1) This document contains 6 math problems involving inequalities, percentages, geometry, and trigonometry. 2) Problem 2 asks to calculate the original price of a flat if it was sold for £43,650 and there was a 3% loss from the original price. 3) Problem 5 gives dimensions for a glass candle holder and asks to calculate its volume.

1. Fourth Level Block 2 Formal Homework 1
1. Solve the following inequalities:
(a) 5x – 2 < 2(7 + 4x) (b)
1
4
(𝑥 + 4) −
3
7
(𝑥 − 3) <
1
2
2. When Sarah sold her flat, she lost 3% of what she
originally paid for it.
She only got £43650 for her flat.
What must Sarah have paid for the flat when she
bought it?
3. (a) Construct a scattergraph for the set of data below :
Height(cm) 140 150 160 110 155 170 160 155 130 120
Weight(kg) 30 45 60 25 45 60 55 50 35 15
(b) Draw a line of best fit on your scattergraph.
(c) From your line of best fit, estimate the height of a girl
who weighs 20 kilograms.
4. The tangent SV touches the circle, centre O, at T.
Angle PTQ is 37° and angle VTR is 68°.
Calculate the size of angle PQR.

2. 5. Prove that one of the following IS a right angled triangle
and the other is NOT.

3. Fourth Level Block 2 Formal Homework 2
1. Put these numbers in order, smallest to largest:
4
80
0.02 3%
1
9
2. Simplify: 2(3x – 4) – (3x + 1) + 5(x – 3)
3. Neil has monthly gross pay of £2800.
He pays Income Tax - £548
National Insurance - £206
Pension – 6% of his gross pay.
Calculate Neil’s monthly net pay.
4. The hire purchase of this freezer is found by:
Calculate the hire purchase price and how much dearer it is
compared with the cash price.
How much fencing will he need?
5. Farmer Ryan wants to put a fence around his rectangular field.
15m
12m

4. Fourth Level Block 2 Formal Homework 3
3. Solve the following equations for x:
(a)
𝑥
3
−
𝑥
5
= 6 (b)
1
4
(3𝑡 − 2) =
1
3
(𝑡 − 1)
(b) Calculate the average speed ‘there and back’ to the nearest
km/hr.
5. Mrs Smith’s earing is in the shape of an isosceles triangle. It
is made out of plastic. Calculate the length of plastic needed
to make the earing.
1.
2.
Calculate: (a) (32
+ 3) x 3 – 5 (b) 2 x (42 ÷ 7 – 6)3
2M2 were asked what their favourite flavours of crisps were.
Flavour Number
Salt and Vinegar 14
Plain 2
Tomato 11
Chicken 9
This information has to be illustrated using a pie chart.
What size of angle would represent each flavour in the pie chart?
4. It is 5400km from Glasgow to New York.
BA 205 made the flight at an average speed of 800km/hr.
Because of a nose wind, it returned at an average speed of 750
km/hr.
(a) Calculate, in minutes, the difference in the times of the two
flights.
12cm
10cm

5. Fourth Level Block 2 Formal Homework 4
1. Calculate:
a) 5
5
6
𝑥 1
3
7
b) 2
4
5
+ 3
3
4
2. Write the following in number form:
(a) 4 x 103
(b) 3.67 x 10-5
(c) 2.7 x 106
(d) 9.07x10-2
3. Electricity prices have increased by 3.5%. Before the
increase my bill was £80 per month.
How much will my electricity bill be now?
4. Calculate the shaded area:
5. Fiona recorded the times it took 11 students to run 200
metres. The times are measured in seconds and are:
27, 38, 42, 35, 43, 49, 50, 37, 38, 41, 48
(a) Draw an ordered stem and leaf diagram to show this
information. (remember key & title!)
(b) Work out the median time.
(c) Work out the range of the times.
(d) How many students finished the run in under 40 seconds?

6. 4. This table shows the cost of hiring a lawn mower for several
days:
No of
days
(D)
1 2 3 4 5 6
Cost in
£ (C)
9 14 19 ? ? ?
a) Copy and complete the table.
b) Write down a formula for determining the cost of hiring the
lawn mower in the form
C = ? x D ___
c) How much will it cost to hire the lawn mower for a
fortnight?
d) Mrs Curley paid £54 to hire the lawn mower. For how many
days did she have it?

7. Fourth Level Block 2 Formal Homework 5
1. Work out the following without a calculator:
(a) 2
5
(b) 5
2
+ 8
3
– 7
2
(c) (-2)
4
(d) (-6)
3
(e) (f) √125
3
2. Write the following numbers in scientific notation:
(a) 231 (b) 0.00006 (c) 6.1 million (d) 0.004703
3. A sphere has a diameter of 8cm.
Calculate its volume giving your answer correct to 3 significant
figures.
How far is it round the island?
5. Calculate the distance between points A and B on the diagram.
6. Find the circumference of this circle:
4. It takes 42 minutes to cycle round an island at an average
speed of 23km/h.

8. Fourth Level Block 2 Formal Homework 6
1. Calculate:
(a)
3
2
5
5
3
7  (b)
7
2
4
3
1
3 
2. Find the volume of each shape below, using the appropriate
formula:
(a) (b)
3. Here is part of a French Railway timetable for a high speed
train.
(a) Calculate the journey time from Paris to Marseille.
(b) Find the speed of the train from Paris to Marseille.
Round your answer to the nearest kilometre per hour.
4. Rachel paid £8500 for a new bathroom.
She paid a 20% deposit and 40 equal payments.
How much was each payment?
Distance fom
Paris (Km)
0 Paris Depart 1644
512 Lyon Depart 1900
617 Valence Depart 1955
742 Avignon Depart 2051
863 Marseille Arrive 2144

9. 5. A glass candle holder is in the shape of a cuboid with a cone
removed. The cuboid measures 4cm by 4cm by 6cm.
The cone has a diameter of 3cm and a height of 5cm.
Calculate the volume of glass in the candle holder.

10. Fourth Level Block 2 Formal Homework 7
1. Round each number to (i) 1 significant figure (ii) 2 significant
figures
(a) 23500 (b) 4567 (c) 0.9372 (d) 0.0982
2. The weight of self-raising flour in making chocolate cakes
should be quite accurate. It is given as:
(255 ± 12.5)g
(a) What is the maximum permitted weight?
(b) What is the minimum permitted weight?
3. A car is travelling at an average speed of 68 km/h (excluding
stop time) over a distance of 221 km. If the car leaves at
0845 and stops at a service station for 30 minutes, what time
will it arrive at its destination?
4. A submarine, S, dives for 300 metres at an angle of 24° to the
surface.
Calculate the depth of the submarine as shown in the diagram.
Do not use a scale drawing.

11. 5. Shown is a pyramid with volume 126cm3
. Find the vertical
height, h.
6. Belfast has a leaning clock tower.
The leaning of the clock tower is shown
in the diagram.
Calculate the size of the
shaded angle.