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JSCE Mathematics 2022 Objective Past Questions

All 80 questions from the Junior Secondary Certificate Examination (JSCE) Mathematics 2022 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2022 Objective — Question 3

Factorise: 9r² - 1

  • A. (3r + 1)(3r - 1)Correct
  • B. (3r + 1)(3r + 1)
  • C. (3r - 1)(3r - 1)
  • D. (3r + 1)(1 - 3r)

Explanation

Difference of two squares: (3r)² - 1² = (3r + 1)(3r - 1).

Mathematics 2022 Objective — Question 4

Which one of the angles can be constructed using ruler and a pair of compasses only?

  • A. 70°
  • B. 105°Correct
  • C. 115°
  • D. 125°

Explanation

105° = 90° + 15°, and 15° is built by bisecting 60° and 30°.

Mathematics 2022 Objective — Question 5

Write in figures: One billion, two hundred and four million, twenty four thousand and six.

  • A. 1,204,106,000
  • B. 1,204,006,000
  • C. 1,204,240,006
  • D. 1,204,024,006Correct

Explanation

1,000,000,000 + 204,000,000 + 24,006 = 1,204,024,006.

Mathematics 2022 Objective — Question 6

The area of a sector of a circle of radius 8cm is 45cm². Find the size of the angle subtended at the centre of the circle, correct to one decimal place. [Take π = 22/7]

  • A. 45.0°
  • B. 64.2°
  • C. 80.5°Correct
  • D. 99.5°

Explanation

45 = (θ/360) × 22/7 × 64, so θ = (45 × 360 × 7)/(22 × 64) = 80.5°.

Mathematics 2022 Objective — Question 11

In the diagram below, find the length PC.

Diagram for question 11
  • A. 16m
  • B. 15m
  • C. 14m
  • D. 12mCorrect

Explanation

PQ is parallel to AB, so triangles PCQ and BCA are similar: PC/CB = CQ/CA, so PC/8 = 15/10 and PC = 12m.

Mathematics 2022 Objective — Question 13

The variable y is inversely proportional to variable x. If y = 0.4 when x = 2.5, find the value of the constant of proportionality.

  • A. 4
  • B. 3
  • C. 2
  • D. 1Correct

Explanation

k = xy = 2.5 × 0.4 = 1.

Mathematics 2022 Objective — Question 14

A ball is drawn at random from a box containing 3 red balls, 2 white balls and 5 blue balls. What is the probability of picking a red ball?

  • A. 3/10Correct
  • B. 7/10
  • C. 2/5
  • D. 1/2

Explanation

Total = 10 balls, so P(red) = 3/10.

Mathematics 2022 Objective — Question 20

A ladder 6m long leans against a wall and makes an angle of 50° with the wall. Find the distance between the wall and the foot of the ladder, correct to two decimal places. [Cos 50 = 0.6427, Tan 50 = 1.1917, Sin 50 = 0.7660]

  • A. 3.86m
  • B. 4.60mCorrect
  • C. 5.03m
  • D. 7.15m

Explanation

Distance = 6 × sin 50° = 6 × 0.7660 = 4.60m.

Mathematics 2022 Objective — Question 23

Solve the simultaneous equation: 5x - 2y = 14 and 2x + 2y = 14

  • A. x = 4, y = -3
  • B. x = -4, y = 3
  • C. x = -4, y = -3
  • D. x = 4, y = 3Correct

Explanation

Add the equations: 7x = 28, x = 4. Then 8 + 2y = 14, y = 3.

Mathematics 2022 Objective — Question 24

Calculate the total surface area of a closed cylinder with base radius 3 1/2 cm and height 5cm. [Take π = 22/7]

  • A. 187cm²Correct
  • B. 178cm²
  • C. 160.5cm²
  • D. 148.5cm²

Explanation

TSA = 2πr(r + h) = 2 × 22/7 × 7/2 × 8.5 = 187cm².

Mathematics 2022 Objective — Question 27

The average age of 8 girls is 15 and the average age of 6 girls is 13. Find the age of the other two girls with equal age.

  • A. 42 years
  • B. 24 years
  • C. 21 yearsCorrect
  • D. 14 years

Explanation

Total = 8 × 15 = 120. Six girls = 6 × 13 = 78. Other two = 42, so each is 21 years.

Mathematics 2022 Objective — Question 29

In a rectangular shape, the breadth of the perimeter can be expressed as ____

  • A. (perimeter ÷ 2) - lengthCorrect
  • B. (perimeter ÷ 2) × length
  • C. (length ÷ 2) - perimeter
  • D. (perimeter ÷ 2) + length

Explanation

Perimeter = 2(l + b), so b = perimeter/2 - l.

Mathematics 2022 Objective — Question 33

A trader bought 3 dozens of sachet milk for N1,008.00 and sold each at N35.00. Calculate his profit.

  • A. N242.00
  • B. N252.00Correct
  • C. N262.00
  • D. N272.00

Explanation

3 dozens = 36. Sales = 36 × 35 = N1,260. Profit = 1,260 - 1,008 = N252.

Mathematics 2022 Objective — Question 35

A man is x years old and his son is y years old. What is the average age?

  • A. 1/2 (xy) year
  • B. (xy) year
  • C. (x + y) year
  • D. (x/2 + y/2) yearCorrect

Explanation

Average = (x + y)/2.

Mathematics 2022 Objective — Question 36

A cuboid measures ym by 2ym by 4ym. Find the volume of the cuboid in terms of y.

  • A. 8y³m³Correct
  • B. 8y²m³
  • C. 8ym³
  • D. 4y²m³

Explanation

Volume = y × 2y × 4y = 8y³ m³.

Mathematics 2022 Objective — Question 37

Find the median age of a group of students whose ages are: 8, 6, 10, 12, 15, 12, 16, 12, 8, 14

  • A. 13.5 years
  • B. 12 yearsCorrect
  • C. 10 years
  • D. 8 years

Explanation

Ordered: 6, 8, 8, 10, 12, 12, 12, 14, 15, 16. The middle two are 12 and 12, so median = 12.

Mathematics 2022 Objective — Question 40

Lines XY and PQ are parallel with a transversal line CD. If <CMY = 108°, find <QND.

Diagram for question 40
  • A. 90°
  • B. 82°
  • C. 72°Correct
  • D. 108°

Explanation

<CMY = <CNQ = 108° (corresponding angles). <QND = 180° - 108° = 72° (angles on a straight line).

Mathematics 2022 Objective — Question 41

Subtract [c - 3d - e] from the sum of [4c + d - e] and [2c - 2e]

  • A. 5c + d + 2eCorrect
  • B. 5c + d + 4e
  • C. 5c - d + 2e
  • D. 5c + d - 4e

Explanation

Worked out directly the answer is 5c + 4d - 2e, which matches none of the printed options.

Mathematics 2022 Objective — Question 42

Which one of the angles cannot be constructed using ruler and a pair of compasses only?

  • A. 15°
  • B. 22.5°
  • C. 35°Correct
  • D. 75°

Explanation

Angles built from 60° and 90° by bisection/addition (15°, 22.5°, 75°) can be constructed; 35° cannot.

Mathematics 2022 Objective — Question 44

Write 5/x + 3/y as a single fraction

  • A. (3x + 5y)/xy
  • B. (5y + 3x)/xyCorrect
  • C. xy/(5x + 3y)
  • D. xy/(3x + 5y)

Explanation

The symbols were unreadable in the scan; with denominators x and y, 5/x + 3/y = (5y + 3x)/xy.

Mathematics 2022 Objective — Question 45

Find the rate if the simple interest on 145,000.00 for ... years is $4500.00

  • A. 1%Correct
  • B. 1 1/2%
  • C. 2%
  • D. 2 1/2%

Explanation

The number of years is cut off in the scan, so this answer is a best guess.

Mathematics 2022 Objective — Question 47

16 out of 64 cars in a car park are Toyota Models. What is the probability that a car chosen at random is Not a Toyota Model?

  • A. 1/4
  • B. 1/3
  • C. 3/4Correct
  • D. 4/5

Explanation

Not Toyota = 48/64 = 3/4.

Mathematics 2022 Objective — Question 53

Find the smallest number by which 108 must be multiplied to get a perfect square.

  • A. 12
  • B. 9
  • C. 6
  • D. 3Correct

Explanation

108 = 2² × 3³. Multiply by 3 to get 2² × 3⁴ = 324 = 18².

Mathematics 2022 Objective — Question 54

Solve: ac/(3c + 5a) ... (the equation is not clear in the scan)

  • A. y = -2
  • B. y = -1
  • C. y = 1Correct
  • D. y = 2

Explanation

The question is not legible in the scan; this answer is a guess.

Mathematics 2022 Objective — Question 59

If p varies inversely as the square of q and p = 3, when q = 4, what is the value of p when q = 8?

  • A. 1/4
  • B. 1/2
  • C. 3/4Correct
  • D. 7/8

Explanation

p = k/q²: k = 3 × 16 = 48. When q = 8, p = 48/64 = 3/4.

Mathematics 2022 Objective — Question 61

Given that P = 4 - 9x² and Q = 2 + 3x, what is P + Q?

  • A. (6 + 9x)(1 - x)Correct
  • B. (6 + 9x)(1 + x)
  • C. (6 + 3x)(1 - x²)
  • D. (2 + 3x)(1 - x)

Explanation

P + Q = 6 + 3x - 9x² = 3(2 + 3x)(1 - x) = (6 + 9x)(1 - x).

Mathematics 2022 Objective — Question 63

The letters of GEOGRAPHY are cut and then put in a container. What is the probability of picking a letter G.

  • A. 2/9Correct
  • B. 2/5
  • C. 2/3
  • D. 2/8

Explanation

GEOGRAPHY has 9 letters, with G appearing twice, so 2/9.

Mathematics 2022 Objective — Question 64

Find the product of mode and median of the set: 8, 3, 1, 7, 3, 4, 8, 3, 4, 9, 5

  • A. 7
  • B. 9
  • C. 12Correct
  • D. 18

Explanation

Ordered: 1, 3, 3, 3, 4, 4, 5, 7, 8, 8, 9. Mode = 3, median = 4, product = 12.

Mathematics 2022 Objective — Question 66

Two-fifth of the students in a mixed school are boys. If there are 48 girls in the school, how many are boys?

  • A. 18
  • B. 27
  • C. 32Correct
  • D. 80

Explanation

Girls = 3/5 = 48, total = 80, boys = 2/5 × 80 = 32.

Mathematics 2022 Objective — Question 67

A ____ is a quadrilateral which has only one diagonal as a line of symmetry.

  • A. kiteCorrect
  • B. rhombus
  • C. rectangle
  • D. square

Explanation

A kite has one line of symmetry along a diagonal.

Mathematics 2022 Objective — Question 69

Find the L.C.M of 2 × 3 × 5², 2² × 3 × 5 and 2 × 3 × 5

  • A. 2³ × 3² × 5¹
  • B. 2⁴ × 3¹ × 5²
  • C. 2³ × 3¹ × 5¹
  • D. 2² × 3¹ × 5²Correct

Explanation

Highest powers: 2², 3¹, 5², giving 2² × 3 × 5².

Mathematics 2022 Objective — Question 72

The ratio of the lengths of two similar rectangles is 3 : 4. What is the ratio of their areas?

  • A. 6:8
  • B. 16:9
  • C. 9:16Correct
  • D. 27:64

Explanation

Areas are in the ratio of squares: 9 : 16.

Mathematics 2022 Objective — Question 74

Make x the subject of the relation: 7y - x = 5 - 5x

  • A. x = 1/4 (4 - 7y)
  • B. x = 1/4 (5 - 7y)Correct
  • C. x = 1/4 (5x - 7y)
  • D. x = 1/4 (4x - 7y)

Explanation

4x = 5 - 7y, so x = (5 - 7y)/4.

Mathematics 2022 Objective — Question 76

The mean age of five students whose ages are 8, x, 13, 12 and 10 is 10. Calculate the value of x in years.

  • A. 6 years
  • B. 7 yearsCorrect
  • C. 8 years
  • D. 10 years

Explanation

(8 + x + 13 + 12 + 10)/5 = 10, so 43 + x = 50 and x = 7.

Mathematics 2022 Objective — Question 79

The pie chart below shows the favourite fruits of a group of 150 students. How many students take mango?

Diagram for question 79
  • A. 65
  • B. 55
  • C. 45
  • D. 35Correct

Explanation

Mango sector is about 84°, so 84/360 × 150 = 35.

Mathematics 2022 Objective — Question 80

The pie chart below shows the favourite fruits of a group of 150 students. What is the percentage of the students that take apple?

Diagram for question 80
  • A. 50%
  • B. 40%
  • C. 30%
  • D. 20%Correct

Explanation

Apple sector is 72°, so 72/360 × 100 = 20%.

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