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Unilorin Post-UTME Mathematics 2014 (Model questions) past questions and answers

8 questions. Try each one, then open the answer to check yourself and read the explanation.

Question 26

Commercial Arithmetic

A car costing ₦ 10; 500 was incurred at 5% simple interest per annum. Find the interest the car would have yielded in 8 years

  1. A.₦4,000
  2. B.₦4,200
  3. C.₦3,000
  4. D.₦4,500
Show the answer and explanation

Answer: B (₦4,200)

Explanation

I = PRT/100 = 10,500 × 5 × 8/100 = ₦4,200.

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Question 28

Linear and Simultaneous Equations

If Ade deserves twice as many marks as Bayo and Bayo deserves half as many marks as Tunde. How many marks does Bayo receive when their total marks is 225

  1. A.45
  2. B.135
  3. C.90
  4. D.75
Show the answer and explanation

Answer: A (45)

Explanation

Ade = 2B and Tunde = 2B, so 5B = 225 and B = 45.

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Question 29

Quadratic Equations

Find the number such that when it is added to 3 and the sum is halved; the result is the same as when 5 is divided by the number

  1. A.2 or 5
  2. B.2 or 5
  3. C.−5 or 2
  4. D.−2 or −5
Show the answer and explanation

Answer: C (−5 or 2)

Explanation

(x + 3)/2 = 5/x gives x2 + 3x − 10 = 0, so x = 2 or −5.

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Question 30

Sets

In a class, 37 students takes at least one of Chemistry, Economics and Government. 8 students take Chemistry, 19 take Economics and 25 take Government. 12 students take Economics and Government but nobody takes Chemistry and Economics. How many students take both Chemistry and Government?

  1. A.3
  2. B.4
  3. C.5
  4. D.6
Show the answer and explanation

Answer: A (3)

Explanation

37 = 8 + 19 + 25 − 12 − 0 − x (no one takes all three, since no one takes Chemistry and Economics), so x = 3.

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Question 32

Algebraic Expressions

If w donuts cost c cents, how many donuts can you get for d dollars?
Note: (1 dollar = 100 cents)

  1. A.dw/(100c)
  2. B.100dw/c
  3. C.100dw
  4. D.dw
Show the answer and explanation

Answer: B (100dw/c)

Explanation

d dollars = 100d cents, and each cent buys w/c donuts, so you get 100dw/c donuts.

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Question 33

Commercial Arithmetic

A bookshop had 650 copies of a book for sale. The books were marked at ₦75 per copy in order to make a profit of 30%. A book seller bought 300 copies at 5% discount. If the remaining copies are sold at ₦75 each. Calculate the percentage profit the bookshop would make on the whole?

  1. A.18%
  2. B.20%
  3. C.27%
  4. D.16%
Show the answer and explanation

Answer: C (27%)

Explanation

Cost = 650 × 75 ÷ 1.3 = ₦37,500. Sales = 300 × 75 × 0.95 + 350 × 75 = ₦47,625. Profit = 10,125/37,500 = 27%.

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Question 34

Linear and Simultaneous Equations

An investor invested ₦x in bank M at the rate of 6% simple interest per annum and ₦y in bank N at the rate of 8% simple interest per annum. If a total of ₦8,000,000.00 was invested in the two banks and the investor received a total of ₦2,320,000.00 as interest from the two banks after 4 years, calculate: The value of x nad y

  1. A.x = 2M, y = 6cm
  2. B.x = 3M, y = 5M
  3. C.x = 2M, y = 8M
  4. D.x = 5M, y = 5M
Show the answer and explanation

Answer: B (x = 3M, y = 5M)

Explanation

x + y = 8,000,000 and 0.24x + 0.32y = 2,320,000 give 0.08y = 400,000, so y = 5M and x = 3M.

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Question 35

Commercial Arithmetic

An investor invested ₦x in bank M at the rate of 6% simple interest per annum and ₦y in bank N at the rate of 8% simple interest per annum. If a total of ₦8,000,000.00 was invested in the two banks and the investor received a total of ₦2,320,000.00 as interest from the two banks after 4 years, calculate: Interest paid by the second bank

  1. A.₦1,880,000
  2. B.₦20,000,000
  3. C.₦1,600,000
  4. D.₦1,500,000
Show the answer and explanation

Answer: C (₦1,600,000)

Explanation

Bank N holds ₦5,000,000 at 8% for 4 years: 5,000,000 × 8 × 4/100 = ₦1,600,000.

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