The 2023 WASSCE Core Mathematics paper will be written on Thursday, 14th September, 2023. All 2023 WASSCE candidates must solve the following likely core mathematics questions. These questions were set based on some analysis and patterns of how WAEC set their questions.
The questions were also set based on some confirmed topics from WAEC. Solve these questions as soon as possible. These questions will guide you and make you abreast of what you are to expect in the main exams. Answers to these questions are also attached.
Question 1
A ladder 10 meters long rests against a wall. If the base of the ladder is pulled away from the wall at a rate of 2 m/s, how fast is the top of the ladder sliding down the wall when it is 6 meters above the ground?
Solution: Using the Pythagorean theorem, the distance between the top of the ladder and the wall is √(10^2 – h^2), where h is the height above the ground. Taking the derivative of both sides with respect to time and using the chain rule, we get dh/dt = (-3h/√(100 – h^2)) m/s when h = 6.
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Question 2
Find the fourth term in the expansion of (2x – 3y)^6.
Solution: The fourth term is the coefficient of (2x)^3(-3y)^1, which is given by the binomial coefficient 6C3 * (-3)^1 * (2)^3 = -960.
Question 3
A circular cylinder with a radius of 5 cm and height of 10 cm is melted down and recast into a sphere. Find the radius of the sphere.
Solution: The volume of the cylinder is Vc = πr^2h = 250π cm^3. The volume of a sphere is Vs = (4/3)πr^3. Equating these volumes and solving for r gives r = 5√6 / 3 cm.
Question 4
Find the equation of the circle passing through the points (1,2), (3,4), and (-1,0).
Solution: The general equation of a circle is (x – h)^2 + (y – k)^2 = r^2. Substituting the three points into the equation gives the system of equations: h^2 + k^2 – 2h – 4k + 5 = 0, h^2 + k^2 – 6h – 8k + 20 = 0, h^2 + k^2 + 2h = Solving this system gives h = 1, k = 2, and r = √10
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