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Graphs of Functions Practice Problems with Solutions - IGCSE Year 9

IGCSE Year 9 | Math | Graphs of Functions
Name: _________________________ Date: _________________________ Score: _______ / 40

The graph of y = x + 2 is a straight line and the gradient of y = 3x − 1 is 3, so this Year 9 sheet begins by reading lines from their equations. The key also names a parabola for quadratic graphs and 0 for a horizontal gradient.

Key Takeaways

Section A: Multiple Choice Questions (1 Mark Each)

Choose the correct option for each question.
1. The graph of y = x + 2 is a
(a) Curve(b) Straight line(c) Circle(d) Parabola
2. The gradient of the line y = 3x - 1 is
(a) 1(b) 3(c) -1(d) 2
3. The y-intercept of the line y = 2x + 5 is
(a) 2(b) 5(c) -5(d) 10
4. The graph of y = x² is a
(a) Straight line(b) Parabola(c) Circle(d) Rectangle
5. At the point where a line crosses the x-axis, the value of y is
(a) 0(b) 1(c) x(d) Never zero
6. The gradient of the line joining (0, 0) and (2, 6) is
(a) 2(b) 3(c) 6(d) 1/3

Section B: Short Answer Type Questions (2 Marks Each)

Show all steps clearly.
7. In the equation y = mx + c, state what m and c represent.
8. Find the gradient of the line y = 5x - 2.
9. Find the y-intercept of the line y = 3x + 7.
10. Write the equation of the horizontal line passing through (0, 4).
11. What shape is the graph of y = x²?
12. Find the gradient of the line passing through (1, 2) and (3, 8).
13. Write the equation of the line passing through the origin with gradient 2.
14. At what point does the line y = x + 3 cross the y-axis?

Section C: Numericals & Word Problems (3 Marks Each)

Apply the concepts to solve the problems. Show all working.
15. Find the gradient and the y-intercept of the line y = 4x - 3.
16. A line has gradient 2 and passes through (0, 5). Write its equation.
17. Plot the graph of y = x + 1 for values of x from 0 to 3.
18. Find the point where the line y = 2x - 4 crosses the x-axis.
19. The cost C of hiring a taxi is given by C = 15 + 10d, where d is the distance in km. State the gradient and what it represents.
20. A line passes through (0, 1) and (2, 5). Find its equation.

Answer Key

1. b) Straight line
2. b) 3
3. b) 5
4. b) Parabola
5. a) 0
6. b) 3
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet

People Also Ask

What shape is the graph of y = x + 2?

A straight line, option (b) in this worksheet (Q1).

What is the gradient of y = 3x − 1?

3, option (b) in this worksheet (Q2).

What shape is a quadratic graph?

A parabola, option (b) in this worksheet (Q4).

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