All 13 questions from the West African Examinations Council (WAEC) Mathematics 2024 Theory paper, with the correct answer and a full explanation for each. Free, no signup needed.
1. The time (t) taken to buy fuel at a filling station varies directly as the number of vehicles (V) in a queue and varies inversely as the number of pumps (P) available at the station. In a station with 5 pumps, it took 10 minutes to fuel 20 vehicles. Find the:
(a) relationship between t, P and V;
(b) time it takes to fuel 50 vehicles at a station with 2 pumps;
(c) number of pumps required to fuel 40 vehicles in 20 minutes.
Model answer
(a) t = 5V/2P
(b) t = 62.5 minutes
(c) P = 5 pumps
2. A car travelled a distance of (2x+13) km at 67.5 km/h and (5x-20) km at 72 km/h. If the total time for the entire journey was 90 minutes, find the value of x.
3. A circular floor of a building is to be tiled with ceramic tiles each of side 40 cm. If the perimeter of the floor is 66 m, calculate, correct to the nearest whole number, the number of tiles required to completely tile the floor. [Take π = 22/7]
4. In the diagram, ABCD is a circle centre O. The quadrilateral OBCD is a rhombus such that ∠ADO = ∠OBA = y and ∠BAD = t. Find:
(a) the value of t;
(b) the value of y;
(c) ∠ADC.
5. A basket contains 3 gold-plated marbles, 4 diamond marbles and some silver marbles, all of the same size and shape. Two marbles were drawn from the basket at random one after the other without replacement. If the probability that the two marbles were all silver is 1/15, find the number of silver marbles.
7. The table below shows the ages of 20 children in a household. Given that x : y = 1 : 2, find the:
(a) values of x and y;
(b) mean age of the children.
Age: 5, 6, 7, 8, 9, 10
Frequency: 2, (2x-1), (y+2), 4, 2, (y-1)
8. Two observers Abu and Badu, 46 m apart, observe a bird on a vertical pole from the same side of the bird. The angles of elevation of the bird from Abu's and Badu's eye are 40° and 48° respectively. If Abu and Badu are on the same horizontal level at the foot of the pole:
(a) illustrate the information in a diagram;
(b) calculate, correct to one decimal place, the height of the pole.
9. The diameter of a circle centre O is 26 cm. If a chord PQ is drawn such that it is 5 cm from O, calculate, correct to the nearest whole number, the:
(a) ∠POQ;
(b) area of the minor segment formed by the chord PQ. [Take π = 22/7]
Model answer
(a) ∠POQ ≈ 135°
(b) Area of minor segment ≈ 139 cm²
10. (a) In a man's will, he gave 2/5 of the total acres of his cocoa farm to the wife and 1/3 of what is left to the family. The rest of the farm was to be shared amongst his three children in the ratio 3 : 5 : 2. Given that the child who had the least share received 8 acres, calculate:
(i) total acres the man left;
(ii) number of acres the wife received.
(b) The list price of a Television set is $1,600.00. It can be purchased by a deposit of $400.00 and the rest of the amount paid by 12 monthly instalments at 25% per annum simple interest. If the Television set is purchased by instalment, find the total cost.
11. (a) Find the equation of the line that passes through the origin and the point of intersection of the lines x + 2y = 7 and x - y = 4.
(b) The ratio of an interior angle to an exterior angle of a regular polygon is 4 : 1. Find the:
(i) number of sides;
(ii) value of the exterior angle;
(iii) sum of the interior angles of the polygon.
Model answer
(a) y = x/5 (or 5y - x = 0)
(b)(i) n = 10
(b)(ii) Exterior angle = 36°
(b)(iii) Sum of interior angles = 1,440°
12. In the diagram, PR is a tangent to the circle centre O at Q. ∠POQ = 56° and PO intersects SO at V such that ∠SVP = 109°. Calculate:
(i) ∠TQP;
(ii) ∠VQO.
13. (a) In the diagram, ABT is a circle centre O. PQ is a tangent to the circle at T and ABC is a straight line. TC bisects ∠BTQ, ∠BAT = 44° and ∠PTA = 60°. Find ∠ACT.
(b) Simplify: (2n² - 3n - 2)/(2n² + 3n + 1) × (n² - 1)/(n² - 4)
Model answer
(a) ∠ACT = 38°
(b) (n - 1)/(n + 2)
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