete the above frequency table.
Find the mean number of tacks per box.
(b) Is the company claim reasonable?
You must give a reason for your answer.
2.
Copy the table and complete the cumulative frequency column.
Cats in
litter
6
7
8
9
10
11
f
2
3
4
6
3
1
Cum.
f
Homework 16 (Covering BF4.2)
1.
2.
a)
Use this information to draw a scattergraph.
b)
Draw a line of best fit.
Homework 16 (Covering BF4.4)
1.
The life-span (in months) of a sample of eleven lightbulbs is shown
below.
2
3
6
7
8
8
9
11
12
14
17
These results are now illustrated using a boxplot.
A
B
C
D
E
life-span (months)
Make a five-figure summary to find the values of A, B, C, D and E.
2.
The boxplot below shows the number of hours overtime worked in a
small factory in
a particular month.
10
20
hours overtime
(a)
What is the greatest and least number of overtime hours worked?
(b)
What is the median of this distribution?
(c) What percentage of the workforce completed between 8 and 17
hours overtime?
(d)
Calculate the range and the semi-interquartile range for this data.
Homework 17 (Covering BF4.5 and BF4.6)
1.
Bottles of juice should contain 50 millilitres.
The contents of seven bottles are checked in a random sample.
The actual volumes in millilitres are as shown below.
52
50
51
49
52
53
50
Calculate the mean and standard deviation of the sample.
2
The heights, in centimetres, of a sample of ten tomato plants were
recorded. The data gave the following summary totals:
 x  320
3
 x 2  11526
(a)
Calculate the mean and standard deviation, giving your answer
correct to 1-decimal place where necessary.
(b)
Another sample of ten plants has a mean height of 28cm and a
standard deviation of 6·3.
How does this second sample compare with the first?
A sample of twelve golf balls were artificially tested by rolling them
across a flat area. The distance travelled, in metres, by each ball, was
recorded. The data gave the following summary totals:
 x  48
 x 2  192  38
(a)
Calculate the mean and standard deviation, giving your answer
correct to 2-decimal places where necessary.
(b)
Another sample of twelve balls has a mean distance of 4·3m and a
standard deviation of 0·81.
How, with consistency in mind, does this second sample compare
with the first?
Homework 18 (Covering BF4.5, BF4.6 and BF4.7)
1.
Fifty people took part in a Health Promotion Campaign. They were
asked whether or not they smoked cigarettes. The following table
summarises the responses.
Smoker
Non
Smoker
Male
3
21
Female
8
18
What is the probability that a person chosen at random from this
group is:
(a) male;
(b) a smoker;
(c) a female who smokes?
2.
3.
Nine wooden balls, numbered one to nine, are placed in a bag.
A ball is removed from the bag.
What is the probability that this ball has a number more than seven?
The heights, in centimetres, of seven netball players are given below.
173
176
168
For this sample, calculate:
(a) the mean;
(b) the standard deviation.
166
170
180
171
Homework 19 (Covering BF5.1 and BF5.2)
1.
2.
State the order of rotational symmetry for each shape.
a)
b)
c)
d)
e)
f)
Copy and complete so that the shape has quarter turn symmetry about
the point O.
O
Homework 20 (Covering BF5.3)
1.
Give the coordinates of A’, B’, C’ and D’ which are the images of A(2, 3),
 4 
B(-3, 5), C(-5, -5) and D(1, 0) under the translation   .
 2
2.
Which of the following translations would result in a displacement
parallel to the x-axis?
0
3.
 1 
5
A=  
 3 
B=  
0
C=  
 1 
Copy the diagram below and show the image of the triangle PQR in the
4
translation   .
 5 
P
Q
R
4.
Using the diagram below write down the translations which translate:
A
D’
B’
C’
D
a) A onto A’;
A’
’
’
B
C
b) B onto B’;
c) C onto C’;
d) D onto D’.