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JAMB UTME Mathematics 2007 past questions and answers

This 2007 JAMB UTME Mathematics set has 40 practice questions. Try these 5 free sample questions, tap a question to reveal the answer and explanation. Then practise the whole 2007 set with instant marking.

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Sample JAMB UTME Mathematics 2007 questions

1. y varies directly as the square of x and inversely as z. If y = 12 when x = 2 and z = 3, find y when x = 3 and z = 2.
  1. 40.5
  2. 27
  3. 18
  4. 13.5

Answer: A. 40.5

Since y = kx^2/z, the first condition gives k = 9 and hence y = 9(3^2)/2 = 40.5.

2. The fourth term of an arithmetic progression is 17 and the ninth term is 37. Find the sum of its first 10 terms.
  1. 105
  2. 230
  3. 125
  4. 145

Answer: B. 230

The common difference is (37 - 17)/5 = 4 and the first term is 5, so S10 = 10(2(5) + 9(4))/2 = 230.

3. If n(A) = 28, n(B) = 21 and n(A intersection B) = 9, how many elements are in A union B?
  1. 31
  2. 38
  3. 40
  4. 58

Answer: C. 40

Using n(A union B) = n(A) + n(B) - n(A intersection B) gives 28 + 21 - 9 = 40.

4. Simplify (3x^2 - 12)/(x^2 - 4x + 4), for x not equal to 2.
  1. 3(x - 2)/(x + 2)
  2. 3(x + 2)/(x + 2)
  3. 3(x - 2)/(x - 2)
  4. 3(x + 2)/(x - 2)

Answer: D. 3(x + 2)/(x - 2)

Factoring the numerator and denominator gives 3(x - 2)(x + 2)/(x - 2)^2, which reduces to 3(x + 2)/(x - 2).

5. How many integers satisfy both 2x - 3 < 7 and x + 1 >= 0?
  1. 6
  2. 5
  3. 7
  4. 8

Answer: A. 6

The inequalities give -1 <= x < 5, so the six integers are -1, 0, 1, 2, 3 and 4.

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