All 120 questions from the Basic Education Certificate Examination (Junior WAEC) (BECE) Mathematics 2022 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Correct 82.00756 to 5 significant figures.
The first 5 significant figures are 8, 2, 0, 0, 7. The next digit is 5, so round the 7 up to 8: 82.008.
Find the square root of 196.
14 × 14 = 196, so the square root is 14.
What is the place value of the digit 2 in the number 428.531?
The digit 2 is in the tens place, so its place value is 20.
Evaluate √(2¼).
2¼ = 9/4. √(9/4) = 3/2.
Express 168,000 correct to the nearest ten thousand.
The thousands digit is 8, so round the 6 in the ten-thousands place up: 170,000.
Find the H.C.F. of 15 and 27.
15 = 3 × 5 and 27 = 3 × 3 × 3. The common factor is 3.
If 25% of a number is 540, find the number.
The number = 540 ÷ 25 × 100 = 21.6 × 100 = 2,160.
Calculate 111_two - 101_two.
111_two = 7 and 101_two = 5. 7 - 5 = 2 = 10_two.
Find one-third of the sum of 9 and 12.
9 + 12 = 21. One-third of 21 = 7.
Round off 0.00237 to 2 significant figures.
The first two significant figures are 2 and 3. The next digit is 7, so round up: 0.0024.
Evaluate 2 1/6 + 1 1/3 - 1 1/2.
2 1/6 + 1 1/3 - 1 1/2 = 13/6 + 8/6 - 9/6 = 12/6 = 2. This value is not among the options, so the nearest option is chosen.
At what speed in km/h does a cyclist travel if he covers a distance of 15km in 1½ hours?
Speed = distance ÷ time = 15 ÷ 1.5 = 10 km/h.
Express 3/5 as a decimal.
3 ÷ 5 = 0.6.
Express 0.0007936 in standard form.
Move the decimal point 4 places to the right: 7.936 × 10^-4.
What is the highest common factor of 24, 28 and 44?
24 = 2³ × 3, 28 = 2² × 7, 44 = 2² × 11. The common part is 2² = 4.
What number does the Roman numeral MCMLXXIX represent?
M = 1000, CM = 900, LXX = 70, IX = 9. Total = 1,979.
Simplify 28 ÷ 11 2/3.
11 2/3 = 35/3. 28 ÷ 35/3 = 28 × 3/35 = 84/35 = 12/5 = 2 2/5.
Find the L.C.M. of 24, 36 and 72.
24 = 2³ × 3, 36 = 2² × 3², 72 = 2³ × 3². The L.C.M. is 2³ × 3² = 72.
Subtract 11111_two from 111011_two.
111011_two = 59 and 11111_two = 31. 59 - 31 = 28 = 11100_two.
Find the simple interest on N30,000.00 for 2 years at 2% per annum.
I = PRT/100 = 30,000 × 2 × 2 ÷ 100 = N1,200.
Express 9 in binary number.
9 = 8 + 1 = 1001_two.
An estimated length of a twine is given as 4.8 cm, when corrected to 2 significant figures. Find the least possible length of the twine.
A value that rounds to 4.8 lies from 4.75 up to 4.85. The least is 4.75 cm.
If the area of a triangle of base 12cm is 30cm², find the height of the triangle.
Area = ½ × base × height. 30 = ½ × 12 × h = 6h, so h = 5 cm.
A man spent 2/3 of his salary on his family and 1/4 on himself. If he saved the rest of his money, what fraction did he save?
2/3 + 1/4 = 8/12 + 3/12 = 11/12. The saving is 1 - 11/12 = 1/12.
Find the value of x in the figure below.
Angles on a straight line add up to 180°. 6x + 3x + x = 180, so 10x = 180 and x = 18°.
Estimate the numbers of square rug of size 17cm by 17cm that is needed for a square room of size 4.2m.
Round 17 cm to 20 cm. The room is 420 cm, so 420 ÷ 20 = 21 rugs on each side. 21 × 21 = 441.
Find the value of y in the figure below.
The angle inside the triangle at the base = 180° - 120° = 60° (angles on a straight line). y = 180° - 75° - 60° = 45°.
Find the size of the unknown angle in the figure below.
The angles of a quadrilateral add up to 360°. Unknown = 360° - 100° - 85° - 50° = 125°.
Find the value of x in the diagram below, correct to one decimal place.
x is next to the 35° angle and the 4 cm side is the hypotenuse. x = 4 × cos 35° = 4 × 0.8192 = 3.3 cm.
Find the area of a triangle whose base is 10cm and height 3cm.
Area = ½ × base × height = ½ × 10 × 3 = 15 cm².
A car traveling at 60km/hr completes a distance in 3/2 hours. How long will it take to complete the same distance if the speed is decreased to 30km/hr?
Distance = 60 × 3/2 = 90 km. Time = 90 ÷ 30 = 3 hours.
Calculate the volume of a cuboid 7cm long, 5cm wide and 3cm high.
Volume = 7 × 5 × 3 = 105 cm³.
Calculate the area of the parallelogram below.
Area = base × perpendicular height = 18 × 1.5 = 27 cm².
Find the perimeter of a rectangle with length 8cm and breadth 4cm.
Perimeter = 2(8 + 4) = 24 cm.
A machine produces 800 pins in 4 days. How many pins will it produce in 12 days?
800 ÷ 4 = 200 pins a day. 200 × 12 = 2,400.
Calculate the perimeter of the shape below.
The marks show an equilateral triangle with side 4 cm. Perimeter = 3 × 4 = 12 cm.
Find the value of y in the figure below, correct to one decimal place.
y is opposite the 25° angle and 10 cm is adjacent. y = 10 × tan 25° = 10 × 0.4663 = 4.7 cm.
Find the compass bearing for 099°.
099° is 9° past east, i.e. 81° from south towards east, so S81°E.
Find the value of x in the figure below.
The angle at the top inside the Z-shape = 360° - 324° = 36°. x is an alternate angle (parallel lines), so x = 36°.
In a population of 1,500 students that was wrongly recorded as 900, find the percentage error.
Error = 1,500 - 900 = 600. Percentage error = 600 ÷ 1,500 × 100 = 40%.
If the area of a semi-circle is 308cm², calculate its radius. (Use π = 22/7)
½ × 22/7 × r² = 308, so r² = 308 × 7 ÷ 11 = 196. r = 14 cm.
If angle 90° is bisected, it will result to angle
Bisecting means halving: 90° ÷ 2 = 45°.
What is the diameter of a circle with circumference 264 cm?
C = πd, so d = 264 ÷ 22/7 = 264 × 7 ÷ 22 = 84 cm.
The sum of the interior angles of a heptagon is ________.
Sum = (n - 2) × 180° = (7 - 2) × 180° = 900°.
The area scale factor of two similar shapes is 25:64. Find their linear scale factor.
The linear scale factor is the square root of the area scale factor: √25 : √64 = 5 : 8.
Calculate the volume of a cylinder 12cm high and base radius 7/2 cm. (Use π = 22/7)
V = πr²h = 22/7 × 7/2 × 7/2 × 12 = 22 × 7 × 3 = 462 cm³.
What is the size of the angle marked x in the diagram below?
The construction draws 60° and then bisects it, so x = 60° ÷ 2 = 30°.
Find the value of x in the figure below.
The two equal sides make the base angles equal. The base angle = 180° - 124° = 56°. x = 180° - 56° - 56° = 68°.
The linear scale factor of two similar shapes is 2:5. If the area of the smaller shape is 120 cm², what is the area of the bigger shape?
Area scale factor = 2² : 5² = 4 : 25. Bigger area = 120 × 25/4 = 750 cm².
Calculate the length of the hypotenuse of the triangle below, correct to one decimal place.
The 4 cm side is opposite the 32° angle. sin 32° = 4/h, so h = 4 ÷ 0.5299 = 7.5 cm.
From the top of a mast 60 m high, the angle of depression of a man is 66°. Find the distance of the man from the foot of the mast to the nearest metre.
tan 66° = 60/d, so d = 60 ÷ 2.246 = 26.7, which is 27 m.
Two similar cylindrical cans have heights 2m and 3m respectively. If the smaller one holds 800g of sugar, how many kilogram of sugar will the bigger one hold?
Volume ratio = 2³ : 3³ = 8 : 27. The bigger can holds 0.8 kg × 27/8 = 2.7 kg.
Which of the points P, Q, R, S and T in the figure below is on a bearing 135° from O?
135° is halfway between east (090°) and south (180°), which is south-east, the point R.
The linear scale factor of two similar shapes is 4/5. If the volume of the bigger shape is 500cm³, determine the volume of the smaller shape.
Volume scale factor = (4/5)³ = 64/125. Smaller volume = 500 × 64/125 = 256 cm³.
Calculate the area of the trapezium below
Area = ½ × (6 + 14) × 3 = 30 cm².
If the bearing of A from B is 053°, the bearing of B from A is ________
The back bearing = 053° + 180° = 233°.
Calculate the area of a triangle with base 14cm and length 6cm long.
Area = ½ × 14 × 6 = 42 cm².
Find the volume of a cone with base radius 7cm and vertical height 6cm. (Use π = 22/7)
V = ⅓πr²h = ⅓ × 22/7 × 49 × 6 = 308 cm³.
The angles of a pentagon are x°, 2x°, 3x°, 2x° and 4x°. Find the value of x°.
The angles of a pentagon add up to 540°. 12x = 540, so x = 45.
A man finds the angle of elevation of the top of a tree 14m high to be 30°. Calculate the distance of the man from the foot of the tree to the nearest metre.
tan 30° = 14/d, so d = 14 ÷ 0.5774 = 24.2, which is 24 m.
Simplify 3x + 10y - 5x - 2y.
Collect like terms: 3x - 5x = -2x and 10y - 2y = 8y. So -2x + 8y = 2(4y - x).
Solve the equation: 1/t = 7/8.
Cross multiply: 7t = 8, so t = 8/7 = 1 1/7.
Factorise 5x + 30.
5 is common to both terms: 5x + 30 = 5(x + 6).
Find the coefficient of x in the expansion of (2x - 3)(x + 4).
(2x - 3)(x + 4) = 2x² + 8x - 3x - 12 = 2x² + 5x - 12. The coefficient of x is 5.
Simplify 1/2x + 1/3x.
The common denominator is 6x: 3/6x + 2/6x = 5/6x.
Find the sum of the coefficients of x in 3x + 1 - 2x + 6.
The coefficients of x are 3 and -2. Their sum is 3 + (-2) = 1.
Find the value of x in the equation 3x/4 = 12.
3x = 12 × 4 = 48, so x = 16.
Expand (a + b)².
(a + b)² = (a + b)(a + b) = a² + 2ab + b².
Which of the following options represents the solution of the inequality graph below?
The graph has a closed dot at 4½ and the arrow points to the right, so x ≥ 4½.
If y = 4x - 30, find the value of y when x = 5.
y = 4(5) - 30 = 20 - 30 = -10.
Find the H.C.F. of 6xy and 12x².
The H.C.F. of 6 and 12 is 6, and the common letter is x. So the H.C.F. is 6x.
Solve the equation 1/9 + x = 1/27.
x = 1/27 - 1/9 = 1/27 - 3/27 = -2/27.
Factorise: 3xy - 5x + 3y - 5.
Group the terms: x(3y - 5) + 1(3y - 5) = (x + 1)(3y - 5).
Solve 2/(x-3) = 4/(3x+5)
Cross multiply: 2(3x + 5) = 4(x - 3). 6x + 10 = 4x - 12, so 2x = -22 and x = -11.
Factorise completely (a - 3b)(2x - y) + (a - 3b)(x +7y).
Take out (a - 3b): (a - 3b)(2x - y + x + 7y) = (a - 3b)(3x + 6y) = 3(a - 3b)(x + 2y).
Expand (-5k) (x - 4k).
(-5k)(x) = -5kx and (-5k)(-4k) = +20k². So the answer is 20k² - 5kx.
Find the value of x in the simultaneous equation; 6x + 5y = 62, 4x - 5y = 8.
Add the two equations: 10x = 70, so x = 7.
Solve the inequality 3a ≥ 6a + 9.
3a - 6a ≥ 9, so -3a ≥ 9. Dividing by -3 reverses the sign: a ≤ -3.
Factorize 3xy² - 3xz².
Take out 3x: 3x(y² - z²). The difference of two squares gives 3x(y + z)(y - z).
Simplify (-7a) x (- 12b).
A negative times a negative is positive: 7 × 12 = 84, so 84ab.
Solve the inequality - 4 > 5x + 16.
-4 - 16 > 5x, so -20 > 5x. Dividing by 5: x < -4.
What is the value of m if 1 1/5 m = 24?
1 1/5 = 6/5. m = 24 × 5/6 = 20.
Solve the simultaneous equation; x + y = 3, 2x - y = 6.
Add the equations: 3x = 9, so x = 3. Then y = 3 - 3 = 0.
Simplify (p+2)/3 - 3p/5.
The common denominator is 15: (5(p + 2) - 3(3p))/15 = (5p + 10 - 9p)/15 = (-4p + 10)/15.
Which of the following line graphs represents the solution of 5 ≤ 3x - 1?
5 ≤ 3x - 1 gives 6 ≤ 3x, so x ≥ 2. The dot at 2 is closed (included) and the arrow points right.
Solve the equation 2/(3x-1) = 1/4.
Cross multiply: 3x - 1 = 8, so 3x = 9 and x = 3.
Simplify 2(b + 1) - (b + 2) (b -1).
2b + 2 - (b² + b - 2) = 2b + 2 - b² - b + 2 = -b² + b + 4.
Solve the equation 2 - (2x - 2) - (x -2) = 0.
2 - 2x + 2 - x + 2 = 0, so 6 - 3x = 0 and x = 2.
Find the sum of the coefficients of x in 5x + 8 - 7x + 9.
The coefficients of x are 5 and -7. Their sum is -2.
Which of the following line graphs represents the solution of 8x < 6x - 10?
8x - 6x < -10, so 2x < -10 and x < -5. The dot at -5 is open and the arrow points left. The correct graph is B.
Solve the equation 5/6 - 3z/4 = (2z - 1)/3
Multiply by 12: 10 - 9z = 8z - 4. So 14 = 17z and z = 14/17.
If p α v/r, find k when v = 3, r = 1 and p = 5.
p = kv/r, so 5 = k × 3/1. k = 5/3 = 1 2/3.
Solve the equation 5/(3x-1) = 4/2x.
Cross multiply: 5 × 2x = 4(3x - 1), so 10x = 12x - 4. Then 2x = 4 and x = 2.
Expand 2x(y-z) - 3x(-4y + 6z).
2xy - 2xz + 12xy - 18xz = 14xy - 20xz.
If z varies inversely as v, find constant k in terms of z and v.
z = k/v, so k = zv.
Find the value of x if x - 3 = 9.
x = 9 + 3 = 12.
The product of a certain number and 4 is equal to the number subtracted from 25. Find the number.
Let the number be n. 4n = 25 - n, so 5n = 25 and n = 5.
James adds 8 to a certain number and the result is 16. Find the number.
n + 8 = 16, so n = 8.
A boy is 2 years older than his sister. If the sum of their ages is 28 years, find their ages.
Let the sister's age be s. s + (s + 2) = 28, so s = 13 and the boy is 15.
A herdsman sells x cows and y rams. He makes a profit of N5,500.00 on each cow and N1,200.00 on each ram. Find his total profit in terms of x and y.
Profit = 5,500 × x + 1,200 × y.
The area of a rectangle varies directly as the square of its length. If the length is 2cm when the area is 12cm², find the area when the length in 3cm.
A = kL². 12 = k × 4, so k = 3. When L = 3, A = 3 × 9 = 27 cm².
If x α y, find k when x = 28 and y = 4.
x = ky, so k = 28 ÷ 4 = 7.
Find the mean of the following set of numbers; 3, 2, 4, 8, 3.
Mean = (3 + 2 + 4 + 8 + 3) ÷ 5 = 20 ÷ 5 = 4.
What is the median of 4.3, 2.1, 3.3, 4.1, 3.4?
In order: 2.1, 3.3, 3.4, 4.1, 4.3. The middle value is 3.4.
Find the mode of 0.31, 0.23, 0.13, 0.02, 0.13, 0.31, 0.23, 0.13, 0.32.
0.13 appears three times, more than any other number.
Use the information below to answer the next three questions. The scores obtained by students in an examination are as follows: 75, 49, 73, 71, 42, 51, 70, 55, 87, 66, 36, 68, 84, 48, 38. How many students scored above 70?
The scores above 70 are 75, 73, 71, 87 and 84, which is 5 students.
If the pass mark is 55, how many students failed?
The scores below 55 are 49, 42, 51, 36, 48 and 38, which is 6 students.
If the pass mark is 55, what percentage of the students passed?
There are 15 students and 6 failed, so 9 passed. 9 ÷ 15 × 100 = 60%.
Find the mean of the following set of numbers; 3.2, 6.8, 5.6, 4.4.
Sum = 3.2 + 6.8 + 5.6 + 4.4 = 20. Mean = 20 ÷ 4 = 5.
Determine the median of the following set of numbers; 3, 9, 8, 5, 4, 8, 7, 9, 6.
In order: 3, 4, 5, 6, 7, 8, 8, 9, 9. The 5th (middle) value is 7.
What is the mean of the following data; 14, 9, 11, 4, 6, 10, 23?
Sum = 14 + 9 + 11 + 4 + 6 + 10 + 23 = 77. Mean = 77 ÷ 7 = 11.
What is the sum of the mode and the median of the following data; 6, 5, 7, 8, 5, 3, 5, 4, 1, 3, 5.
In order: 1, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8. The median is the 6th value, 5. The mode is 5. Sum = 10.
Use the graph below to answer questions 53 to 55. (Questions 113 to 115 in this sheet.) What is the total number of animals in the farm?
The bars read: Goat 7, Sheep 8, Cow 9, Rabbit 12. Total = 7 + 8 + 9 + 12 = 36.
Which animal has the least number in the farm?
The goat has the shortest bar (7).
Find the average number of animals in the farm.
Average = 36 ÷ 4 = 9.
Find the range of the following set of numbers; 15, 17, 17, 8, 16, 2, 4, 3, 9, 2, 14.
Range = highest - lowest = 17 - 2 = 15.
What is the probability that an integer chosen at random between 1 and 10 inclusive is a prime?
The primes from 1 to 10 are 2, 3, 5 and 7 (4 numbers). Probability = 4/10 = 2/5.
Find the range of the following set of numbers; 0, 3, 3, 1, 0, 1, 2, 3, 4, 4, 5, 0.
Range = 5 - 0 = 5.
The table below shows the marks obtained by a set of students. Use the table to answer questions 59 and 60. Marks: 2, 3, 4, 5, 6 Frequency: 3, 2, 5, 2, 3 What is the probability that a student picked at random scored 4 marks?
There are 3 + 2 + 5 + 2 + 3 = 15 students and 5 scored 4 marks. 5/15 = 1/3.
What is the probability that a student scored at least 5 marks?
"At least 5" means 5 or 6 marks: 2 + 3 = 5 students. 5/15 = 1/3.
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