Robinson Tuition
Grade 7 · Higher · free GCSE maths worksheet

Exponential graphs

Recognising y = a^x.

10 original questions, 23 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

Here is a table of values for y = 2x.

x−2−10123
y
  1. Complete the table.
  2. What happens to y as x gets more and more negative?
2 marks
Show answer
a) 1/4, 1/2, 1, 2, 4, 8 b) y gets closer to 0 but never reaches 0
2

Write down the coordinates of the point where the graph of y = 4x crosses the y-axis.

1 mark
Show answer
(0, 1)
3

Here are four equations.

A: y = 3 × 1.2x    B: y = 5 × 0.8x    C: y = 0.5 × 4x    D: y = 2 × (⅓)x

Which of the graphs show exponential decay (the curve goes down as x increases)? Give a reason.

2 marks
Show answer
B and D
4

Complete the table of values for y = 3x

x−10123
y13

2 marks
Show answer
x = -1) 1/3 x = 2) 9 x = 3) 27
5

Lena says, “The graph of y = 3 × 2x goes through the point (2, 36), because 3 × 2 = 6 and 62 = 36.”

Lena is wrong. Explain her mistake and work out the correct y-value when x = 2.

2 marks
Show answer
She squared the 3 as well: the power applies only to the 2. Correct y = 3 x 22 = 12
6

The graph of y = kx, where k is a positive constant, passes through the point (3, 125).

Find the value of k.

2 marks
Show answer
k = 5
7

The table shows some values on a curve with equation y = abx.

x0123
y61854162
  1. Find the values of a and b.
  2. Work out the value of y when x = 5.
3 marks
Show answer
a) a = 6, b = 3 b) 1458
8

The curve y = abx, where b > 0, passes through the points (0, 7) and (2, 63).

Find the value of a and the value of b.

2 marks
Show answer
a) 7 b) 3
9

The curve y = abx, where b > 0, passes through the points (1, 24) and (3, 6).

Find the value of a and the value of b. Is the curve growth or decay?

3 marks
Show answer
a) 48 b) 1/2 type) decay
10

The value, £V, of a car after t years is given by V = 14 000 × 0.85t

  1. Work out the value of the car after 2 years.
  2. What do the numbers 14 000 and 0.85 tell you about the car?
  3. After how many whole years does the value first fall below £7000?
4 marks
Show answer
a) £10 115 b) starting value £14 000; value falls by 15% each year (multiplied by 0.85) c) 5 years

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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