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Coordinate Geometry · Paper 1 — Free Maths AI SL Practice Questions

1FoundationSAQ-SEquation of a straight line and slope-intercept form6 marksPaper 1~9 min

The graph below shows the cost,

C

dollars, of hiring a kayak for

t

hours. The relationship is linear.

(a)

Calculate the slope of the line. [2 marks]

(b)

Find the equation of the line in the form

C = mt + c

. [2 marks]

(c)

A competitor charges according to the model

C = 6t + 5

. Determine the number of hours for which both companies charge the same amount, and state which company is cheaper for a

4

-hour hire. [2 marks]

Solutions

2FoundationSAQ-SEquation of a straight line and slope-intercept form5 marksPaper 1~8 min

The graph below shows the amount of water,

W

litres, remaining in a tank after

t

minutes of draining. The relationship is linear.

(a)

Find the equation of the line in the form

W = mt + c

, showing all working. [3 marks]

(b)

State the value of

m

and explain its meaning in this context. [1 mark]

(c)

Determine the time at which the tank will be empty. State one assumption required for your answer to be valid. [2] > 5-mark version (if total must stay at 5): (a) Find the equation of the line in the form

W = mt + c

, showing all working. [3] (b) State the value of

m

and explain its meaning in this context. [1] (c) Determine the time at which the tank will be empty. [1 mark]

Solutions

3MasterySAQ-SEquation of a straight line and slope-intercept form7 marksPaper 1~11 min

A small business rents office space. The monthly rental cost,

C

dollars, is modelled by a linear function of the floor area,

A

square metres. For a floor area of

40\,\text{m}^2

, the monthly rental cost is USD 1200. For a floor area of

100\,\text{m}^2

, the monthly rental cost is USD 2400.

(a)

Show that the equation of the line relating

C

and

A

C = 20A + 400

. [3 marks]

(b)

Find the monthly rental cost for an office with a floor area of

75\,\text{m}^2

. [1 mark]

(c)

The business has a monthly rental budget of USD 2000. Determine the maximum floor area the business can rent, and comment on whether the

y

-intercept of the model has a meaningful interpretation in this context. [3 marks]

Solutions

4ChallengeSAQ-LEquation of a straight line and slope-intercept form7 marksPaper 1~11 min

A small aircraft is flying from airport A to airport B. An air traffic controller monitors the aircraft's position a radar screen. Distances are measured in km. At 14:00, the aircraft is at point

P(2,\,5)

. The aircraft flies in a straight line. At 14:12, the aircraft is at point

Q(8,\,17)

(a)

Determine the equation of the straight line representing the aircraft's flight path, giving your answer in the form

y = mx + c

. The aircraft continues along the same straight-line path. At 14:24, the aircraft reaches point

R

. [3 marks]

(b)

Determine the coordinates of point

R

. Airport B is located at point

B(k,\,61)

, and the aircraft's flight path passes directly over airport B at some time after 14:24. [2 marks]

(c)

(i) Determine the value of

k

. [1]
(ii) Hence, determine the time at which the aircraft flies directly over airport B. [2 marks]

Solutions

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