Unit 2: Functions

Topic 2.3: Sketching Graphs Questions

Practice 20 exam-style questions for IB Math AA SL Topic 2.3. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Find2 marks

2026

Find the x-intercepts of the graph of y = (x − 2)(x + 4).

Markscheme and model answer locked

Unlock Question

2Find2 marks

2026

Find the x-intercepts of the graph of

y = (x - 2) (x + 4)

Markscheme and model answer locked

Unlock Question

3State1 mark

2026

State the y-intercept of the graph of

y = x^{2} - 5 x + 6

Markscheme and model answer locked

Unlock Question

4State1 mark

2026

State the y-intercept of the graph of y = x² − 5x + 6.

Markscheme and model answer locked

Unlock Question

5Find4 marks

2026

Consider y = (x − 1)(x − 5). (a) Find where the graph meets the axes. (b) Find the coordinates of the vertex.

Markscheme and model answer locked

Unlock Question

6Sketch3 marks

2021

Draw the curve

y = x^{3} - 12 x + 3

. Label where it crosses the

y

-axis and give the coordinates of both turning points.

Markscheme and model answer locked

Unlock Question

7Find4 marks

2026

Consider

y = (x - 1) (x - 5)

. (a) Find where the graph meets the axes. (b) Find the coordinates of the vertex.

Markscheme and model answer locked

Unlock Question

8Find3 marks

2026

Consider the quadratic

y = x^{2} - 6 x + 5

. (a) Find the x-intercepts. (b) State whether the parabola opens up or down.

Markscheme and model answer locked

Unlock Question

9Find3 marks

2026

The graph of

y = a (x - 2)^{2} - 3

has vertex (2, −3) and passes through (0, 1). (a) Write down the vertex. (b) Find the value of a.

Markscheme and model answer locked

Unlock Question

10Sketch4 marks

2021

Sketch the graph of

y = x^{3} - 4 x^{2} + x + 3

for

- 1.5 \leq x \leq 3.5

, labelling the local maximum, the local minimum and the

x

-intercepts.

Markscheme and model answer locked

Unlock Question

11Sketch2 marks

2026

Sketch the graph of

y = 2^{x}

for

- 3 \leq x \leq 3

, showing the

y

-intercept and the behaviour as

x \to - \infty

Markscheme and model answer locked

Unlock Question

12Sketch3 marks

2021

On the same axes, sketch the curves

y^{2} = 9 - 3 x

and

y^{2} = 1 + x

, labelling their

x

-intercepts.

Markscheme and model answer locked

Unlock Question

13Sketch3 marks

2026

Consider the function h(x) = e^−x sin 3x, where 0 ≤ x ≤ π/3.

Sketch the graph of y = h(x), labelling the coordinates of the maximum point.

Markscheme and model answer locked

Unlock Question

14Sketch1 mark

2025

On axes covering

- 2.5 \leq x \leq 2.5

, draw the general shape of

y = x^{4} - 4 x^{2}

Markscheme and model answer locked

Unlock Question

15Find3 marks

2026

The graph of y = a(x − 2)² − 3 has vertex (2, −3) and passes through (0, 1). (a) Write down the vertex. (b) Find the value of a.

Markscheme and model answer locked

Unlock Question

16Sketch3 marks

2021

On a set of axes, draw the curve

y = 4 x - x^{2}

, labelling the points where it meets the

x

-axis and the coordinates of its highest point.

Markscheme and model answer locked

Unlock Question

17Write down2 marks

2026

For the graph of

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

, write down (a) the vertical asymptote and (b) the horizontal asymptote.

Markscheme and model answer locked

Unlock Question

18State2 marks

2026

For a sketch of

y = 2^{x}

, state (a) the y-intercept and (b) the equation of the horizontal asymptote.

Markscheme and model answer locked

Unlock Question

19State2 marks

2026

For a sketch of y = 2ˣ, state (a) the y-intercept and (b) the equation of the horizontal asymptote.

Markscheme and model answer locked

Unlock Question

20Sketch1 mark

2025

On axes covering

- 6 \leq x \leq 6

, draw the general shape of

y = \frac{x ^{3}}{x ^{2} + 4}

Markscheme and model answer locked

Unlock Question

Ready to practice Topic 2.3?

Get instant AI feedback on your answers, view detailed markschemes, and track your progress across all IB Math AA SL topics.

Start Practising Now Math AA SL Study Hub