O Level Elementary Mathematics Algebra Functions Quiz

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O-Level Elementary Mathematics Quiz - Algebra Functions

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

Duration: 60 minutes
Total Marks: 40

Instructions:

• Answer all 20 questions.
• Show your working clearly where required.
• Write your answers in the spaces provided.
• Use a calculator where appropriate.

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

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

Answer: ___________

2. [2 marks] The function $g(x) = x^2 + 2x$ is given. Find the value of $g(-3)$.

Answer: ___________

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

Answer: ___________

4. [2 marks] Let $f(x) = 2x + 1$ and $g(x) = x - 3$. Find $f(g(4))$.

Answer: ___________

5. [2 marks] The mapping shows $x \mapsto 2x + 5$. If the output is 17, what is the input value of $x$?

Answer: ___________

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

6. [2 marks] The linear function $y = 2x - 1$ is given. State the gradient of the line.

Answer: ___________

7. [2 marks] For the quadratic function $y = x^2 - 6x + 8$, find the $y$-intercept.

Answer: ___________

8. [2 marks] Sketch the graph of $y = x^2$ on the grid below. Label the vertex.

Image pending generation: graph for Q8.

Answer: (sketch in grid above)

9. [2 marks] The graph of $y = ax + b$ passes through $(0, 3)$ and $(2, 7)$. Find the value of $a$.

Answer: ___________

10. [2 marks] For the function $y = -x^2 + 4$, state the maximum value of $y$.

Answer: ___________

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Section C: Composite and Inverse Functions (Questions 11–15)

11. [2 marks] Given $f(x) = 4x$ and $g(x) = x + 2$, find $g(f(1))$.

Answer: ___________

12. [3 marks] The function $f(x) = 5x - 3$. (a) Find $f^{-1}(x)$. (b) Hence find $f^{-1}(7)$.

Answer: (a) ___________ (b) ___________

13. [2 marks] A function $h$ is defined by $h(x) = \frac{x}{2}$. Find $h^{-1}(6)$.

Answer: ___________

14. [2 marks] Given $f(x) = x^2$ for $x \geq 0$ and $g(x) = x + 1$, write an expression for $f(g(x))$.

Answer: ___________

15. [3 marks] The functions are $p(x) = 3x - 2$ and $q(x) = \frac{x}{3}$. (a) Find $p(q(x))$. (b) Find $q(p(x))$. (c) Are $p$ and $q$ inverse functions? Give a reason.

Answer: (a) ___________ (b) ___________ (c) ___________

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Section D: Word Problems and Applications (Questions 16–20)

16. [2 marks] A taxi fare is given by $C(d) = 3.50 + 0.80d$, where $d$ is distance in km. Find the fare for 10 km.

Answer: $___________

17. [3 marks] The height of a plant after $t$ weeks is modelled by $H(t) = 2t + 5$ cm. (a) Find $H(4)$. (b) After how many weeks will the plant reach 21 cm?

Answer: (a) ___________ (b) ___________

18. [2 marks] The function $P(n) = 100 \times 1.05^n$ gives the population of bacteria after $n$ hours. Find $P(2)$, correct to the nearest whole number.

Answer: ___________

19. [3 marks] A company's profit (in $000) is$y = -x^2 + 10x - 16$, where$x$is units sold in hundreds. (a) Find the profit when$x = 3$. (b) State the value of$x$ that gives maximum profit.

Answer: (a) ___________ (b) ___________

20. [3 marks] The cost of printing $n$ books is $C(n) = 50 + 2n$. The revenue from selling them is $R(n) = 5n$. (a) Write an expression for the profit $P(n) = R(n) - C(n)$. (b) Find the number of books needed to break even ($P(n) = 0$).

Answer: (a) ___________ (b) ___________

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

Total Marks: 40
Topic: Algebra & Functions (N6, N7)

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Section A: Function Notation and Evaluation

Q1. [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: Function notation $f(x)$ means "replace $x$ with the given number". Common mistake: forgetting to multiply before subtracting.

Q2. [2 marks]
$g(x) = x^2 + 2x$, 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.

Q3. [2 marks]
$h(x) = \frac{10}{x}$, evaluate $h(2)$.
$h(2) = \frac{10}{2} = 5$
Answer: 5

Q4. [2 marks]
$f(x) = 2x + 1$, $g(x) = x - 3$, find $f(g(4))$.
First $g(4) = 4 - 3 = 1$.
Then $f(1) = 2(1) + 1 = 3$.
Answer: 3
Teaching note: Composite means work inside out.

Q5. [2 marks]
$2x + 5 = 17 \Rightarrow 2x = 12 \Rightarrow x = 6$.
Answer: 6

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Section B: Graphs of Functions

Q6. [2 marks]
$y = 2x - 1$ is in form $y = mx + c$, gradient $m = 2$.
Answer: 2

Q7. [2 marks]
$y$-intercept when $x = 0$: $y = 0^2 - 6(0) + 8 = 8$.
Answer: 8

Q8. [2 marks]
Sketch: vertex at (0,0), curve through (-1,1),(1,1),(-2,4),(2,4).
Marking: 1 mark for correct vertex labelled, 1 mark for smooth U-shape through points.

Q9. [2 marks]
Gradient $a = \frac{7 - 3}{2 - 0} = \frac{4}{2} = 2$.
Answer: 2

Q10. [2 marks]
$y = -x^2 + 4$ opens downward, max at $x=0$, $y=4$.
Answer: 4

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Section C: Composite and Inverse Functions

Q11. [2 marks]
$f(1) = 4(1) = 4$; $g(4) = 4 + 2 = 6$.
Answer: 6

Q12. [3 marks]
(a) $y = 5x - 3 \Rightarrow x = \frac{y+3}{5} \Rightarrow f^{-1}(x) = \frac{x+3}{5}$ [2 marks]
(b) $f^{-1}(7) = \frac{7+3}{5} = 2$ [1 mark]
Answers: (a) $\frac{x+3}{5}$ (b) 2

Q13. [2 marks]
$h(x) = x/2 \Rightarrow h^{-1}(x) = 2x \Rightarrow h^{-1}(6) = 12$.
Answer: 12

Q14. [2 marks]
$f(g(x)) = (x+1)^2$.
Answer: $(x+1)^2$

Q15. [3 marks]
(a) $p(q(x)) = 3(\frac{x}{3}) - 2 = x - 2$ [1]
(b) $q(p(x)) = \frac{3x-2}{3} = x - \frac{2}{3}$ [1]
(c) No, because $p(q(x)) \neq x$ and $q(p(x)) \neq x$ [1]
Answers: (a) $x-2$ (b) $x - \frac{2}{3}$ (c) No

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Section D: Word Problems and Applications

Q16. [2 marks]
$C(10) = 3.50 + 0.80(10) = 3.50 + 8.00 = 11.50$.
Answer: $11.50

Q17. [3 marks]
(a) $H(4) = 2(4) + 5 = 13$ cm [1]
(b) $2t + 5 = 21 \Rightarrow 2t = 16 \Rightarrow t = 8$ weeks [2]
Answers: (a) 13 cm (b) 8

Q18. [2 marks]
$P(2) = 100 \times 1.05^2 = 100 \times 1.1025 = 110.25 \approx 110$.
Answer: 110

Q19. [3 marks]
(a) $x=3: y = -(3)^2 + 10(3) - 16 = -9 + 30 - 16 = 5$ [1]
(b) Max at $x = -\frac{b}{2a} = -\frac{10}{2(-1)} = 5$ [2]
Answers: (a) 5 (b) 5

Q20. [3 marks]
(a) $P(n) = 5n - (50 + 2n) = 3n - 50$ [1]
(b) $3n - 50 = 0 \Rightarrow 3n = 50 \Rightarrow n = 16\frac{2}{3} \approx 17$ books [2]
Answers: (a) $3n - 50$ (b) 17