WASSCE 2025 Mathematics Past Questions and Answers

Answer: A. 28
Nth term of a linear sequence
U$_{n}$ = U$_{1}$ + (n-1)d

Where n is the number of terms

U$_{n}$ is the *n*th term

U$_{1}$ is the first term

d is the common difference

d is obtained by subtracting preceding term from succeeding term

Note: a sequence is linear when the intervals (common difference) between the numbers are the same.

Common difference (d) = 11 - 7 = 15 - 11 = 4

U$_{n}$ = 115

U$_{1}$ = 7

115 = 7 + (n - 1) x 4

115 = 7 + 4*n* - 4

115 = 7 - 4 + 4*n*

115 = 3 + 4*n*

115 - 3 = 4*n*

112 = 4*n*

Divide both sides by 4

n = $\frac{112}{4}$

n = 28

Answer: A. 3.52
Mean Deviation
Mean Deviation = $\frac{Σf|(x - µ)|}{Σf}$

Where µ is the mean and |(x - µ)| is the absolute/positive value of (x - µ).

Mean (µ) = $\frac{Σfx}{Σf}$

Σ*fx* = 2 + 5 + 7 + 9 + 15 = 38

Σf = 1 + 1 + 1 + 1 + 1 = 5

Note: f is 1 since each number occurred only once.

Mean (µ) = $\frac{38}{5}$ = 7.6

| x | x - µ | /(x - µ)/ |
|---|---|---|
| 2 | 2 - 7.6 = -5.6 | 5.6 |
| 5 | 5 - 7.6 = -2.6 | 2.6 |
| 7 | 7 - 7.6 = -0.6 | 0.6 |
| 9 | 9 - 7.6 = 1.4 | 1.4 |
| 15 | 15 - 7.6 = 7.4 | 7.4 |
| | | Σf/(x - µ)/ = 17.6 |

Mean Deviation = $\frac{Σf|(x - µ)|}{Σf}$

Σf|(x - µ)| = 17.6

Σf = 5

Mean Deviation = $\frac{17.6}{5}$

Mean Deviation = 3.52

Answer: C. It is the locus of points equidistant from M and N.
Definition of locus: A locus is the set of all points that satisfy a given condition. In this case, the condition is that the distance from a point P to M is equal to the distance from P to N.

Perpendicular bisector property: The perpendicular bisector of a line segment passes through the midpoint of that segment and is perpendicular to it. Any point on the perpendicular bisector is equidistant from the two endpoints of the line segment.

Answer: B. 440 yards
Speed
Speed = $\frac{Distance}{Time}$

Distance = Speed x Time

Speed = 60 miles per hour

3600 s = 1 hour

Notes:
1. 60 minutes = 1 hour
2. 60 seconds = 1 minutes
3. 60 x 60 seconds = 3600 seconds = 1 hour

If 3600 seconds = 1 hour

15 seconds = $\frac{15 seconds x 1 hour}{3600 seconds}$ = 0.00417 hour

Distance = Length of train

Distance = Speed x Time

Distance = 60 miles per hour x 0.00417 hour

Note: per hour cancels hour

Length of train ≈ 0.25 miles

If 1 mile = 1760 yards

0.25 mile = $\frac{0.25 mile x 1760 yards}{1 mile}$ = 440.352 yards ≈ 440 yards

Note: the mile cancel each other

Answer: B. $61.20
Let k = Kwaku's age

Kwaku is 2 years older than Atanga, Atanga's age = k - 2

Kwaku is 6 years younger than Esi, Esi's age = k + 6

Kwaku's age + Atanga's age + Esi's age = 70

k + (k - 2) + (k + 6) = 70

k + k - 2 + k + 6 = 70

k + k + k + 6 - 2 = 70

3*k* + 4 = 70

3*k* = 70 - 4

3*k* = 66

Divide both sides by 3

k = $\frac{66}{3}$

k = 22

Kwaku is 22 years

Atanga's age = 22 - 2 = 20 years

Esi's age = 22 + 6 = 28 years

Ratios of ages = 20 : 22 : 28

Ratios of ages = 10 : 11 : 14

Total ratio = 10 + 11 + 14 = 35

Amount received = $\frac{Ratio}{Sum of ratios}$ x Total Amount

Ratio for the eldest = 14

Sum of ratios = 35

Total amount shared = $153.00

Eldest's share = $\frac{14}{35}$ x $153.00

Eldest's share = $61.20