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JSCE Mathematics 2023 Theory Past Questions

All 17 questions from the Junior Secondary Certificate Examination (JSCE) Mathematics 2023 Theory paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2023 Theory — Question 1

1(a) If V is directly proportional to W and V = 50 when W = 16, find: (i) the formula connecting V and W

Model answer

V = kW. 50 = 16k, so k = 50/16 = 25/8. Formula: V = 25W/8.

Mathematics 2023 Theory — Question 5

(c) The parallel sides of a trapezium are 8cm and 14cm. If the distance between the parallel sides is 10cm, what is the area of the trapezium?

Model answer

Area = 1/2 (a + b) h = 1/2 x (8 + 14) x 10 = 1/2 x 22 x 10 = 110 cm².

Mathematics 2023 Theory — Question 6

2(a) The shadow of a flagpole is 4m long when the altitude of the sun is 54.5°. What is the height of the pole? (Tan 54.5° = 1.4019)

Model answer

tan 54.5° = height / shadow. Height = 4 x 1.4019 = 5.6076 = 5.61m (2 d.p.).

Mathematics 2023 Theory — Question 7

(b) Solve (x − 6)/4 < (−x + 4)/2 − 2. Show the solution on a number line.

Model answer

Multiply by 4: x − 6 < 2(−x + 4) − 8 x − 6 < −2x 3x < 6, so x < 2. Number line: draw a line, place an open circle at 2 and shade (arrow) to the left of 2, for all numbers less than 2.

Mathematics 2023 Theory — Question 8

(c) 1600 people attended a concert, if 80% of them are women and the rest are men, how many more women than men attended the concert?

Model answer

Women = 80/100 x 1600 = 1280. Men = 1600 − 1280 = 320. Difference = 1280 − 320 = 960 more women.

Mathematics 2023 Theory — Question 9

3. Draw the graph of y = 4x − 1 using a scale of 2cm to 1 unit on x-axis and 2cm to 5 units on y-axis. (a) Use the graph to find the value of x when y = 18.

Diagram for question 9

Model answer

Table: x = −1, 0, 1, 2, 3, 4, 5 gives y = −5, −1, 3, 7, 11, 15, 19. Plot the points and join with a straight line (see graph in the Diagram column). From y = 18 on the y-axis, go across to the line, then down to the x-axis: x = 4.75. Check: 4x − 1 = 18, x = 19/4 = 4.75.

Mathematics 2023 Theory — Question 10

(b) POQ is a sector of a circle with angle 60° at the centre. If the sector has an area of 70cm². Find the radius of the circle to 2 d.p. (Take π = 3.142)

Model answer

Area of sector = (θ/360) x πr² 70 = (60/360) x 3.142 x r² r² = 70 x 6 / 3.142 = 420 / 3.142 = 133.67 r = 11.56 cm (2 d.p.).

Mathematics 2023 Theory — Question 11

(c) Evaluate the binary number in base two 111 (110 + 101)

Model answer

110 + 101: 110 (=6) + 101 (=5) = 1011 in base two. 111 x 1011 (in base two): 111 = 7 and 1011 = 11, so 7 x 11 = 77. 77 in base two = 1001101. Answer: 1001101 (base two).

Mathematics 2023 Theory — Question 12

4(a) A friend asked me to think of a number, add 5 to it and then divide the sum by 20. The result is the same as subtracting 4 from the original number and dividing the difference by 15. Find the number.

Model answer

Let the number be x. (x + 5)/20 = (x − 4)/15 15(x + 5) = 20(x − 4) 15x + 75 = 20x − 80 155 = 5x, so x = 31.

Mathematics 2023 Theory — Question 13

(b) How many sides does a polygon with the total angle of 2520° has?

Model answer

Sum of interior angles = (n − 2) x 180° (n − 2) x 180 = 2520 n − 2 = 14, so n = 16 sides.

Mathematics 2023 Theory — Question 14

(c) A woman bought x kg of meat at N50 per kg, y kg of yams at N30 per kg, 8kg of fruits at Nx per kg and 5kg of beans at Ny per kg. How much did the woman spend on these items?

Model answer

Meat = 50x. Yams = 30y. Fruits = 8 x x = 8x. Beans = 5 x y = 5y. Total = 50x + 30y + 8x + 5y = N(58x + 35y).

Mathematics 2023 Theory — Question 15

5(a) The table below gives the number of candidates admitted to army school from five states: Ekiti 20, Kaduna 35, Borno 10, Oyo 25, Abia 30. Represent this information on a bar chart.

Diagram for question 15

Model answer

Draw equal-width bars with equal gaps: Ekiti 20, Kaduna 35, Borno 10, Oyo 25, Abia 30 (see chart in the Diagram column).

Mathematics 2023 Theory — Question 17

(c) If a candidate is selected at random, find the probability that is from neither Borno or Abia State.

Model answer

Borno + Abia = 10 + 30 = 40. Neither = 120 − 40 = 80. P = 80/120 = 2/3.

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