WAEC - Mathematics (1993)

• 1

  S = {1, 2, 3, 4, 5, 6}, T = {2,4,5,7} and R = {1,4, 5}, and (S∩T) ∪ R

  Atsakymas

  (C)

  {1, 2, 4, 5}
• 2

  Simplify: \(\frac{3}{4} \div 1\frac{1}{4} \times (1\frac{1}{2} - \frac{2}{3})\)

  Atsakymas

  (D)

  ¹/₂
• 3

  Solve the inequality: 3m + 3 > 9

  Atsakymas

  (A)

  m > 2
• 4

  Convert 89\(_{10}\) to a number in base two.

  Atsakymas

  (B)

  1011001
• 5

  A stick of length 1.75m was measured by a boy as 1.80m. Find the percentage error in his measurement

  Atsakymas

  (B)

  2⁶/₇%
• 6

  The nth term of a sequence is given by (-1)\(^{n-2}\) x 2\(^{n-1}\). Find the sum of the second and third terms.

  Atsakymas

  (A)

  -2
• 7

  Simplify: \(\frac{4^{-\frac{1}{2}} \times 16^{\frac{3}{4}}}{4^{\frac{1}{2}}}\)

  Atsakymas

  (D)

  2
• 8

  Simplify: \(\frac{\log \sqrt{27}}{\log {81}}\)

  Atsakymas

  (B)

  3/8
• 9

  Factorize the expression 2s\(^2\) - 3st - 2t\(^2\).

  Atsakymas

  (B)

  (2s + t)(s - 2t)
• 10

  Solve the equation x\(^2\) - 2x - 3 = 0

  Atsakymas

  (E)

  (-1, 3).
• 11

  Write as a single fraction: \(\frac{5}{6r} - \frac{3}{4r}\)

  Atsakymas

  (E)

  1/12r
• 12

  Factorize 2x\(^2\) - 21x + 45

  Atsakymas

  (D)

  (2x -15(x - 3)
• 13

  Solve the simultaneous equations y = 3x; 4y - 5x =14

  Atsakymas

  (B)

  2,6
• 14

  A sector of a circle of radius 9cm subtends angle 120° at the centre of the circle. Find the area of the sector to the nearest cm\(^2\) [Take π = 22/7]

  Atsakymas

  (C)

  85cm²
• 15

  Calculate the total surface area of a cone of height 12cm and base radius 5cm. [Take π = 22/7]

  Atsakymas

  (D)

  282\(\frac{6}{7}\)cm\(^2\)
• 16

  A cone is 14cm deep and the base radius is 4\(\frac{1}{2}\)cm. Calculate the volume of water that is exactly half the volume of the cone.[Take π = \(\frac{22}{7}\)]

  Atsakymas

  (C)

  148.5cm³
• 17

  The area and a diagonal of a rhombus are 60 cm\(^2\) and 12 cm respectively. Calculate the length of the other diagonal.

  Atsakymas

  (C)

  10cm
• 18

  The angle of a sector of a circle radius 10.5cm is 120°. Find the perimeter of the sector [Take π = 22/7]

  Atsakymas

  (C)

  43cm
• 19

  

  In the diagram, PQR is a tangent to the circle QST at Q. If |QT| = |ST| and ∠SQR = 68°, find ∠PQT.

  Atsakymas

  (C)

  56^o
• 20

  The sum of an interior angles of a regular polygon is 30 right angles. How many sides has the polygon?

  Atsakymas

  (D)

  17 sides
• 21

  

  In the diagram above, |QR| = 12cm and |QS| = 10cm. If ∠PQR = 90°, ∠RSQ = 90° and PSQ is a straight line, find |PS|

  Atsakymas

  (B)

  4.4cm
• 22

  

  In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30^o and ∠PQR = 80^o. Find ∠SPQ.

  Atsakymas

  (B)

  25^o
• 23

  Two chords PQ and RS of a circle when produced meet at K. If ∠KPS = 31^o and ∠PKR = 42^o, find ∠KQR

  Atsakymas

  (C)

  107^o
• 24

  

  In the diagram above, QRS is a straight line, QP//RT, PRQ = 56°, ∠QPR =84° and ∠TRS = x°. Find x

  Atsakymas

  (B)

  40°
• 25

  Simplify \(\frac{2.25}{0.015}\) leaving your answer in standard form

  Atsakymas

  (E)

  1.5 x 10²
• 26

  State the fifth and seventh terms of the sequence \(-2, -3, -4\frac{1}{2}, ...\)

  Atsakymas

  (A)

  \(-\frac{81}{8}, -\frac{729}{32}\)
• 27

  A plane tiles 90km on a bearing 030° and then flies 150km due east. How far east of the starting point is the plane?

  Atsakymas

  (C)

  195km
• 28

  If sin x = cos 50^o, then x equals

  Atsakymas

  (A)

  40^o
• 29

  From a point on the edge of the sea, one ship is 24km away on a bearing S 50^oE and another ship is 7km away on a bearing S40^oW. How far apart are the ships?

  Atsakymas

  (C)

  25km
• 30

  Given that tan x = 5/12, what is the value of sin x + cos x ?

  Atsakymas

  (D)

  17/13
• 31

  Cos 75^o has the same value as

  Atsakymas

  (C)

  cos 285^o
• 32

  If sin x = 12/13, where 0° < x < 90°, find the value of 1 - cos\(^2\)x

  Atsakymas

  (D)

  144/169
• 33

  The angle of elevation of the top of a tower from a point on the horizontal ground, 40m away from the foot of the tower is 30o. Find the height of the tower.

  Atsakymas

  (B)

  40√3m /3
• 34

  At a point 500m from the base of a water tank the angle of elevation of the top of the tank is 45o. Find the height of the tank,

  Atsakymas

  (E)

  500m
• 35

  Find the median of the following set of numbers: 28, 29, 39, 38, 33, 37, 26, 20, 15, 25

  Atsakymas

  (D)

  28.5
• 36

  

  What is A∩B in the diagram above?

  Atsakymas

  (B)

  (2,3,4)
• 37

  

  The table above shows the scores of a group of 40 students in a physics test.

  If the mode is m and the median is n, then (m,n) is

  Atsakymas

  (A)

  (5,5)
• 38

  

  The table above shows the scores of a group of 40 students in a physics test

  What is the mean of the distribution?

  Atsakymas

  (C)

  4.8
• 39

  Find the median of the set of numbers 12, 15, 13, 14, 12, 12.

  Atsakymas

  (B)

  12.5
• 40

  The distribution by state of 840 students in the Faculty of Science of a Nigerian University in a certain session is as follows:

  Bendel	45
  kwara	410
  Ogun	105
  Ondo	126
  Oyo	154

   

  In a pie chart drawn to represent this distribution, the angle subtended by Ondo is

   

  Atsakymas

  (E)

  54^o
• 41

  

  How many student took the examination

  Atsakymas

  (E)

  24
• 42

  

  How many students scored less than 7 marks?

  Atsakymas

  (B)

  15
• 43

  What is the probability that an integer selected from the set of integers (20, 21, ...., 30) is a prime number?

  Atsakymas

  (A)

  2/11
• 44

  A fair die is rolled once. What is the probability of obtaining a number less than 3?

  Atsakymas

  (B)

  1/3
• 45

  What is the probability of having an even number in a single toss of a fair die?

  Atsakymas

  (C)

  1/2