# WASSCE 2023 Elective Mathematics Questions for Candidates

## Below are three likely Elective Mathematics questions for WASSCE students. Answer the questions based on the given information and provide your solutions.

Question 1: The equation 3x^2 – 4x – 5 = 0 has two roots, α and β. Find the sum and product of the roots.

Footnotes:

- The equation is given in standard form: ax^2 + bx + c = 0, where a, b, and c are coefficients.
- The sum of the roots (α + β) can be found using the formula: α + β = -b/a.
- The product of the roots (α * β) can be found using the formula: α * β = c/a.

Question 2: Given the arithmetic sequence 8, 11, 14, …, 56, find the common difference (d) and the total number of terms (n) in the sequence. Calculate the sum of the terms in the sequence.

Footnotes:

- An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.
- The common difference (d) can be determined by finding the difference between any two consecutive terms.
- The total number of terms (n) can be determined by finding the number of terms from the first term to the last term, including both.
- The sum of an arithmetic sequence can be calculated using the formula: S_n = (n/2)(2a + (n-1)d), where S_n is the sum, n is the number of terms, a is the first term, and d is the common difference.

Question 3: A circle with center O has a radius of 6 cm. PQR is a tangent to the circle at point R, and the line segment OP is extended to point S such that SP = 12 cm. Calculate the length of PR.

Footnotes:

- In a circle, a tangent is a line that touches the circle at exactly one point.
- The radius of a circle is the distance from the center to any point on the circle.
- The line segment connecting the center of the circle to a point on the circle is called a radius.
- The line segment that extends from the center of the circle through a point of tangency to the point outside the circle is called a secant.
- In a circle, the tangent and the radius meeting at the point of tangency form a right angle.
- The lengths of line segments in a right-angled triangle can be determined using the Pythagorean theorem.

Note: The questions provided are sample questions for WASSCE Elective Mathematics and require the application of relevant concepts and formulas to find the solution

## WASSCE 2023 Elective Mathematics Questions for WASSCE Candidates -SET 2

3. Mr. Oppong makes monthly payments into his savings account. He saved GH¢200.00 in the first month, GH¢800.00 in the second month, GH¢3,200.00 in the third month and he continued in the same proportion in subsequent months. In what month would his savings first exceed GH¢200.00?

4. Given that f'(x) = (2x + 3)2 and/(-1) = 3, find f(x)

SHOW ANSWER

5. In a certain village, the probability that a person travelled in the past year is 5/8.

Find the probability that:

a) two people chosen at random from the village travelled in the past year;

b) at least ~me person from three _people chosen at random from the· village travelled in the past year.

6. The masses of 10 athletes in kg are 67, 68, 68, 70, 70, 72, 73, 73, 75 and 80.

Using an assumed mean mass of 70 kg, find the mean mass of the athletes.

7. The position vectors of points A, B and C are -i + j, i + 5j and 3i – j, respectively. If ABC form a triangle, show whether or not triangle ABC is isosceles.

8. A school bell weighing 45 N is suspended by two ropes which make angles of 40° and 63° with the horizontal, respectively.

Find the tensions in the ropes.

9. a) A function, f, is defined on the set, R, of real numbers, by f:x➔ x/x+2,x≠-2.

i) Determine whether or not/is one-to-one.

ii) Find the function g such that f o g = x.

13. A student is to answer IO out of 13 questions in an examination. In how many ways can this be done if he must answer:

a) the first two questions;

b) the first or the second question but not both;

c) exactly three of the first five questions.

d) at least three of the first five; questions.

READ: **2023 WASSCE Elective Mathematics: Examination Scheme And Sample Question**

14. a) A car passes through points A and B with speeds 72 kmh-1 and 108 km h-1 respectively. If the distance between A and B is 600 m, find the time taken by the car to travel from A to B.

b) A 15 N force acts at an angle of 60° on a body of mass 3 kg initially at rest on a smooth horizontal plane. Calculate, correct to two decimal places, the momentum of the body after moving through distance of 3 m.

15. Given the vectors a= Id+ 2j, b = 2i – 4j and c = i – 2j, find:

a) the value of k for which a and bare perpendicular;

b) the unit vector along (b – c).