WASSCE 2024 Mathematics Past Questions and Answers
The WASSCE 2024 Mathematics paper has 50 objective and 13 theory questions. Here are sample objective questions with the correct answers and explanations. Sit the full paper with the real time limit on ePrep.
Sample questions with answers
1. The sum of the interior angles of a polygon is 1260°. Find the number of sides.
- A. 9
- B. 6
- C. 7
- D. 8
Answer: A. 9
Interior angles of a regular polygon
Sum of interior angles = (n - 2) x 180°
Where n = number of sides of the regular polygon.
Sum of interior angles = 1260°
(n - 2) x 180° = 1260°
(n - 2) x 180 = 1260
Divide both sides by 180
n - 2 = $\frac{1260}{180}$
n - 2 = 7
n = 7 + 2
n = 9
Interior angles of a regular polygon
Sum of interior angles = (n - 2) x 180°
Where n = number of sides of the regular polygon.
Sum of interior angles = 1260°
(n - 2) x 180° = 1260°
(n - 2) x 180 = 1260
Divide both sides by 180
n - 2 = $\frac{1260}{180}$
n - 2 = 7
n = 7 + 2
n = 9
2. A building is 12 m high. A football on the ground floor s 30 m away from the foot of the building.
Find, correct to the nearest degree, the angle of depression of the ball from the top of the building.
Find, correct to the nearest degree, the angle of depression of the ball from the top of the building.
- A. 22°
- B. 68°
- C. 66°
- D. 24°
Answer: A. 22°
Angle of depression
The angle of depression is defined as an angle constructed by a horizontal line and the line joining the object and observer's eye.
SOHCAHTOA
SOHCAHTOA is a mnemonic that gives us an easy way to remember the three main trigonometric ratios. They are sine (sin), cosine (cos) and tangent (tan).
SOH
sin(θ) = $\frac{Opposite}{Hypothenuse}$
CAH
cos(θ) = $\frac{Adjacent}{Hypothenuse}$
TOA
tan(θ) = $\frac{Opposite}{Adjacent}$
The longest side (side opposite/facing the right-angle) is the hypotenuse
Using the known sides, tan θ = $\frac{12 m}{30 m}$ where 12 m is the opposite side of θ and 30 m is the adjacent side of θ
tan θ = $\frac{12 m}{30 m}$
tan θ = $\frac{12}{30}$
Take tan$^{-1}$ of both sides.
θ = tan$^{-1}$($\frac{12}{30}$)
θ = 21.80° ≈ 22°(nearest degree)
Angle of depression
The angle of depression is defined as an angle constructed by a horizontal line and the line joining the object and observer's eye.
SOHCAHTOA
SOHCAHTOA is a mnemonic that gives us an easy way to remember the three main trigonometric ratios. They are sine (sin), cosine (cos) and tangent (tan).
SOH
sin(θ) = $\frac{Opposite}{Hypothenuse}$
CAH
cos(θ) = $\frac{Adjacent}{Hypothenuse}$
TOA
tan(θ) = $\frac{Opposite}{Adjacent}$
The longest side (side opposite/facing the right-angle) is the hypotenuse
Using the known sides, tan θ = $\frac{12 m}{30 m}$ where 12 m is the opposite side of θ and 30 m is the adjacent side of θ
tan θ = $\frac{12 m}{30 m}$
tan θ = $\frac{12}{30}$
Take tan$^{-1}$ of both sides.
θ = tan$^{-1}$($\frac{12}{30}$)
θ = 21.80° ≈ 22°(nearest degree)
3. A number is chosen at random from the set {13, 14, ...., 30}. What is the probability that it is a prime number?
- A. $\frac{5}{16}$
- B. $\frac{1}{3}$
- C. $\frac{5}{18}$
- D. $\frac{3}{8}$
Answer: C. $\frac{5}{18}$
Set = {13, 14, ...., 30}
Set = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
Number of samples = 18
Prime numbers are numbers with only two factors (1 and itself). Thus only 1 and the number itself can divide the number without a remainder.
Set of prime numbers from the set = {13, 17, 19, 23, 29}
Number of prime numbers = 5
Probability
Probability = $\frac{Number of possible selection}{Number of samples}$
P(Prime) = $\frac{5}{18}$
Set = {13, 14, ...., 30}
Set = {13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}
Number of samples = 18
Prime numbers are numbers with only two factors (1 and itself). Thus only 1 and the number itself can divide the number without a remainder.
Set of prime numbers from the set = {13, 17, 19, 23, 29}
Number of prime numbers = 5
Probability
Probability = $\frac{Number of possible selection}{Number of samples}$
P(Prime) = $\frac{5}{18}$
4. Regina is 34 years old and her daughter is 5 years. In n years, Regina will be twice as old as her daughter. Find the value of n.
- A. 23
- B. 30
- C. 29
- D. 24
Answer: D. 24
Regina's age now = 34.
In n years time, Regina will be (34 + n) years.
Daughter's age now = 5.
In n years time, the daughter will be (5 + n) years.
In n years, Regina will be twice as old as her daughter
Twice means 2 times (2 x)
Regina's age in n years time = 2 x daughter's age in n years time.
34 + n = 2 x (5 + n)
34 + n = 2 x 5 + 2 x n
34 + n = 10 + 2*n*
34 - 10 = 2*n* - n
24 = n
∴ n = 24
Regina's age now = 34.
In n years time, Regina will be (34 + n) years.
Daughter's age now = 5.
In n years time, the daughter will be (5 + n) years.
In n years, Regina will be twice as old as her daughter
Twice means 2 times (2 x)
Regina's age in n years time = 2 x daughter's age in n years time.
34 + n = 2 x (5 + n)
34 + n = 2 x 5 + 2 x n
34 + n = 10 + 2*n*
34 - 10 = 2*n* - n
24 = n
∴ n = 24
5. If P(-7, 8) is reflected in the line x - 2 = 0, find the coordinates of the image of P.
- A. $(\begin{matrix}5 \\ 8\end{matrix})$
- B. $(\begin{matrix}8 \\ -7\end{matrix})$
- C. $(\begin{matrix}11 \\ -8\end{matrix})$
- D. $(\begin{matrix}11 \\ 8\end{matrix})$
Answer: D. $(\begin{matrix}11 \\ 8\end{matrix})$
Reflection in the line x = k
(a, b) → (2*k* - a, b)
Reflection in the line x - 2 = 0, x = 2
k = 2
(-7, 8) → (2 x 2 - (-7), 8)
(-7, 8) → (4 + 7, 8)
(-7, 8) → (11, 8)
Note:
1. -- = + or -(-) = +
2. -(-7) = + 7
Reflection in the line x = k
(a, b) → (2*k* - a, b)
Reflection in the line x - 2 = 0, x = 2
k = 2
(-7, 8) → (2 x 2 - (-7), 8)
(-7, 8) → (4 + 7, 8)
(-7, 8) → (11, 8)
Note:
1. -- = + or -(-) = +
2. -(-7) = + 7
6. If the variable P is inversely proportional to Q$^{2}$ and P = 2.25 when Q = 6, find P when Q = 3.
- A. 9.5
- B. 7.5
- C. 8.5
- D. 9.0
Answer and explanation: practise this paper on ePrep.
7. Make x the subject of the relation y = $\sqrt{\frac{px}{r}-{r}^{2}x}$.
- A. x = $\frac{r{y}^{2}}{p-{r}^{3}}$
- B. x = $\frac{p-{r}^{3}}{r{y}^{2}}$
- C. x = $\frac{ry}{p-{r}^{3}}$
- D. x = $\frac{{y}^{2}}{p-{r}^{2}}$
Answer and explanation: practise this paper on ePrep.
8. Seven men complete a certain work schedule in 6 days. How long will it take two of the men to complete the same work schedule f they work at the same rate?
- A. 42 days
- B. 35 days
- C. 21 days
- D. 14 days
Answer and explanation: practise this paper on ePrep.
9. If cos y is negative and sin y is negative, in which quadrant would y lie?
- A. First
- B. Fourth
- C. Third
- D. Second
Answer and explanation: practise this paper on ePrep.
10. The volume of a cone s 264 cm$^{3}$. If the base radius is 6 cm, find the height.
[Take π = $\frac{22}{7}$]
[Take π = $\frac{22}{7}$]
- A. 5 cm
- B. 8 cm
- C. 7 cm
- D. 6 cm
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