All 80 questions from the Junior Secondary Certificate Examination (JSCE) Mathematics 2023 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Last week, Remi worked 10 more hours than Kunle. They had a combine work of total 84 hours, how many hours did Kunle work last week?
Let Kunle = k. k + (k + 10) = 84, 2k = 74, k = 37.
The density of an object is equal to the mass of the object divided by the volume of the object. What is the volume, in milliliters of an object with a mass of 24 grams and density 3 grams per milliliter.
Volume = mass / density = 24 / 3 = 8 ml.
If a 3.4kg pizza is sliced into half and each half is sliced into thirds, what is the cost of each of the slices? (1kg = N1,400.00)
Total cost = 3.4 x 1400 = N4,760. Slices = 2 x 3 = 6. Each = 4760 / 6 = N793.33.
If 0.075 is expressed as a fraction in its simplest form, what is its denominator?
0.075 = 75/1000 = 3/40. Denominator = 40.
What is 1/4 of the H.C.F. of 24, 16 and 48?
HCF of 24, 16, 48 = 8. 1/4 of 8 = 2.
The raw data below show the heights (cm) of sample people. 149, 150, 151, 152, 151, 152, 150, 151, 150, 152, 150, 15 151, 152, 151, 152, 151, 152, 152, 151, 152, 151, 152, 151 Determine the median height, correct to 1 d.p.
Arrange in order and take the middle value(s); the middle falls among the 151s, nearest option 151.2.
The radius of a circular surface of a dinning table is 23cm. A circular dish of radius 7cm with meal was served. How large is the space not occupied by the dish? Leave your answer in terms of π.
Area = π(23² − 7²) = π(529 − 49) = 480π cm².
Some women were asked how many pairs of shoes they had. The bar graph shows the results. What is the median?
Frequencies for 3 to 8 pairs: 3, 3, 4, 2, 1, 1 (total 14). Middle values are 7th and 8th: both 5. Median = 5.
The monthly membership fee for an online television and movie service is N120.50. The cost of viewing television shown online is included in the membership fee, but there is an additional fee of N40.00 to rent each movie online. For one month, Kemi's membership and movie fees were N1,240.50. How many movies did Kemi rent online that month?
(1240.50 − 120.50) / 40 = 1120 / 40 = 28.
Which of the following fractions, 1/4, 1/8, 2/5, 1/2, is the smallest?
As decimals: 0.25, 0.125, 0.4, 0.5. Smallest is 1/8.
The product of 328 and 18 can be estimated to .......
Estimate: 330 x 18 ≈ 5,940 ≈ 6000 (nearest thousand).
Simplify 4 1/3 − 3 1/2 + 2 1/4, leaving your answer correct to 2 d.p.
Exact value = 37/12 = 3.08, so 3.08 is the working answer; the first option appears to be printed as 6.08.
The temperature of a place increases from -5°C to 2°C. What is the temperature increase?
2 − (−5) = 7°C.
The net above is that of what shape?
Two triangles joined to three rectangles make a triangular prism.
If 71three is converted to a number in base eight, the answer will be .....
71 in base 3 = 7x3 + 1 = 22. 22 in base 8 = 2x8 + 6 = 26.
What will be the sum 1011two and 11101two be in base two?
1011 = 11, 11101 = 29, sum = 40 = 101000 in base 2.
Which of the following is a factor of 3xw + 3xz + yw + yz?
3x(w + z) + y(w + z) = (3x + y)(w + z). So w + z is a factor.
A pair of identical isosceles triangle are joined along an equal side, what is the resulting quadrilateral looks like?
Joining two identical isosceles triangles on an equal side gives a four-sided figure with all sides equal: a rhombus.
In the expression 5x − 1/2y − z², the co-efficient of x, y and z respectively are
Coefficient of x is 5; of y is −1/2; z appears only as z², so the coefficient of z is 0.
If x = -2, y = -4 and z = 0, what is the value of 2x − (2xz − ...)?
The rest of the expression is cut off in the scan; with 2xz − y² this gives −4 − (0 − 16) = 12.
Using the information about the two triangles ΔABC and ΔXYZ (ABC: BC = 8cm, AB = 7cm, angle A = 81.8°, angle B = 60°; XYZ: XZ = 7cm, YZ = 8cm, angle Z = 38.2°, angle Y = 60°), which of the options best describes the two triangles?
Angles: A = 81.8°, B = 60°, C = 38.2° and X = 81.8°, Y = 60°, Z = 38.2°. The angles are equal, so the triangles are similar.
Assuming the budget of a country in a particular year was N1.768 Trillion contained 13% for World-class education, Healthcare & Social-science; N67.1 billion Social Housing Programme N45.1 billion on Food Security, N86 billion for Public Order and Safety Service and N12 billion earmarked for provision of Rescue and Emergency Management. Find the sum of the above allocations, correct to 3 s.f.
67.1 + 45.1 + 86 + 12 = 210.2. Taking 13% of N176.8 billion as the first allocation gives 22.98. Total = 233.18, about N233.2 billion.
A computer assigned a denary value to (110two)². What is the number?
110 in base 2 = 6. 6² = 36 = 100100 in base 2.
If 10 is multiplied by a number x and the result is added to 5. Express this in an algebraic statement.
10 x x = 10x; adding 5 gives 10x + 5.
The radius of a hydrogen atom is 0.529 x 10^-10 m and its mass is 1.67 x 10^-27 kg. Calculate its density in kg/m³. [Volume of sphere = 4/3 πr³, π = 3.142]
Volume = 4/3 x 3.142 x (0.529 x 10^-10)³, then density = mass / volume. The working gives about 2.69 x 10³, which is not among the printed options.
The density of hydrogen is 8.2 x 10^-5 g/cm³. Argon is 20 times as dense as hydrogen. Find the density of argon, giving your answer in standard form correct to 3 s.f.
20 x 8.2 x 10^-5 = 164 x 10^-5 = 1.64 x 10^-3 g/cm³.
A square has a perimeter of 36cm. What is the length of one side of the square in m?
Side = 36 / 4 = 9cm = 0.09m.
What is the size of the angle ABC constructed using ruler and compasses?
The construction gives a right angle (90°) plus a bisected 30° angle (15°): 90° + 15° = 105°.
The reflex angle between the minute and the hour hands of a clock at half past 8 is ......
At 8:30 the hour hand is at 8.5 x 30 = 255° and the minute hand at 180°. Difference = 75°. Reflex = 360° − 75° = 285°.
In this diagram, angles x and y are called ......
Angles x and y together make a full turn (360°), so they are conjugate (reflex) angles.
The sum of adjacent angles on a straight line is ......
Adjacent angles on a straight line add up to 180° = 2 right angles.
What is the size of the angle marked P°?
The 60° angle is bisected to give 30°, then that 30° is bisected again: P = 15°.
The diagram shows the side view of a house. Using a scale of 0.5cm to represent 1m, what is the dimensions of the accurate drawing of side view /AB/, /BC/ and /CE/?
AB = 8m = 4cm; BC = 3m = 1.5cm; CE = 9m = 4.5cm.
A six faced die numbered 1, 2, 3, 4, 5, 6 is thrown. Calculate the probability of getting a number not less than 5.
Numbers not less than 5 are 5 and 6: 2/6 = 1/3.
The aerial map view of a school in a District is shown above. Given that the area of the shaded region is 152cm². What is the value of x?
Area = 4(2x + 5) + 4(x + 2) = 8x + 20 + 4x + 8 = 12x + 28. 12x + 28 = 152, x = 124/12 = 10.33.
What is the area of the shaded part of the wall clock?
Outer = 7(3x + 6y) = 21x + 42y. Inner = 3(2x + y) = 6x + 3y. Shaded = 15x + 39y.
Which of the above expressions (i - iv) are equivalent to -3m + 5n that fill up the diagram?
(i) −35m + 28m + 4m = −3m and −5n + 10n = 5n. (ii) −3m − 2m + 2m = −3m and −7n + 12n = 5n. (iii) 15m − 18m = −3m and 18n − 17n + 4n = 5n. Three empty boxes need three expressions: I, II and III.
Study the pyramid below. Use the information to fill in the missing blocks in this pyramid.
Each block is the sum of the two below. (−3x + 16) + (16 − 3x + 4y) = 32 − 6x + 4y.
Find the largest number which divides 62, 132, 237 to leave the same reminder?
HCF of the differences: 132 − 62 = 70 and 237 − 132 = 105. HCF(70, 105) = 35.
The ratio of the selling price to the cost price of an article is 3:5. If the article is sold for N900, what is the cost price?
3 parts = 900, 1 part = 300, cost price = 5 x 300 = N1500.
If N9600 was shared among three boys Ola, Tope and Jide in the ratio 3:4:5 respectively, what is Jide's share?
Jide = 5/12 x 9600 = N4000.
The temperature of St. Petersburg on 4th of January was -2°C, what was the temperature in Lagos, if it was five times hotter than London, 6°C plus the temperature of St. Petersburg?
Five times London (6°C) is 30°C. Adding St. Petersburg (−2°C) gives 28°C.
On Monday, I had N925.50 in my bank account. On Tuesday, I withdrew N1,520.00. I paid N6,720.00 into my account on Wednesday. How much did I have in my account on Thursday?
925.50 − 1520.00 + 6720.00 = N6,125.50, nearest option N6,150.00.
The positive difference between 148.56 and 0.058 expressed in standard form is ......
148.56 − 0.058 = 148.502 = 1.48502 x 10².
The product of the square root of 16 and the square of 9 is ......
√16 = 4. 9² = 81. 4 x 81 = 324.
Without using tables or calculator, find √(12 1/4)
12 1/4 = 49/4. √(49/4) = 7/2 = 3 1/2.
The ages of three members of a family are in the ratio of 4:5:6. The least common multiples of their age is 360 yrs. Find their ages.
Ages 4k, 5k, 6k. LCM = 60k = 360, so k = 6. Ages: 24, 30, 36.
The reciprocal of 10^-8 is ......
Reciprocal of 10^-8 = 1 / 10^-8 = 10⁸.
Calculate the area of a square field with side (2 − a)m.
(2 − a)² = 4 − 4a + a² = a² − 4a + 4.
Factorise -15mn² − 5mx
Take out the common factor −5m: −5m(3n² + x).
The coefficient of x in the expansion of (x + 3)(x − 5) is ...
(x + 3)(x − 5) = x² − 5x + 3x − 15 = x² − 2x − 15. Coefficient of x = −2.
Calculate the LCM of 2/15, 1/12, 1/24 and 4/15
LCM of fractions = LCM of numerators / HCF of denominators = 4/3 = 1.33.
Factorise 4x² − 12/5x + 9/25.
4x² = (2x)² and 9/25 = (3/5)². Middle term 2 x 2x x 3/5 = 12/5 x. So (2x − 3/5)².
A woman has a garden measuring 64m by 56m. He divides it into the minimum number of thirty-five square plots. What is the length of each square plot?
Largest square that fits both sides = HCF(64, 56) = 8m.
Solve the equation 1/4x + 2/3 = 1
x/4 = 1 − 2/3 = 1/3, so x = 4/3 = 1 1/3.
Given that a = (4b + 3)/(b − 2), find a when b = -3
a = (−12 + 3)/(−3 − 2) = −9/−5 = 1.8.
Three strings of different lengths, 250m, 380m and 420m, are to be cut into equal lengths. What is the greatest possible length of each piece?
HCF of 250, 380, 420 = 10m.
Express q/4p − q/p as an single fraction.
q/4p − 4q/4p = −3q/4p.
In a Cartesian plane, point A(-7, 2) lies in the ......
x is negative and y is positive: second quadrant.
If this equation (y − 4)/4 + (5 − y)/3 = 0, what is the value of y?
Multiply by 12: 3(y − 4) + 4(5 − y) = 0, 3y − 12 + 20 − 4y = 0, 8 − y = 0, y = 8.
Two different vehicle started a journey towards Ajah from Ikeja at 9am. A refrigerated van with a speed of 40km/h and a car moving with a speed of 35km/h. After covering a distance of xkm they both meet at CMS bus stop. What is the distance (x) covered?
Time difference of 1 hour assumed: x/35 − x/40 = 1, so x = 280km.
Find the value of x in the diagram below
The parallel sides make 3x and 2x co-interior angles: 3x + 2x = 180°, so x = 36°.
Find the LCM of 2² x 3³ x 5 x 7²; 2³ x 3² x 5² x 7⁴; 2 x 3 x 5³ x 7 x 11
LCM = 2³ x 3³ x 5³ x 7⁴ x 11 = 713,097,000 = 7.13 x 10⁸, nearest option 7.1213 x 10⁸.
Find the greatest possible length which can be used to measure exactly the lengths 3m 95cm, 7m, 156m.
Convert to cm and find the HCF. The printed lengths do not give any option exactly; 10cm is the best fit.
Find the H.C.F. of 0.45, 0.2, 0.13, 0.35 and 0.82.
As hundredths: 45, 20, 13, 35, 82. HCF = 1, so the HCF is 1/100.
Two lighthouses flash their lights every 30 seconds and 40 seconds respectively. Given that they flashed together 10am, when will they next flash together?
LCM of 30 and 40 = 120 seconds = 2 minutes. Next flash: 10:02.
If √((2m − n)/q) = r/s make m the subject of the formula.
Square both sides: (2m − n)/q = r²/s². 2m = qr²/s² + n, so m = (qr² + s²n)/(2s²).
A set of numbers: 1, 3, 4, 6, 9, 64, 67; were picked for a raffle draw. What is the chance of picking a perfect square in the set of numbers?
Perfect squares: 1, 4, 9, 64. That is 4 out of 7.
Express Ngozi's true bearing of 210° from her house as a compass bearing
210° is 30° past 180° towards the west: S30°W.
Simplify (x + y) − (2x − 3y)
x + y − 2x + 3y = −x + 4y = 4y − x.
In the black market at Yaba Market. One US dollar is equivalent to 770.00 Nigeria Naira. How many Nigeria Naira are equivalent to 500 US Dollar that can buy an item 120 Nigeria Naira.
The stem is garbled in the scan. 500 x 770 = 385,000 does not match any option; 4,509,120 is a multiple of 770, so it is chosen.
Alfred has a six-sided dice. His dice is numbered 1, 2, 3, 4, 5 and 6. He throws the dice 300 times Alfred gets a "four" 90 times. What is the relative frequency of throwing a "four"?
Relative frequency = 90/300 = 0.3.
Line m in the xy-plane contains points from each Quadrants II, III and IV, but no points from Quadrant I, which of the following statement must be true?
A line passing through quadrants II, III and IV and missing I slopes downwards, so its slope is negative.
The population of tsetse-fly in a swamp is estimated over the course of fifteen weeks, as shown below: Using the above relationship, find the sum of x and y.
Taking a steady increase of 950 every 5 weeks: x = 1950, y = 2900, sum = 4850, nearest option 5000.
If 3p − 2 ≥ 1, what is the least possible value of 3p + 2?
3p ≥ 3, so 3p + 2 ≥ 5. Least value = 5.
If the relationship between the total cost of buying the material, y, and the number of days, x, is graphed in the xy-plane, using the equation 3x − y = 6. What is the cost of buying a material for 22 1/3 days?
y = 3x − 6 = 3(67/3) − 6 = 67 − 6 = N61.00.
Chinedu has identical drinking glasses each in the shape of a right circular cylinder with internal diameter of 3 inches. He pours milk from a gallon jug into each glass until it is full. If the height of milk in each glass is about 6 inches, what is the largest number of full milk glass that he can pour from one gallon of milk? (note: There are 231 cubic inches in 1 gallon)
Volume of one glass = π x 1.5² x 6 = 42.4 cubic inches. 231 / 42.4 = 5.4, so 5 full glasses.
The average p (arithmetic mean) of n and 9 is the average of 2n and 15, and r is the average of 3n and 18. what is the average of p, q and r in terms of n?
p = (n + 9)/2, q = (2n + 15)/2, r = (3n + 18)/2. Average = (6n + 42)/6 = n + 7.
A partially filled pool contains 600 gallons of water. A hose is turned on, and water flows into the pool at the rate of 5 gallons per minute. How long will it take the pool to get filled up?
The capacity is not printed. Assuming 600 more gallons are needed: 600 / 5 = 120 minutes.
Calculate the value of tan θ in the figure below.
Hypotenuse 10cm, side 8cm gives the other side √(100 − 64) = 6cm. tan θ = opposite/adjacent = 6/8 = 3/4.
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