Secondary 4 Elementary Mathematics Algebra Functions Quiz

<!-- TuitionGoWhere generation metadata: stage=3-0; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 2-1 real exam-derived templates and Stage 2-2 exam-enriched syllabus. -->

Secondary 4 Elementary Mathematics Quiz - Algebra Functions

Name: ______________________
Class: ______________________
Date: ______________________
Score: ______________________

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 π = 3.142 where needed unless stated otherwise.

---

Section A (Questions 1–5) — Short Answer [10 marks]

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

---

2. A function is given as $g(x) = x^2 - 5$. Find $g(-2)$.
[2]

---

3. Write the quadratic function $y = x^2 - 6x + 8$ in the form $y = (x - a)(x - b)$.
[2]

---

4. For the function $y = (x - 1)^2 + 2$, state the coordinates of the vertex.
[2]

---

5. Given $h(x) = \frac{1}{x}$, find $h(5)$.
[2]

---

---

Section B (Questions 6–10) — Structured Response [10 marks]

6. (a) Express $y = x^2 + 4x + 3$ in the form $y = (x - p)^2 + q$.
(b) Hence state the turning point of the graph.
[2]

---

7. The function $f(x) = ax^2 + bx + c$ has x-intercepts at $x = -1$ and $x = 3$. Write $f(x)$ in factored form if $a = 1$.
[2]

---

8. Given $y = 3^x$, find the value of $y$ when $x = 2$.
[2]

---

9. A graph of $y = kx^n$ passes through $(1, 4)$ and $n = 2$. Find $k$.
[2]

---

10. Solve the inequality $2x - 5 < 3$. Represent your answer on the number line below.
[2]
Number line: ______________________
Answer: ______________________

---

Section C (Questions 11–20) — Extended Problems [20 marks]

11. (a) Sketch the graph of $y = -(x - 2)^2 + 4$. Mark the vertex and x-intercepts.
(b) State the equation of the axis of symmetry.
[3]

---

12. Given $f(x) = x^2 - 3x - 10$,
(a) factorise $f(x)$,
(b) solve $f(x) = 0$.
[3]

---

13. The function $y = 2^x$ is an exponential function.
(a) Find $y$ when $x = 3$.
(b) Explain why the graph does not cut the x-axis.
[3]

---

14. Complete the square for $y = x^2 - 8x + 5$. Hence find the minimum value of $y$.
[3]

---

15. A quadratic function has vertex $(3, -2)$ and opens upward. Write its equation in vertex form.
[2]

---

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

---

17. The graph of $y = ax^2 + bx + c$ has the following features: vertex at $(1, -4)$, y-intercept at $(0, -3)$. Find $a$, $b$, and $c$.
[3]

---

18. Solve the simultaneous inequalities $x + 1 > 2$ and $3x \le 9$. Show your answer on a number line.
[2]

---

19. A power function is $y = 2x^{-1}$.
(a) Find $y$ when $x = 4$.
(b) State the value of $y$ as $x$ becomes very large.
[2]

---

20. The table below shows values for $y = x^2 - 2x - 3$.

x	-1	0	1	2	3
y	0	?	-4	-3	0

(a) Find the missing value of $y$ when $x = 0$.
(b) Using the table, state the x-intercepts of the graph.
[2]

---

<!-- TuitionGoWhere generation metadata: stage=3-0; model=tencent/hy3:free; model_label=Tencent HY3 Free; generated=2026-07-09; Sources: Stage 2-1 real exam-derived templates and Stage 2-2 exam-enriched syllabus. -->

Answer Key — Secondary 4 Elementary Mathematics Quiz: Algebra Functions

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

---

Section A (Q1–5)

Q1. [2]
$f(x) = 2x + 3$
$f(4) = 2(4) + 3 = 8 + 3 = 11$
Answer: 11
Teaching note: Substitute the input value wherever $x$ appears. A common mistake is to multiply before substituting or to forget the +3.

Q2. [2]
$g(x) = x^2 - 5$
$g(-2) = (-2)^2 - 5 = 4 - 5 = -1$
Answer: -1
Teaching note: Squaring a negative gives positive. $(-2)^2 = 4$, not -4.

Q3. [2]
$y = x^2 - 6x + 8$
We need two numbers that multiply to 8 and add to -6: -2 and -4.
$y = (x - 2)(x - 4)$
Answer: $y = (x - 2)(x - 4)$
Marking: 1 mark for correct factors, 1 mark for written in form.

Q4. [2]
Vertex form: $y = (x - p)^2 + q$ has vertex $(p, q)$.
Here $p = 1$, $q = 2$.
Answer: (1, 2)
Teaching note: The sign inside the bracket flips: $(x - 1)$ means $p = 1$.

Q5. [2]
$h(x) = \frac{1}{x}$
$h(5) = \frac{1}{5} = 0.2$
Answer: $\frac{1}{5}$ or 0.2

---

Section B (Q6–10)

Q6. [2]
(a) $y = x^2 + 4x + 3$
$= (x^2 + 4x + 4) - 4 + 3 = (x + 2)^2 - 1$
So $p = -2$, $q = -1$.
(b) Turning point = $(-2, -1)$
Marking: 1 mark completion, 1 mark turning point.

Q7. [2]
x-intercepts -1 and 3 → factors $(x + 1)(x - 3)$. With $a=1$:
$f(x) = (x + 1)(x - 3)$
Answer: $f(x) = (x + 1)(x - 3)$

Q8. [2]
$y = 3^x$, $x = 2$ → $y = 3^2 = 9$
Answer: 9

Q9. [2]
$y = kx^n$, $n=2$, through (1,4): $4 = k(1)^2$ → $k = 4$
Answer: $k = 4$

Q10. [2]
$2x - 5 < 3$ → $2x < 8$ → $x < 4$
Number line: open circle at 4, arrow left.
Answer: $x < 4$

---

Section C (Q11–20)

Q11. [3]
(a) Vertex (2,4), opens down, x-intercepts: $0 = -(x-2)^2+4$ → $(x-2)^2=4$ → $x=0,4$. Sketch with peak at (2,4).
(b) Axis: $x = 2$
Marking: 1 sketch, 1 intercepts, 1 axis.

Q12. [3]
(a) $x^2 - 3x - 10 = (x - 5)(x + 2)$
(b) $(x - 5)(x + 2)=0$ → $x=5$ or $x=-2$
Marking: 1 factorise, 2 solve.

Q13. [3]
(a) $y = 2^3 = 8$
(b) $2^x > 0$ for all $x$; as $x \to -\infty$, $y \to 0$ but never 0.
Marking: 1 value, 2 explanation.

Q14. [3]
$x^2 - 8x + 5 = (x^2 - 8x + 16) - 16 + 5 = (x - 4)^2 - 11$
Min value = -11 (at $x=4$).
Marking: 2 completion, 1 min.

Q15. [2]
Vertex (3,-2), upward → $y = (x - 3)^2 - 2$
Answer: $y = (x - 3)^2 - 2$

Q16. [2]
$g(2) = 2^2 = 4$; $f(4) = 2(4)-1 = 7$
Answer: 7

Q17. [3]
Vertex (1,-4): $y = a(x-1)^2 - 4$. At (0,-3): $-3 = a(1) - 4$ → $a=1$.
Expand: $y = x^2 - 2x - 3$ → $b=-2, c=-3$.
Answer: $a=1, b=-2, c=-3$

Q18. [2]
$x+1>2$ → $x>1$; $3x\le9$ → $x\le3$. So $1 < x \le 3$.
Number line: open at 1, closed at 3.

Q19. [2]
(a) $y = 2(4)^{-1} = 2/4 = 0.5$
(b) As $x \to \infty$, $y \to 0$.

Q20. [2]
(a) $x=0$: $y = 0 - 0 - 3 = -3$
(b) x-intercepts where $y=0$: $x = -1, 3$.