Formal Homeworks

1. Third Level Block 3 Formal Homework 1
1. Calculate:
(a) 196 – 23.76 (b) 389 x 42 (c) 45 ÷ 500
2. Solve the following equations:
(a) 5r + 14 = 31 (b) 4(3e – 1) = 20 (c) 3(2y – 1) = 5(y – 4)
3. Write down all the multiples of 8 between 35 and 70.
4. What is the highest common factor of 12 and 32.
5. A circle has a radius of 18cm.
Calculate its: (a) circumference
(b) area
6. Grandpa Jim, his son Joe and his two grandchildren go the
circus.
They can either pay normal fare where Grandpa gets a
concession ticket, or take up the special offer.
Which is the better deal and by how much?

2. Third Level Block 3 Formal Homework 2
1. Find:
(a)
3
5
of £80 (b) 2% of £1200 (c) 75% of £4000
2. Simplify the following ratios:
(a) 3:9 (b) 16:24 (c) 50:75 (d) 180:40
3. Copy and complete the following square so that each row and
column add up to the same number.
4. An amusement arcade has a lighting effect in the shape of
triangles with coloured lights attached.
The lighting effect can be assembled in sections as shown below.
(a) Copy and complete the table below.
(b) Write down a formula for calculating the number of
coloured lights (c) when you know the number of sections
(s).
(c) The amusement arcade’s lighting effect uses 116 coloured
lights.
How many sections are in the lighting effect ?

3. 5. 3 speed cyclists set off together round a
Circular speedway track.
● Lewis can complete a lap in 20 seconds.
● Jodie can complete a lap in 25 seconds.
● Marc can complete a lap in 30 seconds.
How many seconds will it take for all 3 cyclists to pass the
starting line at the same time ?

4. Third Level Block 3 Formal Homework 3
1. For a=3 b=5 c=-2, find the value of:
(a) 2a + 5b (b) b2
– c (c) 2c2
+2(3a – b)
2. Find the highest common factor of 24 and 40.
3. A website shows some extreme temperatures
recorded on Earth.
The highest temperature recorded was 58°C
in Libya in 1922.
The lowest temperature recorded was - 64°C
in Siberia in 1973.
Find the difference between these two temperatures.
4. Put these numbers in order, smallest to largest:
80%
1
4
0.23 0.71 5%
3
5
5. In chemistry a certain family of related substances called
Alkanes exist. Alkanes consist entirely of Hydrogen and
Carbon atoms which are connected together in a certain
pattern.
The diagrams show the first three alkanes.
1 2 3
The first alkane has 1 carbon atom and 4 hydrogen atoms.
The second alkane has 2 carbon atoms and 6 hydrogen atoms.
The third alkane has 3 carbon atoms and 8 hydrogen atoms.

5. (a) Copy and complete the following table.
(b) Write down the formula which connects C and H.
(c) If there were 250 Carbon atoms, use your formula to calculate
the number of hydrogen atoms.
(d) If there were 992 Hydrogen atoms, use your formula to calculate
the number of Carbon atoms.

6. Third Level Block 3 Formal Homework 4
1. Find :
(a) 2 x 4 + 5 (b)
1
2
(
1
2
+
1
4
) (c) 12 + 5(4 – 1)
2. Write 72 as a product of prime factors. (Show all working)
3. Copy the diagram below and fill in the sizes of as many angles as
you can.
4. The diagram shows a rectangular steel plate with five holes,
each with a radius of 4cm, drilled through it.
Calculate the shaded area.
5. A luxury cruiser has a maximum speed of 28 km/h.
(a) How far can the boat sail in 34
1
hours at top speed?
(b) On a journey from one island to another the cruiser has
to navigate between two reefs, breaking the crossing into
three stages.
Stage 1 : 2 hours at half-speed.
Stage 2 : 42
1
hours at full speed.
Stage 3 : 3 hours at one-quarter speed.
Calculate the total distance travelled on the journey.

7. Third Level Block 3 Formal Homework 5
1. (a) Change 1.2 cm into millimetres.
(b) Change 3.25 km into metres.
(c) Change 5 cm into metres.
(d) Change 2624 mm into kilometres.
2. What is the 3-figure bearing of South-West?
3. Write 84 as a product of prime factors. (Show all working)
4. A group of S3 pupils produced the following set of Bleep Test
results in PE before they started the National 5 course.
58, 36, 31, 24, 67, 61, 30, 55, 46, 52, 38, 51, 36, 45,
41, 50, 47
(a) Construct an ordered stem and leaf diagram on the grid below
to illustrate the data.
(b) Find the median of the data.
5. The garden drawn has been drawn to scale.
The scale is 1cm = 60cm.
Calculate the perimeter of the garden.
6. The volume of a cuboid is 400cm3
.
If the length is 10cm and breadth is 4cm, calculate the height
of the cuboid.

8. Third Level Block 3 Formal Homework 6
1. Evaluate the following:
(a) 62
(b) 23
(c) 122
(d) 30
(e) √49 (f) √400 (g) √64
3
2. The cost of 4 books is £48.40.
Calculate the cost of 3 books.
3. Copy each of the following diagrams and fill in the missing
angles:
4. Write down a formula connecting X and Y.
5. The Triangle Pizza Co packages its pizzas in
boxes made from this net.
Measurements are given correct to 1 decimal place where
necessary.

9. (a) What is the mathematical name for the 3D shape which
can be made from this net?
(b) Use the diagram to calculate the area of card needed to make
this box. [Ignore any overlaps]

10. Third Level Block 3 Formal Homework 7
1. Write each of the following as a percentage:
(a) 0.45 (b) 0.04 (c)
19
100
(d)
13
20
2. This spinner is used in a game.
What is the probability of getting
(a) a 6 (b) a number greater than 5
(c) a multiple of 3 (d) a factor of 8
3. Copy and complete the pattern so that it has turn symmetry of
order 4.
4. The probability of choosing a page from a newspaper with no
adverts in it is known to be 0.18.
If there are 45 pages in this newspaper, how many pages don’t
have any adverts?
5.