OAU Mathematics 2009/2010 Past Questions

Question 1

The expression a³ + b³ is equal to

A.(a² + b)(a - ab + b²)
B.(a + b)(a² - ab + b²)
C.(a - b²)(a² - ab + b²)
D.(a - b)(a²+ ab + b²)

Objective

Question 2

Factorize 16(3x + 2y)² — 25(a + 2b)²

A.(12x + 8y - 5a - 10b)(12x + 8y - 5a - 10b)
B.20(3x + 2y - a - 2b)(3x + 2y + a + 1 - 2b)
C.(12x + 8y + 5a + 10b)(12x + 8y - 5a - 10b)
D.20(3x + 2y + a + 2b)(3x + 2y + a + 2b)

Objective

Question 3

A cone has base radius 4cm and height 3cm. The area of its curved surface is

A.12πcm²
B.20πcm²
C.24πcm²
D.15πcm²

Objective

Question 4

A cylinder has height 4cm and base radius 5cm. its volume to 3 significant figure is

A.314.2cm²
B.31.42 cm²
C.251.4 cm²
D.251 cm²

Objective

Question 5

Let 3logx + logy = 3. Then, y is

A.(x/10)³
B.(x/10)^-3
C.(10/x)^-3
D.(10/x)³

Objective

Question 6

If ${x^2}/{a^2} - {y^2}/{b^2} = 1$, then y is

A.±b/a√(a² - x²)
B.±b/a√(x² - a²)
C.√(a² - x²)
D.±a/b√(a² - x²)

Objective

Question 7

A cyclist rode for 30 minutes at x km/hr and due to a breakdown, he had to push the hike for 2hrs at (x - 5)km/hr. if the total distance covered is less than 60km, what is the range of values for x?

A.x < 14
B.x < 29
C.x < 28
D.x < 20

Objective

Question 8

The expression ax² + bx takes the value 6 when x = 1 and 10 when x = 2. Find its value when x = 5

A.10
B.12
C.6
D.-10

Objective

Question 9

Dividing 2x³ - x² - 5x + 1 by x + 3 gives the remainder

A.-3
B.47
C.61
D.-47

Objective

Question 10

Let f(x) = 2x³ - 3x² - 5x + 6. If x - 1 divides f(x) find the zero of the function.

A.1, 2, 3/2
B.1, 2, -3/2
C.-1, 2, 3,
D.1, -2, -3/2

Objective

Question 11

The difference of two numbers is 10, while their product is 39. Find these numbers

A.-3 and 10 or 13 and 10,
B.3 and -10 or 3 and 13,
C.3 and -3 or 3 and 13,
D.-3 and -13 or 13 and 3

Objective

Question 12

The average age of x pupils in a class is 14 years 2 months. A pupil of 15 years 2 months joins the class and the average age is increased by one month. Find x.

A.12
B.6
C.11
D.14

Objective

Question 13

All the 120 pupils in a school learn Yoruba or Igbo or both. Given that 75 learn Yoruba and 60 learn Igbo. How many learn both languages?

A.60
B.45
C.15
D.120.

Objective

Question 14

All the 120 pupils in a school learn Yoruba or Igbo or both. Given that 75 learn Yoruba and 60 learn Igbo. How many learn Igbo only?

A.45
B.30
C.15
D.60

Objective

Question 15

Suppose we have matrices A = $(\table 1, -1; 2, 3)$ and B = $(\table 0, 2; 4, 3)$
Find $A^2$ + AB - 2A

A.({-5, -5}, {12, 14})
B.({-1, -4}, {8, 7})
C.({-4, -4}, {12, 13})
D.({0, -4}, {-8, -6})

Objective

Question 16

Evaluate the integral $∫^2 _1 (x^2 + 1/x)dx$

A.8/3 + In2
B.7/3 + In2,
C.7/3 - In3
D.8/3

Objective

Question 17

If the distance covered by a body in time t seconds is s = t³ - 6t² - 5t, what is its initial velocity?

A.0ms^-1
B.-4 ms^-1
C.(13t² - 12t + 5) ms^-1
D.5ms^-1

Objective

Question 18

Suppose D,E and P are subset of a universal set U. Let U be the set of natural numbers not greater than 10, while D,E and P are respectively the set of odd numbers, even numbers and prime numbers. For any set X, its complement X and Q denote the empty set.

Display the set D ∩ P

A.{3,5,7)
B.{2}
C.{4,6,8,10}
D.{2,3,5,7}

Objective

Question 19

Suppose D,E and P are subset of a universal set U. Let U be the set of natural numbers not greater than 10, while D,E and P are respectively the set of odd numbers, even numbers and prime numbers. For any set X, its complement X and Q denote the empty set.

Find D ∩ E

A.{2}
B.{3,5}
C.{1,2,3,4,5,6,7,8,9,10}
D.∅

Objective

Question 21

A bag contains 10 balls of which 3 are red and 7 are white. Two balls are drawn at random. Find the probability if none of the balls is red if the draw is with replacement

A.0.9
B.1
C.0.4
D.0.49

Objective

Question 22

A bag contains 10 balls of which 3 are red and 7 are white. Two balls are drawn at random. Find the probability if none of the balls is red if the draw is without replacement

A.0.1
B.0.47
C.0.42
D.0.21

Objective

Question 23

In a throw of a fair die, the probability of obtaining an even number is

A.1
B.2/3
C.1/6
D.2/3

Objective

Question 24

Two fair coins are tossed simultaneously. What is the probability of obtaining at least 1 tail turns up?

A.1/4
B.3/4
C.1/2
D.1

Objective

Question 25

Let α and β be the roots of the equation x^2 - 5x + 4 = 0. Find the values of 1/α - 1/β

A.±4/3
B.3/4
C.±3/4
D.1/5

Objective

Question 27

One angle of an octagon is 100° while the other sides are equal. Find each of these exterior angles.

A.80°
B.60°
C.140°
D.40°

Objective