46 questions. Try each one, then open the answer to check yourself and read the explanation.
Use the information below to answer questions 1 and 2. The weekly cost C of running a household of P people is given by the formula C = 180P + 450.
Find the weekly cost for 5 people
Answer: A (₦1,350)
C = 180 × 5 + 450 = ₦1,350.
A woman bought some certain number of oranges for ₦15 and sold them at ₦15.50. calculate the percentage profit or loss
Answer: A (3.33% profit)
Profit = ₦0.50 on ₦15, and 0.5/15 × 100 = 3.33% profit.
The time t (min) to cook meat is given by the formula t = 40m + 25 where m is the mass of the meat (kg).
Find how long it takes to cook a piece of meat of mass 1.2kg
Answer: C (1hr 13mins)
t = 40 × 1.2 + 25 = 73 minutes = 1 hr 13 mins.
The time t (min) to cook meat is given by the formula t = 40m + 25 where m is the mass of the meat (kg).
Find the mass of a piece of meat which takes 2hrs 9min to cook
Answer: B (2.6kg)
2 hrs 9 min = 129 min, so 40m = 104 and m = 2.6 kg.
The ages of two sisters are 11 and 8 years. In how many years time will the product of their ages be 208?
Answer: A (5 years)
(11 + x)(8 + x) = 208 gives x² + 19x − 120 = 0, (x + 24)(x − 5) = 0, so x = 5.
A plate costs ₦x and a bow costs ₦y. If the price of each is raised by ₦20, the ratio of their prices become 5:2 respectively. If the price of each is reduced by ₦5, the ratio becomes 5:1. Express the ratio x:y in its lowest term
Answer: B (4:1)
2(x + 20) = 5(y + 20) and x − 5 = 5(y − 5) give y = 20 and x = 80, so x:y = 4:1.
The product of two consecutive positive odd numbers is 195. Find the two numbers
Answer: B (13 and 15)
n(n + 2) = 195 gives n² + 2n − 195 = 0, (n + 15)(n − 13) = 0, so the numbers are 13 and 15.
A student bought some packets of pens for ₦2,160. If she had paid ₦24 less for each packet, she could have bought three more packets. How many packets did she buy?
Answer: C (15)
(2160/x − 24)(x + 3) = 2160 simplifies to x² + 3x − 270 = 0, so x = 15 (check: ₦144 each; ₦120 × 18 = ₦2,160).
A trader buys t tins of milk for n naira and sells them at m naira each. What is the profit?
Answer: D (tm − n)
He receives tm naira for t tins, and they cost n naira, so profit = tm − n.
If 4x−1 = 8, find x
Answer: B (2½)
2^(2x − 2) = 2³, so 2x − 2 = 3 and x = 2½.
The first term of an arithmetic progression is 8. If the tenth term doubles the second term, find the common difference
Answer: A (8/7)
8 + 9d = 2(8 + d) gives 7d = 8, d = 8/7.
In a class of 40 students, 15 offer physics, 20 offer history and 3 offer both physics and history. How many students offer neither physics nor history?
Answer: D (8)
At least one subject: 15 + 20 − 3 = 32, so neither = 40 − 32 = 8.
A sum of money is shared between the students so that the first gets ₦80, the next gets ₦105, the next, ₦130 and so on. How much does the tenth student get?
Answer: B (₦305)
An AP with a = 80 and d = 25: T₁₀ = 80 + 9 × 25 = ₦305.
Calculate the amount if simple interest is paid yearly at 12% per annum for 3years on a principal of ₦150,000
Answer: A (₦204,000)
I = 150,000 × 12 × 3/100 = ₦54,000, so the amount is ₦204,000.
A radio costs ₦16,000 and depreciates by 25% in the first year and by 20% in the second years. Find its value after 2 years
Answer: C (₦9,600)
16,000 × 0.75 = 12,000, then 12,000 × 0.8 = ₦9,600.
A woman borrowed ₦500,000 from a lender and pays interest at 12% per annum. If she repaid ₦100,000 at the end of each year, what amount does she owe at the end of two years?
Answer: C (₦415,200)
Year 1: 500,000 × 1.12 − 100,000 = 460,000. Year 2: 460,000 × 1.12 − 100,000 = ₦415,200.
The fourth term of an arithmetic progression (A.P) is 1 less than twice the second term. If the sixth term is 7, find the first term
Answer: B (2)
a + 3d = 2(a + d) − 1 gives d = a − 1; a + 5d = 7 gives 6a − 5 = 7, so a = 2.
log10(3x + 1) + log10(½) − log10(2x − 5) = 0
Answer: A (11)
(3x + 1)/(2(2x − 5)) = 1, so 3x + 1 = 4x − 10 and x = 11.
The probabilities that kwakye and sekyere will pass an examination are 2/3 and 3/4 respectively. If both of them take the examination, find the probability that exactly one of them would pass
Answer: C (5/12)
(2/3)(1/4) + (1/3)(3/4) = 2/12 + 3/12 = 5/12.
The mean of marks scored by 3 students in a test is 9. If the modal mark is 11, find the lowest mark
Answer: B (5)
The total is 27; the mode 11 must appear twice (22), so the lowest mark is 27 − 22 = 5.
A trader bought an article in Sierra Leone at Le 360,000. He paid 25% of the cost price as import duty on entering Nigeria. If the rate of exchange is ₦1.00 = Le 16.00, how much, in naira, did he pay as import duty?
Answer: B (₦5,625)
Duty = 25% of Le 360,000 = Le 90,000 = 90,000 ÷ 16 = ₦5,625.
9 notebooks cost ₦364.5. How many can be bought for ₦526.50?
Answer: A (13)
One notebook costs 364.5 ÷ 9 = ₦40.50, and 526.50 ÷ 40.50 = 13.
In a certain year, a new bed cost ₦16,000. If the rate of inflation was 50% for the next two years, what would the same bed cost at the end of this period
Answer: B (₦36,000)
Each year the price rises by half: 16,000 → 24,000 → ₦36,000.
Find the amount if simple interest is paid on ₦150,000 at 12% per annum for 3 years.
Answer: A (₦204,000)
Interest = 150,000 × 0.12 × 3 = ₦54,000; amount = ₦204,000.
The ages of a parent and child add up to 39 years. In 3 years the parent will be 4 times as old as the child. Find the ages of the parent and the child. Assuming the age of the parent and child are x and y respectively
Answer: A (x = 33 years, y = 6 years)
x + y = 39 and x + 3 = 4(y + 3) give 5y = 30, so y = 6 and x = 33.
A die is rolled once. What is the probability of obtaining a prime number or a number greater than 5?
Answer: A (2/3)
Primes 2, 3, 5 or the number 6: four outcomes out of six, 4/6 = 2/3.
Sule; Tayo and Uche agreed to share the expenses for an evening out in the ratio of 2:3:4 respectively. Sule paid 2030 for the taxi, Tayo paid ₦4,900 for food and Uche paid ₦3,150 for the cinema. How much should Sule and Uche pay Tayo to settle their agreed shares?
Answer: C (Sule = ₦210 Uche = ₦1,330)
Total ₦10,080. Shares: Sule 2/9 = ₦2,240, Uche 4/9 = ₦4,480. Sule owes 2,240 − 2,030 = ₦210 and Uche 4,480 − 3,150 = ₦1,330.
Find the sum to infinity of the GP 9 − 3 + 1...
Answer: D (6¾)
a = 9, r = −1/3, so S∞ = 9 ÷ (4/3) = 27/4 = 6¾.
A sack of grain can feed 80 chickens for 18 days. How many days will it last 120 chickens?
Answer: B (12)
80 × 18 = 1,440 chicken-days, and 1,440 ÷ 120 = 12 days.
A hall contains 175 people, 12% of them are children and there are 56 men. How many women are there in the hall
Answer: C (98)
Children = 12% of 175 = 21; women = 175 − 21 − 56 = 98.
A car which cost ₦1.8million when new depreciates by about 12% in the first 6 months. Find its value after 6 months to 2s.f.
Answer: B (₦1.6m)
1,800,000 × 0.88 = ₦1,584,000 ≈ ₦1.6m (2 s.f.).
Simplify 25½ × 8−⅔
Answer: B (1¼)
25^½ = 5 and 8^(−2/3) = 1/4, so the product is 5/4 = 1¼.
The first term of an Arithmetic Progression (AP) is −7 and the ratio of the 8th term to the 3rd term is 7:1. Calculate the common difference of the A.P
Answer: A (6)
−7 + 7d = 7(−7 + 2d) gives −7d = −42, so d = 6.
Find the value of x for which (x − 2)2 : (x + 3)2 = 1 : 4
Answer: A (1/3 or 7)
2(x − 2) = ±(x + 3), giving x = 7 or 3x = 1, x = 1/3.
A boy thinks of a number. He squares it and subtracts from it the original number, the result is 42. What is the number?
Answer: B (7 or −6)
x² − x − 42 = 0, (x − 7)(x + 6) = 0, so x = 7 or −6.
In a class of 40 students, 30 take agriculture and 20 take physics. If 8 students take neither agriculture nor physics, find the number of students who take agriculture but not physics
Answer: C (12)
32 take at least one, so both = 30 + 20 − 32 = 18, and agriculture only = 30 − 18 = 12.
In a fund-raising lottery, 42% of the money collected is given as cash prizes. There are eight cash prizes altogether. The first price winner gets ₦3,500, the second gets ₦3,100, the third gets ₦2,700 and so on.
How much money does the eight persons get?
Answer: B (₦700)
Prizes form an AP with a = 3,500 and d = −400: the 8th prize is 3,500 − 7 × 400 = ₦700.
In a fund-raising lottery, 42% of the money collected is given as cash prizes. There are eight cash prizes altogether. The first price winner gets ₦3,500, the second gets ₦3,100, the third gets ₦2,700 and so on.
How much price money is there altogether?
Answer: A (₦16,800)
S₈ = 8/2 × (2 × 3,500 + 7 × (−400)) = 4 × 4,200 = ₦16,800.
In an examination; Adenike obtained 19 marks more than Musa. If Adenike had obtained one and a half times her own mark, she would have scored 6 marks more than twice Musa's mark. Find the marks scored by each. Representing Musa with M and Adenike with A.
Answer: B (M = 45, A = 64)
1.5(M + 19) = 2M + 6 gives 0.5M = 22.5, M = 45 and A = 64.
Five years ago, a mother was twice as old as her son. In 6 years time, the sum of their ages will be 82. Find their present ages
Answer: B (25years, 45 years)
m − 5 = 2(s − 5) and m + s + 12 = 82 give s = 25 and m = 45.
A street trader spent ₦550 on x articles, each costs ₦(2x − 28). Find x
Answer: D (25)
x(2x − 28) = 550 gives x² − 14x − 275 = 0, (x − 25)(x + 11) = 0, so x = 25.
If 13 times a number is subtracted from the square of the number, the result is 30. Find the number
Answer: B (15 or −2)
x² − 13x − 30 = 0, (x − 15)(x + 2) = 0, so x = 15 or −2.
Find the sum of all the multiples of 7 between 0 and 300
Answer: B (6321)
7, 14, …, 294 is an AP of 42 terms, so the sum is 42/2 × (7 + 294) = 6,321.
There are twelve cards numbered 1 to 12. A card is selected at random, what is the probability that it is either even or a perfect square
Answer: D (2/3)
Even: 2, 4, 6, 8, 10, 12; perfect squares: 1, 4, 9. Together (4 counted once) that is 8 cards, so 8/12 = 2/3.
The nth term of a sequence is n2 − n − 2. Find the sum of its first and third terms
Answer: C (2)
U₁ = 1 − 1 − 2 = −2 and U₃ = 9 − 3 − 2 = 4, so the sum is 2.
If z = √(x2 − y2), express x interms of y and z
Answer: A (x = √(z2 + y2))
Square: z² = x² − y², so x² = z² + y² and x = √(z² + y²).