O Level Elementary Mathematics Algebra Functions Quiz

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O-Level Elementary Mathematics Quiz - Algebra Functions

Name: ___________________________
Class: ___________________________
Date: ___________________________
Score: _______ / 40

Duration: 50 minutes
Total Marks: 40
Topic: Algebra Functions (N6: Functions and Graphs; N5/N7 support)

Instructions:

• Answer all 20 questions.
• Show your working clearly where space is provided.
• Use the given answer spaces.
• Calculators may be used.

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Section A: Basic Function Notation and Evaluation (Questions 1–5)

1. [2 marks] Given $f(x) = 3x - 4$, find $f(5)$.

Answer: ___________

2. [2 marks] Given $g(x) = x^2 + 2x$, find $g(-3)$.

Answer: ___________

3. [2 marks] A function is defined by $h(x) = \frac{10}{x}$, where $x \neq 0$. Find $h(2)$.

Answer: ___________

4. [2 marks] The function $p(x) = 5 - x$ is given. Find the value of $x$ for which $p(x) = 0$.

Answer: ___________

5. [2 marks] Given $f(x) = 2x + 1$, find $f(a+1)$ in terms of $a$.

Answer: ___________

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Section B: Graphs of Linear and Quadratic Functions (Questions 6–10)

6. [2 marks] For the linear function $y = 2x + 3$, state the gradient and the y-intercept.

Gradient: ___________
y-intercept: ___________

7. [2 marks] Sketch the graph of $y = 4 - x$ on the grid below. Mark the x-intercept and y-intercept.

Image pending generation: graph for Q7.

8. [2 marks] The quadratic function $y = x^2 - 4$ crosses the x-axis at two points. Find the x-intercepts.

Answer: ___________

9. [2 marks] For the quadratic function $y = (x-1)^2 + 2$, state the coordinates of its minimum point.

Answer: ___________

10. [2 marks] Given the graph of $y = f(x)$ below, write down the value of $f(2)$.

Image pending generation: graph for Q10.

Answer: ___________

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Section C: Function Forms, Gradient, and Simple Modelling (Questions 11–15)

11. [2 marks] A power function is given as $y = 2x^3$. Find the value of $y$ when $x = 2$.

Answer: ___________

12. [2 marks] The exponential function $y = 3 \times 2^x$ is given. Find $y$ when $x = 3$.

Answer: ___________

13. [2 marks] Find the gradient of the line passing through the points $(1, 2)$ and $(4, 11)$.

Answer: ___________

14. [2 marks] The function $y = ax + b$ passes through $(0, -2)$ and $(2, 4)$. Find $a$ and $b$.

$a =$ ___________
$b =$ ___________

15. [2 marks] A taxi fare is modelled by $C(d) = 3.50 + 0.80d$, where $d$ is distance in km. Find the fare for 10 km.

Answer: $ ___________

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Section D: Extended Function Reasoning (Questions 16–20)

16. [2 marks] Given $f(x) = x^2$ and $g(x) = x + 1$, find $f(g(2))$.

Answer: ___________

17. [3 marks] A quadratic function has the form $y = x^2 + bx + c$. It passes through $(0, 3)$ and $(1, 6)$. Find $b$ and $c$.

$b =$ ___________
$c =$ ___________

18. [3 marks] The graph of $y = -x^2 + 4x$ has a maximum point. Find the x-coordinate of the maximum point by completing the square or using symmetry. Show your working.

Working:

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Answer: ___________

19. [3 marks] The function $y = ka^x$ passes through $(0, 5)$ and $(1, 15)$. Find $k$ and $a$.

$k =$ ___________
$a =$ ___________

20. [3 marks] The cost of producing $n$ items is given by $C(n) = 50 + 4n$. The revenue from selling $n$ items is $R(n) = 9n$. Form an expression for the profit $P(n)$ and find the profit when $n = 20$.

Working:

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Answer: $ ___________

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O-Level Elementary Mathematics Quiz - Algebra Functions (Answer Key)

Topic: Algebra Functions
Total Marks: 40
Level: O-Level Elementary Mathematics

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Section A: Basic Function Notation and Evaluation

1. [2 marks]
Given $f(x) = 3x - 4$, find $f(5)$.

• Substitute $x = 5$: $f(5) = 3(5) - 4 = 15 - 4 = 11$.
  Answer: 11
  Teaching note: A function $f(x)$ means "replace x with the given number". Common mistake: forgetting to multiply before subtracting.

2. [2 marks]
Given $g(x) = x^2 + 2x$, find $g(-3)$.

• $g(-3) = (-3)^2 + 2(-3) = 9 - 6 = 3$.
  Answer: 3
  Teaching note: $(-3)^2 = 9$, not $-9$. Squaring a negative gives positive.

3. [2 marks]
$h(x) = \frac{10}{x}$, find $h(2)$.

• $h(2) = \frac{10}{2} = 5$.
  Answer: 5

4. [2 marks]
$p(x) = 5 - x$, find $x$ when $p(x) = 0$.

• $5 - x = 0 \Rightarrow x = 5$.
  Answer: 5
  Marking: 1 mark for equation, 1 mark for solution.

5. [2 marks]
$f(x) = 2x + 1$, find $f(a+1)$.

• $f(a+1) = 2(a+1) + 1 = 2a + 2 + 1 = 2a + 3$.
  Answer: $2a + 3$
  Teaching note: Replace every x with $(a+1)$ inside brackets.

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Section B: Graphs of Linear and Quadratic Functions

6. [2 marks]
$y = 2x + 3$: gradient = 2, y-intercept = 3.
Answer: Gradient 2, y-intercept 3
Teaching note: For $y = mx + c$, $m$ is gradient, $c$ is y-intercept.

7. [2 marks]
Sketch $y = 4 - x$: line through $(0,4)$ and $(4,0)$.
Answer: Correct straight line with both intercepts labelled.
Marking: 1 mark line, 1 mark intercepts.

8. [2 marks]
$y = x^2 - 4 = 0 \Rightarrow x^2 = 4 \Rightarrow x = 2$ or $x = -2$.
Answer: $x = 2, -2$

9. [2 marks]
$y = (x-1)^2 + 2$: minimum at $(1, 2)$.
Answer: $(1, 2)$
Teaching note: Vertex form $(x-h)^2 + k$ has minimum at $(h,k)$.

10. [2 marks]
From graph through $(0,1)$ and $(3,7)$, at $x=2$, $y=5$.
Answer: 5

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Section C: Function Forms, Gradient, and Simple Modelling

11. [2 marks]
$y = 2x^3$, $x=2 \Rightarrow y = 2(8) = 16$.
Answer: 16

12. [2 marks]
$y = 3 \times 2^x$, $x=3 \Rightarrow y = 3 \times 8 = 24$.
Answer: 24

13. [2 marks]
Gradient = $\frac{11-2}{4-1} = \frac{9}{3} = 3$.
Answer: 3

14. [2 marks]
Through $(0,-2) \Rightarrow b = -2$. Through $(2,4): 4 = 2a - 2 \Rightarrow a = 3$.
Answer: $a=3, b=-2$

15. [2 marks]
$C(10) = 3.50 + 0.80(10) = 3.50 + 8 = 11.50$.
Answer: $11.50

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Section D: Extended Function Reasoning

16. [2 marks]
$g(2) = 3$, $f(3) = 3^2 = 9$.
Answer: 9

17. [3 marks]
Pass (0,3): $c = 3$. Pass (1,6): $1 + b + 3 = 6 \Rightarrow b = 2$.
Answer: $b=2, c=3$ (1 mark each + 1 for method)

18. [3 marks]
$y = -x^2 + 4x = -(x^2 - 4x) = -(x-2)^2 + 4$. Max at $x=2$.
Answer: 2
Marking: 2 marks working, 1 mark answer.

19. [3 marks]
$(0,5): k=5$. $(1,15): 5a=15 \Rightarrow a=3$.
Answer: $k=5, a=3$

20. [3 marks]
$P(n) = R(n) - C(n) = 9n - (50 + 4n) = 5n - 50$.
$P(20) = 5(20) - 50 = 50$.
Answer: $P(n)=5n-50$, profit $50
Marking: 1 expression, 2 substitution/answer.