Simplify $\dfrac{x^2 - 9}{x^2 - x - 6}$.

A) $\dfrac{x - 3}{x - 3}$

B) $\dfrac{x + 3}{x + 2}$

C) $\dfrac{x - 3}{x + 2}$

D) $\dfrac{x + 3}{x - 3}$

---

Solve for $x$: $2x^2 - 8 = 0$.

A) $x = 4$

B) $x = \pm 4$

C) $x = \pm 2$

D) $x = 2$

---

Which value of $x$ satisfies $\dfrac{3}{x-1} = 6$?

A) $x = \dfrac{1}{2}$

B) $x = \dfrac{3}{2}$

C) $x = 2$

D) $x = 3$

---

Factorise completely: $2x^2 + 5x - 3$.

A) $(2x - 1)(x + 3)$

B) $(2x + 1)(x - 3)$

C) $(x + 3)(2x - 1)$

D) $(2x - 3)(x + 1)$

---

The solution set of $-3x + 6 \geq 0$ is:

A) $x \geq 2$

B) $x \leq 2$

C) $x \geq -2$

D) $x \leq -2$

---

If $a = 3$ and $b = -2$, evaluate $a^2 - 2ab + b^2$.

A) 1

B) 25

C) 13

D) 17

---

Solve the simultaneous equations $x + y = 5$ and $x - y = 1$.

A) $x = 3,\ y = 2$

B) $x = 2,\ y = 3$

C) $x = 4,\ y = 1$

D) $x = 1,\ y = 4$

---

The expression $\dfrac{4^{x+1}}{2^{x-1}}$ simplifies to:

A) $2^{x+3}$

B) $2^{x+1}$

C) $4^{x+2}$

D) $8^x$

---

Solve for $x$: $|x - 3| = 5$.

A) $x = 8$ or $x = 2$

B) $x = 8$ only

C) $x = -2$ or $x = 8$

D) $x = 2$ only

---

Which expression is equivalent to $(x + 2)(x - 3) - x(x + 3)$?

A) $-4x - 6$

B) $-4x + 6$

C) $2x - 6$

D) $2x + 6$

---

The 15th term of the AP $3,\ 7,\ 11,\ \ldots$ is:

A) 57

B) 59

C) 55

D) 61

---

A GP has $T_3 = 18$ and common ratio $r = 3$. Find $T_1$.

A) 3

B) 2

C) 6

D) 9

---

Evaluate $\displaystyle\sum_{k=1}^{5} (2k - 1)$.

A) 25

B) 20

C) 15

D) 30

---

An infinite GP has $a = 10$ and $r = \dfrac{1}{5}$. Find $S_\infty$.

A) 25

B) 50

C) 12.5

D) 2

---

The sum $S_n = \dfrac{n}{2}(2a + (n-1)d)$ for the AP $6,\ 10,\ 14,\ \ldots$ The value of $S_8$ is:

A) 148

B) 160

C) 144

D) 128

---

The graph of $f(x) = x^2 - 4x + 3$ cuts the $x$-axis at:

A) $x = 1$ and $x = 3$

B) $x = -1$ and $x = -3$

C) $x = 2$ and $x = 3$

D) $x = 1$ and $x = 4$

---

The turning point of $g(x) = -(x - 2)^2 + 5$ is:

A) $(2,\ -5)$

B) $(-2,\ 5)$

C) $(2,\ 5)$

D) $(-2,\ -5)$

---

The domain of $f(x) = \dfrac{1}{x - 3}$ is:

A) $x \in \mathbb{R}$

B) $x \neq 0$

C) $x > 3$

D) $x \neq 3$

---

The graph of $f(x) = 2^x$ passes through which point?

A) $(0,\ 2)$

B) $(1,\ 0)$

C) $(0,\ 1)$

D) $(2,\ 0)$

---

A function $f$ has the property $f(x) = f(-x)$ for all $x$. This means $f$ is:

A) Strictly increasing

B) Odd

C) Even

D) Linear

---

The line $y = 2x - 3$ has gradient:

A) $-3$

B) $3$

C) $-2$

D) $2$

---

The graph of $y = -\dfrac{2}{x}$ is a hyperbola in quadrants:

A) I and II

B) I and III

C) II and IV

D) II and III

---

For $f(x) = 3x - 6$, find $f^{-1}(x)$.

A) $\dfrac{x - 6}{3}$

B) $\dfrac{x + 6}{3}$

C) $\dfrac{x}{3} + 6$

D) $3x + 6$

---

The $y$-intercept of $y = \log_2(x + 4)$ is:

A) $y = 4$

B) $y = 2$

C) $y = 0$

D) $y = \log_2 4$

---

Which of the following is a function?

A) $x^2 + y^2 = 4$

B) $y = \pm\sqrt{x}$

C) $y = x^2$

D) $x = y^2$

---

Which of the following is irrational?

A) $\sqrt{49}$

B) $\dfrac{22}{7}$

C) $\sqrt{5}$

D) $0.\overline{6}$

---

Express $0.0045 \times 10^6$ in standard form.

A) $4.5 \times 10^3$

B) $4.5 \times 10^2$

C) $4.5 \times 10^4$

D) $0.45 \times 10^4$

---

Simplify $\sqrt{50} - \sqrt{18}$.

A) $\sqrt{32}$

B) $3\sqrt{2}$

C) $2\sqrt{2}$

D) $4\sqrt{2}$

---

R8 000 is invested at 10 % p.a. compound interest for 2 years. The accumulated amount is:

A) R9 600

B) R9 680

C) R10 000

D) R9 728

---

A car bought for R120 000 depreciates at 20 % p.a. (reducing balance). Its value after 3 years is:

A) R61 440

B) R72 000

C) R57 600

D) R48 000

---

The ratio $\sqrt{8} : \sqrt{2}$ in simplest form is:

A) $4 : 1$

B) $2 : 1$

C) $8 : 2$

D) $\sqrt{4} : 1$

---

Elon exchanges R10 000 to US dollars at a rate of R18.50 per dollar. He receives approximately:

A) \$185 000

B) \$541

C) \$500

D) \$1 850

---

Which of the following represents a 15 % increase on R240?

A) R255

B) R276

C) R252

D) R264

---

In right triangle $ABC$, $\sin A = \dfrac{3}{5}$. Find $\cos A$.

A) $\dfrac{4}{5}$

B) $\dfrac{3}{4}$

C) $\dfrac{5}{3}$

D) $\dfrac{5}{4}$

---

$\tan 45° \times \cos 60° = $

A) $\dfrac{1}{2}$

B) $\dfrac{\sqrt{2}}{2}$

C) $1$

D) $\dfrac{\sqrt{3}}{2}$

---

The general solution of $\sin\theta = \dfrac{1}{2}$ is:

A) $\theta = 30° + 360°n$

B) $\theta = 30° + 180°n$

C) $\theta = 30° + 360°n$ or $\theta = 150° + 360°n$

D) $\theta = 150° + 360°n$

---

A triangle has sides 5, 12, 13. Which angle is 90°?

A) The angle opposite the side of length 5

B) The angle opposite the side of length 12

C) The angle opposite the side of length 13

D) All angles are equal to 60°

---

Point $P(3,\ 4)$ lies on a circle centred at the origin. The radius is:

A) 7

B) 25

C) 4

D) 5

---

The value of $\sin^2 30° + \cos^2 30°$ is:

A) $\dfrac{3}{4}$

B) $\dfrac{1}{2}$

C) $\dfrac{7}{4}$

D) $1$

---

In a regular hexagon, each interior angle measures:

A) $60°$

B) $108°$

C) $150°$

D) $120°$

---

Two triangles are similar. Their perimeters are 18 cm and 30 cm. If the shorter triangle has an area of $27\ \text{cm}^2$, what is the area of the larger triangle?

A) $45\ \text{cm}^2$

B) $54\ \text{cm}^2$

C) $75\ \text{cm}^2$

D) $108\ \text{cm}^2$

---

A sphere has radius 3 cm. Its volume is:

A) $9\pi\ \text{cm}^3$

B) $36\pi\ \text{cm}^3$

C) $27\pi\ \text{cm}^3$

D) $12\pi\ \text{cm}^3$

---

The midpoint of the line segment joining $(-2,\ 6)$ and $(4,\ -2)$ is:

A) $(1,\ 2)$

B) $(3,\ 4)$

C) $(2,\ 4)$

D) $(1,\ 4)$

---

An angle in a semicircle is always:

A) $45°$

B) Obtuse

C) $90°$

D) $60°$

---

The gradient of a line perpendicular to $y = \dfrac{2}{3}x + 1$ is:

A) $\dfrac{2}{3}$

B) $-\dfrac{3}{2}$

C) $\dfrac{3}{2}$

D) $-\dfrac{2}{3}$

---

The dataset $\{4,\ 7,\ 7,\ 9,\ 13\}$ has a mean of:

A) 7

B) 8

C) 9

D) 10

---

The interquartile range of $\{2,\ 5,\ 8,\ 10,\ 14,\ 18\}$ is:

A) 9

B) 16

C) 8

D) 12

---

A bag contains 3 red and 7 blue marbles. A marble is drawn at random. $P(\text{red}) = $

A) $\dfrac{7}{10}$

B) $\dfrac{3}{7}$

C) $\dfrac{3}{10}$

D) $\dfrac{7}{3}$

---

Events $A$ and $B$ are mutually exclusive. $P(A) = 0.3$ and $P(B) = 0.5$. Find $P(A \cup B)$.

A) $0.15$

B) $0.65$

C) $0.8$

D) $1.0$

---

In how many ways can 4 books be arranged on a shelf?

A) 4

B) 16

C) 24

D) 12

---

The standard deviation measures:

A) The middle value of a dataset

B) The most frequent value

C) The spread of data around the mean

D) The difference between the largest and smallest values

---

From a class of 30 students, 12 play sport and 10 study music. 5 do both. How many do neither?

A) 8

B) 12

C) 13

D) 17

---

A fair coin is tossed 3 times. The probability of getting exactly 2 heads is:

A) $\dfrac{1}{4}$

B) $\dfrac{3}{8}$

C) $\dfrac{1}{2}$

D) $\dfrac{1}{8}$

---

The range of $\{3,\ 8,\ 2,\ 15,\ 7,\ 1\}$ is:

A) 7

B) 13

C) 14

D) 15

---

The cumulative frequency at the upper boundary of a class interval represents:

A) The frequency of that class only

B) The total frequency up to and including that class

C) The mean of that class

D) The percentage in that class

---

The gradient of the line joining $(1,\ 3)$ and $(5,\ 11)$ is:

A) $1$

B) $3$

C) $2$

D) $4$

---

Solve $3(x - 2) = 2(x + 1)$.

A) $x = 8$

B) $x = 7$

C) $x = 4$

D) $x = 2$

---

The value of $\log_3 81$ is:

A) $3$

B) $27$

C) $9$

D) $4$

---

Which transformation maps $f(x) = x^2$ to $g(x) = x^2 + 3$?

A) Horizontal shift 3 units right

B) Vertical stretch by factor 3

C) Vertical shift 3 units up

D) Horizontal shift 3 units left

---

A rectangle has length $(x+3)$ cm and width $(x-1)$ cm. Its area in expanded form is:

A) $x^2 + 2x - 3$

B) $x^2 - 2x + 3$

C) $2x + 2$

D) $x^2 + 4x - 3$

---

Mock Exam 1 — Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	2	C	3	B	4	A	5	B
6	B	7	A	8	A	9	C	10	A
11	B	12	B	13	A	14	C	15	B
16	A	17	C	18	D	19	C	20	C
21	D	22	C	23	B	24	B	25	C
26	C	27	A	28	C	29	B	30	A
31	B	32	B	33	B	34	A	35	A
36	C	37	C	38	D	39	D	40	D
41	C	42	B	43	A	44	C	45	B
46	B	47	A	48	C	49	C	50	C
51	C	52	C	53	B	54	C	55	B
56	C	57	A	58	D	59	C	60	A

---

Mock Exam 2

---

Simplify $\dfrac{2x^2 - 8}{x - 2}$.

A) $2x - 4$

B) $x + 2$

C) $2(x + 2)$

D) $2x + 4$

---

Solve $x^2 - 5x + 6 = 0$.

A) $x = 1$ or $x = 6$

B) $x = -2$ or $x = -3$

C) $x = 2$ or $x = 3$

D) $x = -1$ or $x = -6$

---

Which is the correct factorisation of $6x^2 - x - 2$?

A) $(3x + 2)(2x - 1)$

B) $(6x + 1)(x - 2)$

C) $(2x + 1)(3x - 2)$

D) $(3x - 1)(2x + 2)$

---

Solve for $y$: $\dfrac{2y - 1}{3} = 5$.

A) $y = 4$

B) $y = 7$

C) $y = 9$

D) $y = 8$

---

The inequality $x^2 - 4 < 0$ is satisfied by:

A) $x > 2$

B) $x < -2$

C) $-2 < x < 2$

D) $x < -2$ or $x > 2$

---

Simplify: $\dfrac{a^3 b^2}{a^2 b^4}$.

A) $ab^2$

B) $\dfrac{a}{b^2}$

C) $\dfrac{b^2}{a}$

D) $a^2b^{-2}$

---

Solve $2|x| - 3 = 7$.

A) $x = 5$

B) $x = \pm 5$

C) $x = -5$

D) $x = 2$

---

The product $(a - b)^2$ expands to:

A) $a^2 + b^2$

B) $a^2 - b^2$

C) $a^2 + 2ab + b^2$

D) $a^2 - 2ab + b^2$

---

For which values of $x$ is $\dfrac{x-1}{x^2-4}$ undefined?

A) $x = 1$

B) $x = 0$

C) $x = \pm 2$

D) $x = 1$ and $x = 2$

---

Solve the system: $2x + y = 10$ and $x - y = 2$.

A) $x = 3,\ y = 4$

B) $x = 5,\ y = 0$

C) $x = 4,\ y = 2$

D) $x = 6,\ y = -2$

---

The AP $2,\ 6,\ 10,\ 14,\ \ldots$ has $S_{10}$ equal to:

A) 160

B) 200

C) 140

D) 120

---

In a GP, $T_2 = 6$ and $T_5 = 162$. Find the common ratio.

A) 2

B) 4

C) 3

D) 6

---

The sum $\displaystyle\sum_{k=2}^{5} k^2$ equals:

A) 50

B) 54

C) 30

D) 55

---

Insert 3 arithmetic means between 5 and 21. The three values in order are:

A) 8, 12, 16

B) 9, 13, 17

C) 7, 11, 15

D) 9, 12, 15

---

An infinite GP converges to 36 with $r = \dfrac{2}{3}$. Find the first term.

A) 18

B) 24

C) 12

D) 30

---

Which of the following is the graph of an exponential decay function?

A) $y = 2^x$

B) $y = x^2$

C) $y = \left(\dfrac{1}{3}\right)^x$

D) $y = 2x$

---

The axis of symmetry of $f(x) = x^2 - 6x + 8$ is:

A) $x = -3$

B) $x = 6$

C) $x = 4$

D) $x = 3$

---

The range of $f(x) = -x^2 + 4$ is:

A) $y \geq 4$

B) $y \leq -4$

C) $y \leq 4$

D) $y \geq -4$

---

The equation of the asymptote of $y = \dfrac{3}{x-2} + 1$ is:

A) $y = 2$ and $x = 1$

B) $x = -2$ and $y = -1$

C) $x = 2$ and $y = 1$

D) $x = 3$ and $y = 0$

---

If $f(x) = 2x + 1$ and $g(x) = x^2$, find $f(g(3))$.

A) 37

B) 49

C) 19

D) 25

---

The graph of $y = \log_3 x$ passes through:

A) $(0,\ 1)$

B) $(1,\ 3)$

C) $(3,\ 1)$

D) $(3,\ 0)$

---

A line through $(0,\ -2)$ with gradient 3 has equation:

A) $y = 3x$

B) $y = 3x + 2$

C) $y = 3x - 2$

D) $y = -2x + 3$

---

The distance between $(-3,\ 0)$ and $(1,\ 3)$ is:

A) 5

B) 4

C) 7

D) 3

---

Which function has no $x$-intercept?

A) $y = x - 5$

B) $y = x^2 - 4$

C) $y = 2^x$

D) $y = x^2 - 9$

---

Simplify $\log_2 8 + \log_2 4$.

A) $5$

B) $7$

C) $\log_2 32$

D) Both A and C

---

$\dfrac{3}{4}$ expressed as a percentage is:

A) $34\%$

B) $0.75\%$

C) $75\%$

D) $43\%$

---

Rationalise $\dfrac{6}{\sqrt{3}}$.

A) $\dfrac{6\sqrt{3}}{3}$

B) $2\sqrt{3}$

C) $\sqrt{3}$

D) $3\sqrt{3}$

---

R15 000 earns simple interest of 8 % p.a. for 3 years. Total interest earned is:

A) R1 200

B) R3 600

C) R4 800

D) R2 400

---

A machine worth R60 000 depreciates at 10 % p.a. straight-line for 5 years. Its book value is:

A) R6 000

B) R30 000

C) R54 000

D) R36 000

---

Which of the following is a perfect square?

A) 50

B) 75

C) 144

D) 200

---

The exchange rate is R18 per US dollar. Convert \$250 to rands.

A) R250

B) R450

C) R4 500

D) R3 600

---

A price of R600 is increased by 25 %. The new price is:

A) R150

B) R750

C) R625

D) R800

---

Evaluate $3^{-2} + \left(\dfrac{1}{2}\right)^{-1}$.

A) $\dfrac{17}{9}$

B) $\dfrac{19}{9}$

C) $\dfrac{7}{9}$

D) $\dfrac{5}{9}$

---

$\sin 60° = $

A) $\dfrac{1}{2}$

B) $\dfrac{\sqrt{3}}{2}$

C) $\dfrac{\sqrt{2}}{2}$

D) $1$

---

If $\cos\theta = -\dfrac{1}{2}$ and $\theta \in [0°,\ 360°]$, find all values of $\theta$.

A) $\theta = 60°$ only

B) $\theta = 120°$ or $\theta = 240°$

C) $\theta = 120°$ only

D) $\theta = 60°$ or $\theta = 300°$

---

In $\triangle PQR$, $PQ = 10$, $QR = 6$, and $\angle Q = 90°$. Find $PR$.

A) 4

B) 16

C) $\sqrt{136}$

D) 8

---

Which of the following is an identity?

A) $\sin\theta = \cos\theta$

B) $\tan\theta = \dfrac{\cos\theta}{\sin\theta}$

C) $\sin^2\theta + \cos^2\theta = 1$

D) $\tan^2\theta = 1$

---

In $\triangle ABC$, $a = 8$, $b = 6$, $\angle C = 90°$. Find $\tan A$.

A) $\dfrac{3}{4}$

B) $\dfrac{4}{3}$

C) $\dfrac{3}{5}$

D) $\dfrac{4}{5}$

---

Two parallel lines are cut by a transversal. Alternate interior angles are:

A) Supplementary

B) Equal

C) Complementary

D) Vertically opposite

---

The exterior angle of a triangle equals:

A) The largest interior angle

B) The sum of all interior angles

C) The sum of the two non-adjacent interior angles

D) $90°$

---

A rectangle is 12 cm by 5 cm. What is the length of its diagonal?

A) 17 cm

B) 60 cm

C) 13 cm

D) 7 cm

---

The total surface area of a cube with side 4 cm is:

A) $64\ \text{cm}^2$

B) $24\ \text{cm}^2$

C) $16\ \text{cm}^2$

D) $96\ \text{cm}^2$

---

The line segment from the centre of a circle to a point where a tangent touches it is:

A) A chord

B) An arc

C) Parallel to the tangent

D) Perpendicular to the tangent

---

The gradient of the line segment joining $(2,\ 5)$ and $(6,\ 13)$ is:

A) 3

B) 4

C) 2

D) 1

---

A regular polygon has interior angle of $108°$. It is a:

A) Hexagon

B) Heptagon

C) Pentagon

D) Octagon

---

The mean of a dataset is 12 and the median is 9. The data is:

A) Symmetrical

B) Skewed to the left (negatively skewed)

C) Skewed to the right (positively skewed)

D) Bimodal

---

A die is thrown once. $P(\text{even number}) = $

A) $\dfrac{1}{6}$

B) $\dfrac{1}{3}$

C) $\dfrac{2}{3}$

D) $\dfrac{1}{2}$

---

Two events $A$ and $B$ are independent. $P(A) = 0.4$ and $P(B) = 0.5$. Find $P(A \cap B)$.

A) $0.9$

B) $0.1$

C) $0.2$

D) $0.8$

---

Given the frequency table below, the modal class is 10–20.

Class	Frequency
0–10	4
10–20	11
20–30	8
30–40	3

The relative frequency of the 10–20 class is:

A) $\dfrac{11}{26}$

B) $\dfrac{11}{22}$

C) $\dfrac{11}{30}$

D) $\dfrac{11}{15}$

---

In how many ways can a president and a secretary be chosen from a group of 8 people?

A) 8

B) 16

C) 64

D) 56

---

A box contains 5 red, 3 blue, and 2 green pens. A pen is chosen at random. $P(\text{not red}) = $

A) $\dfrac{1}{2}$

B) $\dfrac{3}{5}$

C) $\dfrac{1}{5}$

D) $\dfrac{2}{5}$

---

The variance of $\{2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9\}$ requires first finding the mean. The mean is:

A) 4

B) 4.5

C) 5

D) 6

---

Which type of graph is best for showing how a quantity changes over time?

A) Bar chart

B) Pie chart

C) Line graph

D) Histogram

---

$P(A') = 0.35$. Find $P(A)$.

A) $0.35$

B) $1.35$

C) $0.65$

D) $0.55$

---

A student scores 60 out of 80. Express this as a percentage.

A) $60\%$

B) $80\%$

C) $75\%$

D) $70\%$

---

The $n$th term of the sequence $1,\ 4,\ 9,\ 16,\ 25,\ \ldots$ is:

A) $2n - 1$

B) $n + 3$

C) $n^2$

D) $3n - 2$

---

Solve $4^x = 8$.

A) $x = 2$

B) $x = \dfrac{3}{2}$

C) $x = \dfrac{1}{2}$

D) $x = 3$

---

The expression $\log_a(xy) = $

A) $\log_a x \cdot \log_a y$

B) $(\log_a x)(\log_a y)$

C) $\log_a x + \log_a y$

D) $\log_a x - \log_a y$

---

Evaluate $\dfrac{0!}{3!}$.

A) $0$

B) $\dfrac{1}{6}$

C) $\dfrac{1}{3}$

D) $3$

---

A line is perpendicular to $y = 4x - 1$ and passes through $(4,\ 2)$. Its equation is:

A) $y = 4x - 14$

B) $y = -\dfrac{1}{4}x + 3$

C) $y = \dfrac{1}{4}x + 1$

D) $y = -4x + 18$

---

Mock Exam 2 — Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	C	2	C	3	C	4	D	5	C
6	B	7	B	8	D	9	C	10	C
11	B	12	C	13	B	14	B	15	C
16	C	17	D	18	C	19	C	20	C
21	C	22	C	23	A	24	C	25	D
26	C	27	B	28	B	29	B	30	C
31	C	32	B	33	B	34	B	35	B
36	C	37	C	38	A	39	B	40	C
41	C	42	D	43	D	44	C	45	C
46	C	47	D	48	C	49	A	50	D
51	A	52	C	53	C	54	C	55	C
56	C	57	B	58	C	59	B	60	B

---

Mock Exam 3

---

Simplify $\dfrac{3x^2 - 12}{x + 2}$.

A) $3x + 6$

B) $3(x - 2)$

C) $3(x + 2)$

D) $x - 2$

---

Solve for $x$: $x^2 - 3x - 10 = 0$.

A) $x = 5$ or $x = -2$

B) $x = -5$ or $x = 2$

C) $x = 5$ or $x = 2$

D) $x = -5$ or $x = -2$

---

Which inequality is equivalent to $-4 \leq 2x < 6$?

A) $-2 < x \leq 3$

B) $-2 \leq x < 3$

C) $-8 \leq x < 12$

D) $2 \leq x < 10$

---

Simplify $\dfrac{x^2 - 1}{x^2 + x}$.

A) $\dfrac{x-1}{x}$

B) $\dfrac{x+1}{x}$

C) $\dfrac{x-1}{x+1}$

D) $\dfrac{1}{x}$

---

Find the value of $p$ if $3^p = \dfrac{1}{27}$.

A) $p = 3$

B) $p = \dfrac{1}{3}$

C) $p = -\dfrac{1}{3}$

D) $p = -3$

---

The expression $\left(\dfrac{27}{8}\right)^{2/3}$ equals:

A) $\dfrac{9}{4}$

B) $\dfrac{3}{2}$

C) $\dfrac{27}{4}$

D) $\dfrac{4}{9}$

---

Solve for $x$: $\log_2 x = 5$.

A) $x = 10$

B) $x = 25$

C) $x = 32$

D) $x = 16$

---

The product $\dfrac{x+1}{x-2} \cdot \dfrac{x^2-4}{x^2-1}$ simplifies to:

A) $\dfrac{x+2}{x-1}$

B) $\dfrac{x-2}{x+1}$

C) $\dfrac{x+1}{x+2}$

D) $\dfrac{x-1}{x+2}$

---

Which value of $k$ makes $kx^2 - 3x + 1 = 0$ have equal roots?

A) $k = \dfrac{9}{4}$

B) $k = 3$

C) $k = 9$

D) $k = \dfrac{1}{4}$

---

Simplify $\dfrac{2^{n+2} - 2^n}{2^n}$.

A) $2^n$

B) $4$

C) $3$

D) $3 \cdot 2^n$

---

The AP $-5,\ -1,\ 3,\ 7,\ \ldots$ Find $T_{20}$.

A) 71

B) 75

C) 67

D) 79

---

A GP has $T_1 = 4$ and $T_4 = 32$. Find $r$.

A) $r = 4$

B) $r = 8$

C) $r = 2$

D) $r = 3$

---

Evaluate $\displaystyle\sum_{k=1}^{4} 3 \cdot 2^{k-1}$.

A) 24

B) 45

C) 48

D) 51

---

The sum of an infinite GP is 45 and the first term is 15. Find $r$.

A) $r = \dfrac{1}{4}$

B) $r = \dfrac{2}{3}$

C) $r = \dfrac{1}{2}$

D) $r = \dfrac{1}{3}$

---

The AP has $S_n = 4n^2 + 2n$. Find $T_1$.

A) 4

B) 8

C) 6

D) 2

---

The function $f(x) = \sqrt{x - 2}$ has domain:

A) $x > 2$

B) $x \geq 2$

C) $x \geq 0$

D) $x \neq 2$

---

The graph of $y = (x - 1)^2 - 9$ has $x$-intercepts at:

A) $x = 1 \pm 3$

B) $x = -1 \pm 3$

C) $x = 1 \pm 9$

D) $x = -9$ and $x = 1$

---

For $h(x) = 2 \cdot 3^x$, find $h(2)$.

A) 36

B) 12

C) 18

D) 6

---

The graph of $y = \dfrac{2}{x} - 3$ has a horizontal asymptote at:

A) $y = 2$

B) $y = 0$

C) $y = -3$

D) $x = 0$

---

A function $f$ is increasing on its domain if, for $x_1 < x_2$:

A) $f(x_1) = f(x_2)$

B) $f(x_1) > f(x_2)$

C) $f(x_1) < f(x_2)$

D) $f(x_1) \geq f(x_2)$

---

The equation $y = 3^x$ and its inverse are reflections in:

A) The $x$-axis

B) The line $y = -x$

C) The line $y = x$

D) The $y$-axis

---

Which function has the smallest $y$-intercept?

A) $y = 2x + 3$

B) $y = x^2 + 1$

C) $y = 3 \cdot 2^x$

D) $y = -x + 5$

---

The range of $f(x) = x^2 - 6x + 10$ is:

A) $y \geq 1$

B) $y \leq 1$

C) $y \geq 3$

D) $y \leq 10$

---

$\log_5 25 - \log_5 5 = $

A) $0$

B) $5$

C) $\log_5 20$

D) $1$

---

Find the equation of the line through $(2,\ 3)$ with gradient $-2$.

A) $y = -2x + 7$

B) $y = -2x - 1$

C) $y = 2x - 1$

D) $y = 2x + 7$

---

$\sqrt{3} \times \sqrt{12} = $

A) $\sqrt{36}$

B) $6$

C) $\sqrt{15}$

D) Both A and B

---

Simplify $\dfrac{\sqrt{48}}{\sqrt{3}}$.

A) $\sqrt{16}$

B) $16$

C) $4$

D) Both A and C

---

R20 000 is invested at 15 % p.a. compound interest for 3 years. The accumulated amount is:

A) R29 000

B) R30 418

C) R30 000

D) R23 000

---

Inflation averages 6 % p.a. A grocery basket currently costs R500. Its cost in 2 years will be approximately:

A) R560

B) R530

C) R562

D) R556

---

Which of the following is rational?

A) $\sqrt{7}$

B) $\pi$

C) $\sqrt[3]{27}$

D) $\sqrt{2}$

---

R5 000 is borrowed at 12 % p.a. simple interest. The total repayment after 2.5 years is:

A) R6 500

B) R6 000

C) R6 200

D) R5 600

---

A car bought for R200 000 depreciates at 15 % p.a. compound. After 2 years its value is:

A) R140 000

B) R145 000

C) R144 500

D) R138 000

---

The value of $\cos 0°$ is:

A) $0$

B) Undefined

C) $\dfrac{1}{2}$

D) $1$

---

$\sin(90° - \theta) = $

A) $-\sin\theta$

B) $\cos\theta$

C) $-\cos\theta$

D) $\sin\theta$

---

In $\triangle ABC$, $AB = 10$, $BC = 6$, $\angle C = 90°$. Find $\sin A$.

A) $\dfrac{3}{4}$

B) $\dfrac{3}{5}$

C) $\dfrac{4}{5}$

D) $\dfrac{5}{3}$

---

The period of $y = \sin 2x$ is:

A) $360°$

B) $720°$

C) $90°$

D) $180°$

---

A ladder 10 m long leans against a wall making a $60°$ angle with the ground. The height it reaches is:

A) $5\sqrt{3}$ m

B) $5$ m

C) $10\sqrt{3}$ m

D) $5\sqrt{2}$ m

---

A tangent and a radius meet at the point of tangency at:

A) $45°$

B) $60°$

C) $90°$

D) $180°$

---

The sum of interior angles of a pentagon is:

A) $360°$

B) $720°$

C) $540°$

D) $450°$

---

Two similar triangles have corresponding sides in ratio $3 : 5$. Their areas are in ratio:

A) $3 : 5$

B) $6 : 10$

C) $9 : 25$

D) $27 : 125$

---

A cylinder has radius 3 cm and height 8 cm. Its volume is:

A) $24\pi\ \text{cm}^3$

B) $48\pi\ \text{cm}^3$

C) $72\pi\ \text{cm}^3$

D) $96\pi\ \text{cm}^3$

---

A chord subtends a central angle of $120°$ in a circle of radius 6. The chord length is:

A) $6\sqrt{2}$

B) $3\sqrt{3}$

C) $6\sqrt{3}$

D) $6$

---

The $y$-intercept of the line joining $(-2,\ 4)$ and $(4,\ 1)$ is:

A) $y = 3$

B) $y = 4$

C) $y = 2$

D) $y = 5$

---

A right circular cone has base radius 4 cm and slant height 5 cm. Its curved surface area is:

A) $20\pi\ \text{cm}^2$

B) $16\pi\ \text{cm}^2$

C) $40\pi\ \text{cm}^2$

D) $25\pi\ \text{cm}^2$

---

A point lies at $(-4,\ 3)$. Its distance from the origin is:

A) $7$

B) $1$

C) $5$

D) $\sqrt{7}$

---

The five-number summary of a dataset is: minimum $= 5$, $Q_1 = 12$, median $= 18$, $Q_3 = 25$, maximum $= 40$. The IQR is:

A) 13

B) 35

C) 18

D) 7

---

P(drawing a heart from a standard deck) = ?

A) $\dfrac{1}{52}$

B) $\dfrac{1}{4}$

C) $\dfrac{13}{52}$

D) Both B and C

---

A survey of 50 people: 30 like tea, 25 like coffee, and 10 like both. How many like neither?

A) 5

B) 45

C) 10

D) 15

---

In a dataset, if the mean equals the median, the distribution is:

A) Skewed right

B) Skewed left

C) Bimodal

D) Symmetrical

---

Two letters are chosen from $\{A, B, C, D\}$ without repetition. The number of ordered pairs is:

A) 4

B) 6

C) 8

D) 12

---

A standard deviation of 0 means:

A) The mean is 0

B) All data values are equal

C) There are no data values

D) The data is evenly spread

---

The probability that it rains on any given day is 0.3. The probability it does NOT rain two days in a row is:

A) $0.42$

B) $0.49$

C) $0.09$

D) $0.6$

---

In a histogram, the area of each bar is proportional to the:

A) Class width

B) Class midpoint

C) Frequency

D) Cumulative frequency

---

Given the data set $\{5,\ 5,\ 6,\ 7,\ 9,\ 10\}$, the mode is:

A) 6

B) 7

C) 5

D) 6.5

---

A two-way table shows: P(male and passes) = 0.35, P(male) = 0.50. If gender and result are independent, P(passes) = ?

A) $0.35$

B) $0.65$

C) $0.70$

D) $0.50$

---

Solve $\sqrt{2x - 3} = 5$.

A) $x = 14$

B) $x = 4$

C) $x = 7$

D) $x = 28$

---

Which of the following is NOT a real number?

A) $\sqrt{-4}$

B) $-\sqrt{4}$

C) $\sqrt[3]{-8}$

D) $\sqrt{0}$

---

The equation of a circle with centre $(2,\ -3)$ and radius 5 is:

A) $(x-2)^2 + (y+3)^2 = 25$

B) $(x+2)^2 + (y-3)^2 = 25$

C) $(x-2)^2 + (y-3)^2 = 5$

D) $(x-2)^2 + (y+3)^2 = 5$

---

$4! - 3! = $

A) $1$

B) $3$

C) $18$

D) $20$

---

The graph of $y = |x - 2|$ has a vertex (lowest point) at:

A) $(0,\ 2)$

B) $(2,\ 2)$

C) $(0,\ -2)$

D) $(2,\ 0)$

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Mock Exam 3 — Answer Key

Q	Ans	Q	Ans	Q	Ans	Q	Ans	Q	Ans
1	B	2	A	3	B	4	A	5	D
6	A	7	C	8	A	9	A	10	C
11	A	12	C	13	B	14	B	15	C
16	B	17	A	18	C	19	C	20	C
21	C	22	B	23	A	24	D	25	A
26	D	27	D	28	B	29	C	30	C
31	A	32	C	33	D	34	B	35	B
36	D	37	A	38	C	39	C	40	C
41	C	42	C	43	A	44	A	45	C
46	A	47	D	48	A	49	D	50	D
51	B	52	B	53	C	54	C	55	C
56	A	57	A	58	A	59	C	60	D

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