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JAMB UTME Mathematics 2023 past questions and answers

This 2023 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 2023 set with instant marking.

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Sample JAMB UTME Mathematics 2023 questions

1. If theta is an acute angle and sin(theta) = 3/5, find tan(theta).
  1. 3/4
  2. 4/3
  3. 3/5
  4. 4/5

Answer: A. 3/4

The corresponding right triangle has opposite side 3 and hypotenuse 5, so its adjacent side is 4 and tan(theta) = 3/4.

2. A chord of a circle of radius 13 cm is 5 cm from the centre. Find the length of the chord.
  1. 10 cm
  2. 24 cm
  3. 26 cm
  4. 12 cm

Answer: B. 24 cm

The perpendicular from the centre bisects the chord, giving a half-chord of sqrt(13^2 - 5^2) = 12 cm, so the full chord is 24 cm.

3. Differentiate y = x^3 - 4x^2 + 2x with respect to x.
  1. 3x^2 - 4x + 2
  2. x^2 - 8x + 2
  3. 3x^2 - 8x + 2
  4. 3x^2 - 8x

Answer: C. 3x^2 - 8x + 2

Applying the power rule term by term gives dy/dx = 3x^2 - 8x + 2.

4. Find the mean of 4, 7, 8 and 11.
  1. 6.5
  2. 7
  3. 8
  4. 7.5

Answer: D. 7.5

The sum is 30 and 30 divided by the four observations is 7.5.

5. A bag contains 3 red and 2 blue balls. Two balls are drawn one after the other without replacement. What is the probability that both are red?
  1. 3/10
  2. 1/5
  3. 2/5
  4. 1/2

Answer: A. 3/10

The probability is (3/5)(2/4) = 3/10.

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