Shawlands Academy
Mathematics Department
S4 Credit Homework
S4 Credit Homework 1
1. Find the value of
(a) 1.36 + 1.7 x 4
(b) 2.61 x 300
(c) 35% of £260
3
(d) of £140
4
2.. Simplify the expression 5( 2n – 3r ) – 2( n – r )
3. (a) The diameter of a sodium atom is 0. 000 000 3 millimetres.
Write this in Scientific Notation.
(b) Loch Ness has volume 7.443 × 109 cubic metres. Write this
as an ordinary number.
4.. Expand the brackets and simplify ( 3a + 4)( 2a – 5 )
5.. The diagram opposite shows a toy box.
Calculate the volume of the toy box.
40 cm
30 cm
65 cm
90 cm
80 cm
S4 Credit Homework 2
1 3
1
1. Express as a single fraction 4 - of 2
2 4
3
2. (a) The marks of 7 pupils in an advanced higher maths exam were
71 66 45 88 69 90 75
Calculate the mean and standard deviation of these marks.
(b)
Another group of 7 pupils who sat the same exam had a mean of 78 and a standard
deviation of 3.2.
Make two comparisons of the marks of the two groups.
3. Solve the pair of equations
4x – 3y = 12
and
3x = 26 – 2y
4. The value of a boat decreased from £35 000 to £32 200 in one year.
(a) What was the percentage decrease?
(b) If the value of the boat continues to fall at this rate, what would its value be
after a further 3 years?
S4 Credit Homework 3
Non-calculator section:
5
 2 1
of  - 
9
 5 4
2
2. (a) Factorise x – 3x – 10
1. (a) Evaluate
(b) Hence simplify
x 2 - 3x - 10
2x 2 - 10x
Calculator section:
3. (a) The prices of a bag of sugar in 6 different shops are
84p
90p
83p
80p
82p
85p
Calculate the mean and standard deviation of these prices.
(b) In 6 different shops the same bag of sugar has a mean price of 87 pence and
a standard deviation of 5.2 pence.
Make two comparisons between the prices in the two sets of shops.
4. A multinational car making company made a loss of £2.55 x 108 in 2005.
Calculate the loss made by the company per minute.
Give your answer in Scientific Notation.
S4 Credit Homework 4
Non-Calculator section:
1. Evaluate 2 35 - 34 of 3 13
2. . Expand the brackets and simplify (2x – y)2 + 4xy
Calculator section:
3. In 2006 a painting was valued at £26000. One year later the painting had increased
in value to £29900. If the painting continues to increase in value at the same percentage
rate, calculate its expected value in 2012.
4. The diagram shows an arc,AB, of a circle with radius 25 cm.
A
The arc AB is also 25 cm long, calculate the size of angle x0.
25 cm
x0
25 cm
B
S4 Credit Homework 5
Non-Calculator section:
2
1. Express as a single fraction (1 23 ) - 2 12
2. P varies as the square of Q and inversely as R.
(a) Write down a formula connecting P, Q and R.
(b) If Q is trebled and R is halved, what effect will this have on P.
Calculator section:
3. The speed of light in a vacuum is approximately 2.998 x 108 metres per second.
How far does light travel in one year?
Give your answer in Scientific Notation.
A
30cm
4. A logo for a company is in the shape of a circle
with a horizontal top.
The radius OA of the circle is 20 cm and the
20cm
distance AB is 30 cm.
O
Calculate h, the height of the logo.
B
h
S4 Credit Homework 6
Non-Calculator :
1. (a) Evaluate 36 – 1.34 x 20
(c) Simplify (2x – y)(3x + y)
2. (a) Find the equation of the line shown opposite
(b) Does the point (-4,-4) lie on this line.
3. (a) Factorise fully 2x2 – 10x
(b) Hence simplify
2x 2 − 10 x
2 x 2 - 11x + 5
4. The average monthly temperature in a holiday resort was recorded.
Month
Temperature ( 0C )
Jan Feb Mar Apr May Jun Jul
8
11 11 14
16 21 26
Aug Sep Oct Nov Dec
28 22 14 12 9
Draw a suitable statistical diagram to illustrate the median and quartiles of this data.
5. H varies as the square of L and inversely as M.
(a)
(b)
Find a formula connecting H, L and M.
L is doubled and M is halved. What effect does this have on H?
S4 Credit Homework 7
Calculator :
1. In Astronomy, distances can be measured using different units.
For example
1 parsec = 3.08 x 1013 kilometres
1 Astronomical Unit = 1.49599 x 108 kilometres
Calculate the number of Astronomical Units in a parsec.
Write your answer in Scientific Notation.
2. Niruz earns £26 500 per annum. She agrees a pay deal with her employer which
will see her get a pay rise of 4.6% pa for each of the next 4 years.
Niruz has calculated that she will be earning more than £32 000 in
4 years time. Is she correct?
3. A factory building has volume 2640 m3. The crosssection of the building consists of a rectangle and a
4m
triangle.
Calculate the width of the building.
9m
20m
width
S4 Credit Homework 8
Non-calculator section:
1. Find the value of 4.18 – 15% of 22
2. (a) Expand the brackets and simplify (3x + 2)(2x – 1).
Calculator section:
3. A drinks container is in the shape of a cylinder with
radius 20 cm and height 50cm.
(a)
Calculate the volume of this container.
Give your answer correct to 2 significant figures.
( volume of cylinder = πr2h )
(b)
Liquid from this full container can fill 800 cups,
in the shape of cones, each of radius 3cm.
What will be the height of each cone?
2
(volume of cone = 13 π r h )
20 cm
50 cm
3 cm
S4 Credit Homework 9
Calculator:
1. (a) In the first 6 games of the season an American Football team
score the following numbers of points
17
24
38
12
21
26
Calculate the mean and standard deviation of these scores.
(b) In the next 6 games the same team had a mean score of 27 points
and a standard deviation of 2.8. Make two appropriate comments
comparing the scores in the first 6 games and the second 6 games.
2. A relationship between A and B is such that A varies inversely as the
cube of B.
When B is doubled, what is the effect on A?
3. A prism has a cross-section in the shape of
the sector of a circle, radius 14 cm.
Calculate the volume of this prism
0
1475
cm
S4 Credit Homework 10
Non-Calculator:
1. Evaluate 21.4 ÷ 4 + 0.172
2. Solve the equations 5g + 2h = 7
2g – 3h = 18
3. (a) Find the equation of the line opposite.
(b) The point (-14,u) lies on this line.
Find u.
4. (a) Expand the brackets and simplify (2x – 4)(x2 + 2x + 4)
(b) Solve 6x – 3 = 2 – 4(1 – x)
17 cm
S4 Credit Homework 11
Calculator:
1. (a) The costs of the same toaster in 7 different shops are given below.
Calculate the mean and standard deviation of these costs.
13
16
20
12
16
18
17
(b) Each shop decreases the cost of the toaster by £5.
Write down the mean and standard deviation of the costs now.
2. Jessica uses her credit card to buy a mobile phone costing £189.
She is charged interest at a rate of 2.6% per month. If she does
not repay any money calculate how much she will owe in
8 months time.
3.. The stem and leaf diagram below shows the marks of 20 pupils in a Maths test.
0
1
2
3
4
7
3
4
2
0
8
5
6
0
6
7
0
9
8
5
8
6
7
9
9
1 3 represents 13
n = 20
(a) Write down the modal mark
(b) Show the information in a boxplot.
O
4.. A piece of metal is in the shape of prism whose
cross-section is made from 2 sectors of circles
with radii as shown.
The depth of the metal is 30 mm.
40mm
1200
25mm
Calculate the volume of this piece of metal.
S4 Credit Homework 12
Non-calculator:
1. Evaluate
(a) 4.5 – 155 ÷ 50
(b) 35% of £15 000
2. (a) Expand the brackets and simplify
(c) ⅔ of £711
4 – (3x – 2)2.
(b) Solve the equation 3(2x – 4) + 5x = 2(4x – 3)
3. (a) Find the equation of the line shown opposite
(b) The point (9,m) lies on this line. Find m.
y
8
6
4
2
x
-5 -4 -3 -2 -1
-2
-4
-6
-8
1 2 3 4 5 6 7 8 9
S4 Credit Homework 13
Non-calculator :
1. Evaluate
(a) 4.6 – 27.6 ÷ 40
(b) 65 % of £144
2. Simplify
(a) 3(2x – 1) – (x – 4)
(c) ⅝ of £22
y
B(2,11)
(b) 4p – (2p – 3)2
3. (a) Find the equation of the line joining
the points A(-1,-4) and B(2,11).
(b) Find the coordinates of the points
where this line cuts the x and y axes.
x
A(-1,-4)
4. A group of teachers and pupils go to the theatre. There are 18 people in the group
altogether.
(a) Using x to represent the number of teachers in the group and y to represent the
number of pupils construct an equation in x and y.
Tickets cost £7 for teachers and £4 for pupils. The total cost of the tickets is £84.
(b) Construct a second equation in x and y.
(c) Find the number of pupils going to the theatre.
(d)
S4 Credit Homework 14
Non-Calculator:
1. Find (a) 21.3 – 4 x 3.45
(b) 27 ÷ 60
(c) ⅝ of £34
Calculator:
2. Calculate the simple interest on £540 at a rate of 6.2% per annum for
a period of 5 months.
3. A house valued at £85 000 in 1998 fell in value at a rate of 5% per annum for the
next two years before rising in value at a rate of 5% per annum for the following
two years. Find the value of the house in the year 2002.
4. A garden shed is shown opposite.
The cross-section of the shed is in
the shape of a rectangle and a
right-angled triangle.
If the volume of this shed is 200 m3,
find the width of the shed.
3m
5m
12 m
width
S4 Credit Homework 15
Non-Calculator:
1. Expand the brackets and simplify
(a) 5(x – 3) – 2(x – 5)
(b) (2a – 3c)2
2. Find the equation of the line below.
y
30
25
20
15
10
5
-30 -25 -20 -15 -10
-5
-5
x
5
10
15
20
25
30
35
-10
-15
-20
-25
-30
-35
3 Solve
(a) 3(2x – 4) > 6
(b) 4(2n + 1) = 5n – 5
4. A line has equation y = 3x – 4
(a) Copy and complete the table below.
x
y
3
-1
0
(b) Show this line on a graph.
(c) Write down the gradient of this line.
S4 Credit Homework 16
Calculator:
1. A computer costs £1200 cash. It can also be bought on credit at a deposit of 15% plus
monthly payments over 2 years of £49.95.
Find the difference between the cash price and the credit price.
2. The sector opposite has radius 18 cm.
Calculate its area.
18cm
200
3. The shape opposite has a cross-section in the
form of a rectangle and a semi-circle.
Calculate its volume.
4.2 m
14 m
6m
S4 Credit Homework 17
Non-Calculator:
1. Find (a) 21.4 – 8.6 ÷ 4
(b) 65% of £32
(c) 0.061 x 40
(d) ¾ of 18 kg
2. P = 2x2 – 3xy. Calculate P when x = -4 and y = -2
3. A line has equation y = 3x – 4.
(a)
Copy and complete the table below.
x
3
-1
y
Draw this line on a graph.
Write down the gradient of the line y = 3x – 4
1
(b)
(c)
(d)
4. Expand the brackets and simplify
(a) 5(2m – n) – 3(m + 2n)
(b) (x – 2)(x2 + 2x – 1)
S4 Credit Homework 18
Calculator :
1. (a) In a survey of 2400 people, 35% went abroad on holiday in 2005. How many people
went abroad in 2005?
(b) 12.5% of those who went abroad visited Florida. How many went to Florida?
2. The cross-section of the shape opposite
consists of a rectangle with semi-circular
ends.
Calculate the volume of this shape.
30 cm
16 cm
28 cm
3. A formula is given as
T=
u(u + 3v)
. Find T when u = 9 and v = 1.5
v2