Unit 2: Functions

Topic 2.1: Linear Functions Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.1. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Show that1 mark

2026

Show that the lines are perpendicular.

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2Show that1 mark

2023

At every point

(x, y)

of a curve, the tangent is perpendicular to the line joining

(x, y)

(0, 3)

.

Show that

\frac{d y}{d x} = - \frac{x}{y - 3}

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3Write down1 mark

2026

A line has gradient 4 and y-intercept −7. Write down its equation in the form y = mx + c.

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4Find2 marks

2026

Find the gradient of a line perpendicular to

y = \frac{3}{4} x + 1

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5Choose1 mark

Two lines are perpendicular. What is true about their gradients?

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6Write down1 mark

2026

Write down the gradient of a line parallel to y = −2x + 9.

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7Find2 marks

2026

Find the gradient of the line passing through A(−1, 3) and B(2, 12).

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8Show that2 marks

2024

Points

B (2, - 1)

and

C (- 4, 2)

are given.

Show that the line through

B

and

C

has equation

y = - \frac{1}{2} x

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9Find2 marks

2026

Find the gradient of the line passing through

A (- 1, 3)

and

B (2, 12)

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10Show that1 mark

2026

Show that its gradient is

- \frac{3}{4}

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11Write down1 mark

2026

Write down the gradient of a line parallel to

y = - 2 x + 9

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12Write down1 mark

2026

Write down the coordinates of the midpoint of

PQ

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13Choose1 mark

A line has gradient

\frac{2}{5}

. What is the gradient of any line at right angles to it?

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14Write down1 mark

2023

A general point

P (x, y)

is joined to the fixed point

(1, 2)

by a straight line.

State the slope of this line as an expression in

x

and

y

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15Write down1 mark

2026

A line has gradient 4 and y-intercept −7. Write down its equation in the form

y = m x + c

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16Write down1 mark

2023

A line through the origin makes an angle

θ

with the positive

x

-axis, where

0 < θ < \frac{π}{2}

.

Write down the gradient of the line in terms of

θ

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17Find2 marks

2026

Find the gradient of a line perpendicular to y = (3/4)x + 1.

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18Write down2 marks

2025

A straight line has x-intercept 3 and y-intercept 2.

Write down the equation of the line in the form y = mx + c.

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19Write down2 marks

2025

A line crosses the x-axis at (−4, 0) and the y-axis at (0, 2).

Write down its equation in the form y = mx + c.

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20Show that1 mark

2023

At every point

(x, y)

of a curve, the tangent is perpendicular to the line joining

(x, y)

(2, 0)

.

Show that

\frac{d y}{d x} = - \frac{x - 2}{y}

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