New

Year 10

Higher

Drawing exponential graphs

I can generate coordinate pairs for an exponential graph from its equation and then draw the graph.

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New

Year 10

Higher

Drawing exponential graphs

I can generate coordinate pairs for an exponential graph from its equation and then draw the graph.

Download all resources

Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

A table of values can be useful to identify coordinate pairs which satisfy the equation.
By substituting the values for x, you can calculate corresponding values for y.
If used correctly, your calculator can be a powerful tool to speed up calculations.

Keywords

Exponential - The general form for an exponential equation is $y = a b^{x}$ where $a$ is the coefficient, $b$ is the base and $x$ is the exponent.

Common misconception

$y = 2^{x}$ evaluates to $0$ when $x = 0$

Remind pupils of the laws of indices that can be used to show that $b^{0} = 1$

To help you plan your year 10 maths lesson on: Drawing exponential graphs, download all teaching resources for free and adapt to suit your pupils' needs...

Making connections is really powerful when learning mathematics.

2^{(- 1)} = 1 o v e r 2^{(1)} = 1 o v e r 2

and

2^{(- 2)} = 1 o v e r 2^{(2)} = 1 o v e r 4

is utilising pupils' knowledge of indices.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Worksheet

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Starter quiz

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6 Questions

Q1.

Match each equation to its type of graph.

Correct Answer:

y = x^{2}

,quadratic curve

quadratic curve

Correct Answer:

y = x + 2

,linear

linear

Correct Answer:

y = x^{3}

,cubic curve

cubic curve

Correct Answer:

y = \frac{3}{x}

,reciprocal curve

reciprocal curve

Q2.

Given the equation

y = 3^{x}

. When

x = 2

then

y

= .

Correct Answer: 9

Q3.

Find the missing term in the geometric sequence: 0.2, , 5, 25, 125, ...

Correct Answer: 1, one

Q4.

Given the equation

y = 3^{x}

. Find the value of

y

when

x = - 1

- 1

- 3

0.3

Correct answer:

\frac{1}{3}

\frac{- 1}{3}

Q5.

Given the equation

y = 3 \times 2^{x}

. When

x = 4

then

y =

Correct Answer: 48

Q6.

Match each geometric sequence to its missing term.

Correct Answer:1, 2, 4,

◻

, 16, 32,8

Correct Answer:2, 6,

◻

, 54, 162,18

Correct Answer:3, 6, 12,

◻

, 48, 96,24

Correct Answer:1,

◻

, 36, 216, 1296,6

Correct Answer:3888, 648, 108, 18,

◻

Exit quiz

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6 Questions

Q1.

The general form for __________ equation is

y = a b^{x}

a constant

Correct answer: an exponential

a power

a quadratic

a reciprocal

Q2.

Select the coordinates that lie on the curve

y = 2^{x}

(0.5, 1)

Correct answer: (1, 2)

(2, 1)

Correct answer: (3, 8)

(0, 2)

Q3.

Match each curve to its equation.

Correct Answer:A,

y = 4^{x}

$y = 4^{x}$

Correct Answer:B,

y = 3^{x}

$y = 3^{x}$

Correct Answer:C,

y = 2^{x}

$y = 2^{x}$

Correct Answer:D,

y = 1^{x}

$y = 1^{x}$

Q4.

The table of values for the curve

y = 4^{x}

is shown. Which

y

value is incorrect?

\frac{1}{64}

\frac{1}{8}

Q5.

Jacob draws the graphs of

y = 2^{(} - x)

and

y = 2^{x}

on the same pair of axes. Which of these statements are correct.

Correct answer: The curves will intersect the

y

axis.

The curves will intersect the

x

axis.

The curves are symmetrical about the

x

axis.

Correct answer: The curves are symmetrical about the

y

axis.

Q6.

Which of these could be the equation of this curve?

y = 4^{x}

Correct answer:

y = - 4^{x}

y = 4^{- x}

y = - 4^{- x}

Drawing exponential graphs

Drawing exponential graphs

These resources will be removed by end of Summer Term 2025.

Slide deck

Lesson details

Key learning points

Keywords

Common misconception

How to plan a lesson using our resources

Licence

Lesson video

Worksheet

Starter quiz

6 Questions

Exit quiz

6 Questions