Okuas Core Mathematics Mock Questions And Answers

Okuas Core Mathematics Mock Questions And Answers

Okuapeman SHS core mathematics mock questions and answers: The core mathematics mock questions and answers is a rehearsal of standard tutorial that was given to the candidates. Candidates who perform well in this questions will pass the WASSCE examination creditably well.

Download the Okuapeman SHS core mathematics questions here: Okuas core maths questions

Download the marking scheme of Okuapeman SHS core maths mock questions here: Marking scheme of Okuas core mathematics mock questions

See also: Wesley Girls’ Core Mathematics Mock Questions

OKUAS, 2023 GENERAL MATHEMATICS/MATHEMATICS (CORE): Time – 2 1/2hours: Marks – 100 marks

SECTION A [ 40 marks]: Answer all the questions in this section. All questions carry equal marks.

1. (a) Without using mathematical tables or calculators, evaluate (0.567 x 0.0015) / (0.0005 x 0.0189), leaving your

answer in the form k × 10ⁿ, where k is the first non – zero figure.

b) If (5y – x)/ (8y + 3x) = 1/5, find, correct to three significant figures, the value of x/y

2. Given that m = ((px/y) – p²x))^-3/2

I. Make x the subject

II. Find the value of x when m = -8, y = 1 an p = 3

Okuapeman SHS core mathematics mock questions and answers

3. a. Given that p = tan 30 and q = tan 45, simplify without using calculator, (p-q)/ pq, leaving your answer in a surd form

b). Find the truth set of the equation log(9x + 3) − log(x + 2) = log(x + 3)

4. In the diagram ABCD is a circle with center E, < BCD = (2x + 40)°, < BED = (5x − 35)°, < BAD = (2y + 10)° and < EDC = 40°. Find the values of x and y.

b) In how many years will GH¢312.50 invested at 4% per annum simple interest amount to GH¢500.00?

Okuapeman SHS core mathematics mock questions and answers

5. The fifth term of an arithmetic progression is three times the first term. If a quarter of the fifth term is 9. Find,

i. the first term and common difference

ii. the sum of the first eight terms

SECTION B [60 marks]: Answer five questions only from this section. All questions carry equal mark

6. The following is a frequency table of marks scored by some candidates in an examination.

a) Construct a cumulative frequency table and use it to draw a cumulative frequency curve for the distribution.

b) Use your curve to estimate the;

i inter – quartile range.

ii percentage of candidates who scored at least 65 marks.

Okuapeman SHS core mathematics mock questions and answers

7. a) If (y − x) is partly constant and partly varies as x. Given that y = 8 when x = 3 and y = 12 when x = 5, find

(i) a relation connecting y and x

(ii) the value of x when y = 20.

b) A solid cube of side 8cm was melted to form a solid circular cone. The base radius of the cone is 4cm. Calculate, correct to one decimal place, the height of the cone [Take π = 22/7)

8. a) The probability that an athlete will not win any of the three races is 1/4. If the athlete runs in all the races, what is the probability that the athlete will win

i only the second race

ii all the three races

iii only two of the races?

(b) The exterior angles of a polygon are 42° , 38° , 57°, x°, (x + y)°, (2x − 15)° and (3x − y)°. If x is 7° less than y, find the values of x and y.

Okuapeman SHS core mathematics mock questions and answers

9. The relation y = mxଶ + nx + r, where m ,n and r are constants on the interval −3 ≤ x ≤ 4 has an uncomplete table shown below.

a) Use your table to find the value of m ,n and r.

b) Using a scale of 2cm to 1unit on both axes, draw a graph for the function on the given interval.

c) From your graph, find
i. The value of p for which x = 2.2 and is a member of the truth set of the equation mxଶ + nx + r = p.

ii. The equation of axis of symmetry of the curve.

iii. The truth set of the equation 12 + 3x − 2x² = 0.

Okuapeman SHS core mathematics mock questions and answers

10. Sylvester, Bentil and Dereck are partners in a business and their contributions to the capital are GH₵ 15,000.00, GH₵ 25,000.00 and GH₵ 30,000.00 respectively. They agreed to share 40% of any net profit in the ratio of their contributions to the capital. In 2021, their profit before tax was GH₵16,800 and 45% of this was paid to the government as tax.

a) Calculate the share of the profit received by each partner.

b) Dereck invested his share of the profit in 2021 at 12% per annum simple interest. Calculate the interest earned in 8 years.

c) Express Dereck’s share of the profit in 2021 together with the interest earned on it in 8 years as a percentage of his initial contribution to the capital.

Okuapeman SHS core mathematics mock questions and answers

11. a) In the diagram ABC is a semicircle, center O and radius 9cm. the line BD is perpendicular to the diameter AC and < AOB = 135°. i. Find the length of BD, leave your answer in surd form.

ii. Find the perimeter of the shaded region

iii. Find the area of the unshaded region.

b) Find the value(s) of x which 2/ (x² + x – 6)

12. a) Using a scale of 2cm to 2 units on both axes, draw on a sheet of graph paper two perpendicular axes 0x and 0y for −10 ≤ x ≤ 10 and −10 ≤ y ≤ 10.

b) Given points E(3, 2), F(−1, 5) and the vectors   →      1    and  →        3

FG = 3            GH = -1, find the coordinates of the points G and H.

c) Draw on the same graph, indicating clearly the vertices and their coordinates, the:

i. quadrilateral EFGH.

ii. image EଵFଵGଵHଵ of the quadrilateral EFGH under an anticlockwise rotation of 90° about the origin where E → E₁, F → F₁, G → G₁, H → H₁.

d) The side E₁F₁ of the quadrilateral E₁F₁G₁H₁ cuts the x axis at the point P. Calculate, correct to one decimal place, the area E₁H₁G₁P

Okuapeman SHS core mathematics mock questions and answers

13. a.) The operation ∆ is defined on the set of real numbers by x ∆ y = 9 – 2xy in modulo arithmetic 11.

i Draw a table for ∆ on the set T = {5, 7, 9,10}

ii from your table find the truth set of: α) n ∆ (n + 2) = n β) n ∆ n = 1

b) Find the truth set of 1/2x – 1/3(x + 3)  x + 1  1/3 where x is a real number and Illustrate your answer on a number line