Year 11 Maths A Revision - Term 2 2015

Trigonometry

100

The 2 sides of a right angled triangle are 6cm and 12cm. What is the hypotenuse?

13.42cm

200

There is a pair of similar triangles. One triangle has a base of 1.26m and a perpendicular height of 1.8m. The other triangle has a base of 3.92m. What is its perpendicular height?

5.6m

300

A wall frame 3.4m long and 2.1m high is to have a diagonal brace fitted. How long must the brace be?

4m

400

Draw a right angled triangle with a base of 12cm and x as the perpendicular height. The angle between the base and the hypotenuse is 40 degrees. What is the height of x (perpendicular height)?

tan 40 degrees = x/12 x = 12 tan 40 degrees Perpendicular height (x) = 10.1cm

500

A ship sails due north for 120km then turns and sails due east for 180km. How far is the boat now directly from its starting position? Draw a diagram to help you.

x squared = 120 squared + 180 squared x = 216.3 km The boat is now directly 216.3km from its starting position.

Trigonometry

100

The two sides of a right angled triangle are 10m and 15m. What is the hypotenuse?

11.18m

200

If angle 'A' is the right angle of a triangle, what side is 'a'?

Hypotenuse

300

A shadow stick of 3m casts a shadow of 2.4m. At the same time, a building casts a shadow of 18m. What is the height of the building?

22.5m

400

Draw a right angled triangle with 14m as the hypotenuse and x as the perpendicular height. The base is unknown. The angle between the top of the hypotenuse and the top of the perpendicular height is 42 degrees. Find the perpendicular height (x).

cos 42 degrees = x/14 x = 14 cos 42 degrees x = 10.4m

500

Ben is standing 120m from the base of a building. He looks up to the top of the building at an angle of elevation of 36 degrees. How high is the building? Draw a diagram to help you.

Triangle 120m as the base and angle betwen base and hypotenuse is 36 degrees. tan 36 degrees = x/120 x = 120 tan 36 degrees x = 87.2m The building is 87.2m high

Managing Money

100

Mary earns $839.80 for working a 38 hour week. What is her hourly rate of pay?

$22.10

200

Riley is paid on a commission only basis according to his monthly sales. His commission is 0.75% of total sales. If Riley's sales for May were $65 000, how much does he receive in commission?

$487.50

300

Normal hours for a work week are 38 hours. Overtime is paid at time and a quarter. If Josh works 38 normal hours and 3 hours overtime, calculate his gross weekly pay if his hourly rate is $18.50. Give your answer in real terms ie round to nearest five cents.

38 x 18.50 = $703 3 x 18.50 x 1.25 = $69.375 $772.38 Therefore $772.40

400

Sharni's gross weekly pay is $819. She worked 38 normal hours and 2 hours overtime at double time. What is Sharni's hourly rate?

(38x) + (2 x 2 x x) = 819 38x + 4x = 819 42x = 819 x = $19.5 Hourly rate is $19.50

500

Sarah is paid on a commission + retainer basis. She is paid a retainer of $120 per week and 1.3% of sales in excess of $1500. In this particular week she makes $4400 in sales. Calculate Sarah's gross weekly pay.

$120 + 1.3% x (4400 - 1500) $120 + $37.70 $157.70

Managing Money

100

Jo earns $602.30 for working a 38 hour week. What is her hourly rate?

$15.85

200

Richard is a salesperson paid a weekly retainer of $115 plus a percentage of his sales. Richard receives 0.9% of sales. Richard is paid fortnightly. If in a fortnight Richard makes $36 000 in sales, calculate his gross fortnightly pay.

$115 x 2 = $230 Plus commission 0.009 of $36000 = $324 Gross fortnightly pay = $230 + $324 = $554

300

Normal hours for a work week are 38 hours. Overtime is paid at time and a half. If Christopher works 38 normal hours and 7 hours overtime, calculate his gross weekly pay if his hourly rate is $13.20. Give your answer in real terms ie round to nearest five cents.

38 x 13.20 = $501.60 7 x 13.20 x 1.5 = $138.60 Total is $640.20

400

Shane's gross weekly pay is $960.05. He worked 38 normal hours and 5 hours overtime at time and a half. What is Shane's hourly rate?

38x + 5 x 1.5 x x = 960.05 38x + 7.5x = 960.05 45.5x = 960.05 x = $21.10 Hourly rate is $21.10

500

John is paid on a commission + retainer basis. He is paid a retainer of $85 per week and 4.5% of sales in excess of $1000. In this particular week he makes $5800 in sales. Calculate John's gross weekly pay.

$85 + 4.5% x (5800 - 1000) $85 + $216 $301

Scale

100

A map has a scale of 1:200 000. 10cm on the map would represent how many kilometres in real terms?

20km (200 000 x 10) / 100 000

200

A map has a scale of 1:50 000. 8cm on the map would represent how many kilometres in real terms?

50 000 x 8 = 400 000cm 400 000 / 100 000 = 4km

300

The scale of a model aeroplane is 1:250. The real aeroplane has a wing span of 40m. What is the wing span of the aeroplane on the model?

40m is 4000cm 4000 / 250 = 16cm 16cm is the wingspan of the model

400

The scale of a model aeroplane is 1:200. If the length of the model aeroplane is 300mm, what is the length of the 'real' aeroplane?

200 * 300 = 60 000mm 60 000 / 1000 = 60m 60m is the length of the real aeroplane

500

If the area of the footings of a building were 12 square metres and the depth of the footings were to be 500mm, calculate how much it would cost for concrete for the footings if concrete is $250 a cubic metre?

Volume = area of footings x depth 12 x 0.5 = 6 cubic metres Concrete is $250 x 6 = $1500 is the cost of concrete