Home › Worksheets › IGCSE Year 10 Math › Functions and Graphs Prepared by Mohsim Digital Education
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f(4) for f(x) = 2x + 3 is 11 and g(−3) for g(x) = x² is 9, so this Year 10 sheet opens by substituting into function rules. The key records a parabola graph and an x-intercept of (2, 0).
Key Takeaways
f(4) = 11 when f(x) = 2x + 3 (Q1).
g(−3) = 9 when g(x) = x² (Q2).
Q3 records a parabola as the quadratic graph.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
Given f(x) = 2x + 3, find f(4).
(a) 8 (b) 11 (c) 7 (d) 24
2.
Given g(x) = x², find g(-3).
(a) -9 (b) 6 (c) 9 (d) -6
3.
The graph of y = x² is called a what?
(a) straight line (b) cubic curve (c) parabola (d) hyperbola
4.
The line y = 2x - 4 crosses the x-axis at which point?
(a) (0, -4) (b) (4, 0) (c) (2, 0) (d) (-2, 0)
5.
The gradient of the line y = 3x + 1 is what?
(a) 3 (b) 1 (c) 4 (d) 13
6.
A function machine doubles a number then adds 3. What is the output for an input of 7?
(a) 17 (b) 20 (c) 10 (d) 14
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
If f(x) = 5x - 2, find f(3).
8.
If f(x) = x² + 1, find f(2).
9.
State the gradient and the y-intercept of the line y = 2x - 7.
10.
If f(x) = 3x, find the value of x such that f(x) = 18.
11.
A function is f(x) = x - 4. Find f(f(10)).
12.
State the coordinates of the turning point of the graph y = (x - 2)² + 3.
13.
The lines y = x + 1 and y = 2x - 1 intersect where x = what?
14.
Given g(x) = x², evaluate g(2) + g(3).
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
The cost in dollars of hiring a bike is C = 5 + 3h where h is the number of hours. Find the cost for 4 hours.
16.
The area of a circle is A = πr². Find A when r = 2, taking π = 3.14.
17.
A taxi charges a flat fee of 3 dollars plus 2 dollars per km. Write a formula for the cost C in terms of the distance d in km.
18.
A colony starts with 50 bacteria and its population doubles every hour. Find the population after 4 hours.
19.
The height of a projectile is h = 30t - 5t². Find its height after 2 seconds.
20.
A line has equation y = 3x - 2. Find the y-coordinate of the point on the line where x = 5.
Answer Key
1. b) 11
2. c) 9
3. c) parabola
4. c) (2, 0)
5. a) 3
6. a) 17
7. Refer to solution guide.
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11. Refer to solution guide.
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20. Refer to solution guide.
End of Worksheet
People Also Ask
What is f(4) when f(x) = 2x + 3?
11, option (b) in this worksheet (Q1).
What is g(−3) when g(x) = x²?
9, option (c) in this worksheet (Q2).
What shape is the graph of a quadratic?
A parabola, option (c) in this worksheet (Q3).