passwella.
Menu

UI Post-UTME Mathematics 2021 (Model questions) past questions and answers

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

Question 5

Surds

Simplify 4√27 + 5√12 − 3√75

  1. A.7
  2. B.−7
  3. C.−7√3
  4. D.7√3
Show the answer and explanation

Answer: D (7√3)

Explanation

12√3 + 10√3 − 15√3 = 7√3.

Open this question

Question 6

Polynomials

What is the quotient if 4x3 − 3x + 1 is divided by 2x − 1?

  1. A.2x2 + x − 1
  2. B.2x2 − x + 1
  3. C.2x2 − x − 1
  4. D.2x2 + x + 1
Show the answer and explanation

Answer: A (2x2 + x − 1)

Explanation

Check: (2x − 1)(2x² + x − 1) = 4x³ + 2x² − 2x − 2x² − x + 1 = 4x³ − 3x + 1.

Open this question

Question 7

Binary Operations

The operation * on the set ℝ of real number is defined by x * y = 3x + 2y − 1, find 3 * −1

  1. A.6
  2. B.−6
  3. C.9
  4. D.−9
Show the answer and explanation

Answer: A (6)

Explanation

3 * (−1) = 3(3) + 2(−1) − 1 = 9 − 2 − 1 = 6.

Open this question

Question 9

Coordinate Geometry

If the line y = 5x + 3 is parallel to the line y = wx + 5. Find the value of w

  1. A.7
  2. B.5
  3. C.6
  4. D.3
Show the answer and explanation

Answer: B (5)

Explanation

Parallel lines have the same gradient, so w = 5.

Open this question

Question 10

Mensuration of Plane Shapes

An arc of the length 16πcm subtends an angle of 80° at the centre of the circle. Find the radius of the circle

  1. A.32cm
  2. B.36cm
  3. C.28cm
  4. D.24cm
Show the answer and explanation

Answer: B (36cm)

Explanation

(80/360) × 2πr = 16π gives (4/9)r = 16, so r = 36 cm.

Open this question

Question 12

Number Bases

Given that 23x + 101x = 130x, find the value of x

  1. A.4
  2. B.5
  3. C.6
  4. D.7
Show the answer and explanation

Answer: A (4)

Explanation

(2x + 3) + (x² + 1) = x² + 3x, so x = 4.

Open this question

Question 16

Triangles and Quadrilaterals

From the diagram, find the value of RÔP

Diagram for this question
  1. A.95°
  2. B.85°
  3. C.70°
  4. D.110°
Show the answer and explanation

Answer: A (95°)

Explanation

PQRO is a cyclic quadrilateral; the exterior angle RQ̂T (95°) equals the interior opposite angle RÔP.

Open this question

Question 17

Algebraic Expressions

If N = (P/2)((T1 − T2)/T1). Find P when N = 12, T1 = 27 and T2 = 24

  1. A.216
  2. B.54
  3. C.106
  4. D.48
Show the answer and explanation

Answer: A (216)

Explanation

12 = (P/2)(3/27) = P/18, so P = 216.

Open this question

Question 19

Trigonometry

If cos θ = x and sin 60° = x + 0.5, where 0° < θ < 90°. Find correct to the nearest degree, the value of θ

  1. A.40°
  2. B.60°
  3. C.69°
  4. D.32°
Show the answer and explanation

Answer: C (69°)

Explanation

x = 0.8660 − 0.5 = 0.366, so θ = cos⁻¹ 0.366 ≈ 68.5° ≈ 69°.

Open this question

Question 21

Trigonometry

If x + y = 90, simplify (sin x + sin y)2 − 2 sin x sin y

  1. A.0
  2. B.1
  3. C.−1
  4. D.2
Show the answer and explanation

Answer: B (1)

Explanation

sin y = sin(90° − x) = cos x, so the expression is (sin x + cos x)² − 2 sin x cos x = sin²x + cos²x = 1.

Open this question

Question 22

Coordinate Geometry

Find the equation of a line which is from the origin and passes through the point (−3, −4)

  1. A.y = 3x/4
  2. B.y = 4x/3
  3. C.y = 2x/3
  4. D.y = x/2
Show the answer and explanation

Answer: B (y = 4x/3)

Explanation

Through the origin the gradient is −4/−3 = 4/3, so y = 4x/3.

Open this question

Question 23

Indices

If (27x × 31−x)/92x = 1, what is the value of x?

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

Answer: C (1/2)

Explanation

3^(3x + 1 − x − 4x) = 3⁰, so 1 − 2x = 0 and x = 1/2.

Open this question

Question 25

Probability

The probability that Olu, Ade and shola will hit a target are 2/3, 3/4 and 4/5 respectively. Find the probability that only Olu will hit the target

  1. A.7/60
  2. B.1/30
  3. C.1/60
  4. D.2/5
Show the answer and explanation

Answer: B (1/30)

Explanation

Olu hits and the other two miss: 2/3 × 1/4 × 1/5 = 2/60 = 1/30.

Open this question