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