Blue Course
Mathematics
Revision
G
BG1.1 Distance, Speed and Time
1. The rail distance from Manchester to Glasgow is 357km.
If a high speed train averages 140 km/h, find the time taken in hours and
minutes.
2. A yacht leaves Largs and sails a distance of 74km.
If the yacht averages a speed of 14km/h, calculate the time
taken for the journey correct to the nearest minute.
3. A car leaves Dumfries at 1.25pm and reaches Edinburgh at 2.53pm.
(a) How long did the journey take?
(b) If the distance travelled was 84 miles, calculate the
average speed of the car correct to the nearest mile
per hour.
BG1.2 Interpreting distance/time graphs
Mr Munro drove his car from Edinburgh to York and back.
The record of his journey is shown in the graph.
(a) He rested on his way to York.
For how long did he rest?
(b) Calculate his average speed
from York back to Edinburgh.
(c) Calculate his average speed
for the whole journey (do not
include the stops). Give your
answer correct to 1 d.p.
07 00 08 00 09 00 10 00 11 00 12 00 13 00 14 00 15 00
50
100
150
200
250
km
time
Edinburgh
York
BG2.3 Right angled trigonometry to calculate an angle
Find the size of the angle marked by x
1. 2.
3. 4.
BG2.1 and BG2.2 Right angled trigonometry to find a side
Find the size of the side marked by x
1. 2.
x°
12
8
x°
11
10
x°
3·2
5·1
x°
2·0 2·5
1·5
37°
17
x
56°
14
x
3. 4.
BG2.4 Right angled trigonometry in problems
1. John stands 10 metres from the base
of a tree.
He measures the angle of elevation
from his eye level to the top of the
tree as 57 °.
John’s eye level is 1·5 metres above
ground level.
Calculate the height of the tree.
2. The army are making a death slide.
The rope making the slide is 50
metres long and runs from the top of
a tower to the ground. The angle of
depression at the point which
attaches the rope to the top of the
tower is 32 degrees.
(a) Calculate the height of the tower.
(b) Calculate the distance from the base of the tower to the point at which the rope
is fixed to the ground.
32°
31°
x
7·3
12°
3·7 x
57°
1·5 metres
3. In the diagram, the angle of elevation from point A to the top of
the building at point T is 23 °.
The angle of elevation from point B to point T is 37 °.
The height of the tower (ST) is 200
metres.
Calculate the size of AB.
4. A boat travels 50 km east from Point S to Point T.
It then changes course on a bearing of
238° and travels until it is due south of
Point S.
How far has the boat travelled since leaving Point S?
S T
238°
North
A
B
T
S
23°
37°
BG3.3 Simple and Compound Interest
1. Paula invests £3400 in a Savings Account.
The interest rate is 4·7% per annum.
How much interest would Paula earn in 5 months?
2. Jorge buys a new house for £80 000. The value of the house depreciates by 8%
in the first year.
However it appreciates by 14% in the
second year. How much would his
house be worth at the end of the second
year?
3. Patrick buys £1400 of bonds which have a guaranteed return on investment of
5·3% per annum compounded for 4 years.
How much will the bonds be worth at the end of the fourth year?
4. Katie invested £550 on the stock exchange.
However her investment was not
a good one and her shares lost 8%
of their value every year for three
years.
How much was her investment
worth at the end of the third
year?
Free Spirit Card
1·4% commission on
all withdrawals
abroad.
Footloose Card
£2.40 charge for each
cash withdrawal
abroad.
BG3.4 Comparing and contrasting financial products
1. Look at the information below on two debit cards.
Joana withdraws £200 worth of dollars from a cash machine abroad.
Which card would charge the least for this transaction?
2. Two loan companies, Wonky Loans and Prudent Loans, advertise their
products as shown below.
Wonky Loans Loan amount Loan Period Total Repayable
£1000 3 months £1100.00
£1000 6 months £1210.00
£1000 9 months £1331.00
£1000 12 months £1464.10
Prudent Loans Interest on all loans 14.8% per annum
(£40 administration fee applicable for all loans)
Which company would be cheapest for a 12 month loan of £1000?
Justify your answer
3. Look at the mortgage charges described below.
Murray Bank Interest of 5·6% per annum, charge monthly on
outstanding balances.
Westwood Bank Interest of 4·25% per annum, charge monthly on
outstanding balances.
How much less interest would you pay per month on an outstanding balance
of £120 000 at the Westwood Bank?
4. The four pay monthly plans shown below each cost the same price.
Plan A Plan B Plan C Plan D
300 text 400 text 500 text 600 text
Unlimited calls 500 mins 300 mins 100 mins
750 Mb Data 500 Mb 500 Mb None included
John uses on average 450 texts, 230 mins of calls and 500Mb of data usage.
Which plan do you think would be best for him?
Justify your answer
BG3.1 and BG3.2 Bills, VAT, Percentage Profit and Loss
1. Kirsty looks at her bill for some car repairs.
Labour £223·00
Parts £50·00
VAT @20% £56·40
Total £329·40
Is the bill correct? Justify your answer
2. Jack bought some buckets for £25 and sold them for £32.
Jill bought some pots for £56 and sold them for £67.
Who made the best percentage profit, jack or Jill?
3. A car manufacturer had a drop in sales last year.
Sales dropped from £60 million to
£54 million.
The same percentage drop is
predicated for this year. If the
prediction is correct, how much will
the sales be worth this year?
BG3.1 Insurance Premiums and Hire Purchase
1. Sara wants to insure a valuable watch.
She is told that the insurance premium will be £2·10 for every one hundred
pounds insured.
How much would the insurance premium be if the watch is valued at £3800?
2. Two shops, Sonic Power and Picture House, allow customers to buy goods on
Hire Purchase.
Kenny is planning to buy a new TV.
The two shops offer different payment plans.
Sonic Power - deposit of £60·50 then 12 payment of £15·80
Picture House - deposit of £25 then 12 payment of £18
Which shop do you think is best?
Justify your answer.
3. A shop offers interest free credit on computers.
The payment plan offered is a deposit of 35% with the balance being settled in
12 equal monthly payments.
John buys a computer priced a £499 using this payment plan.
Calculate John’s monthly payments.
BG4.1 to BG4.3 Perimeter and Area
1. The shape shown below
comprises of a semicircle and
an isosceles triangle.
(a) Calculate the height (h cm) of the isosceles triangle.
(b) Calculate the distance around the outside of the shape.
(c) Calculate the area of the whole shape.
BG4.4 and BG4.5 Sectors of a circle
1. Find the arc length and area of each sector
(a) (b)
2. The slice of pizza has an arc
length of 10 cm and a radius of
5cm
Calculate the area of the slice of
pizza.
8 cm
h cm 5 cm
50°
100°
6 cm
4 cm
BG4.7 and BG4.8 Volumes of shapes
1. This barrel is cylindrical in shape.
Calculate the volume of the barrel.
2. Find the volume of each of these two shapes.
(a) Sphere (b) Pyramid
3. The shape below consists of a cylinder and two hemispherical ends.
Find the volume of the shape.
75 cm
1·2 m
23 cm 5 cm
6 cm
4. A toy is made from a cone onto of a
hemisphere.
Calculate the volume of the toy.
5. A Chocolate tub is in the shape of a
truncated cone as shown in the
diagrams.
Calculate the volume of the tub.
6. A container for soup
is in the shape of a
prism as shown.
Calculate the volume
of the soup container
BG5.1 to BG5.4 Factorisation
1. Factorise
(a) 6𝑥2 + 8𝑥 (b) 3𝑎𝑥 + 6𝑎𝑦 + 9𝑎2 (c) 20𝑎2 − 16𝑎𝑏
2. Factorise
(a) 9𝑥2 − 16𝑦2 (b) 25𝑎2 − 4 (c) 𝑝4𝑞2 − 𝑟6
3. Factorise
(a) 𝑥2 + 𝑥 − 6 (b) 6𝑥2 + 11𝑥 + 3 (c) 2𝑥2 − 𝑥 − 3
(d) 6𝑥2 − 19𝑥 + 10 (b) 5𝑥2 + 13𝑥 − 6 (c) 4𝑥2 + 8𝑥 − 21
4. Factorise
(a) 3𝑥2 − 12𝑥 (b) 6𝑥2 − 18𝑥 + 12 (c) 𝑥3 − 𝑥𝑦2
(d) 15𝑥3 − 25𝑥2 − 10𝑥 (e) 6𝑥2 + 17𝑥𝑦 + 5𝑦2 (f) 𝑥4 − 2𝑥2 − 15