WAEC SSCE - General Mathematics - 1993 (Objective)

Question 1 Report

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

3.3cm

4.4cm Correct answer

5cm

5.5cm

6.6cm

Answer Details

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Question 2 Report

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.

20m

40√3m /3

Correct answer

20√3m

40√3m

60cm

Answer Details

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Angles Of Elevation And Depression

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Question 3 Report

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

5cm

6cm

10cm Correct answer

12cm

15cm

Answer Details

The area of a rhombus is half the product of the lengths of its diagonals. Therefore, if we know the area of the rhombus and one of its diagonals, we can use this formula to find the length of the other diagonal. Let's call the length of the first diagonal 12 cm, and let's call the length of the other diagonal d cm. The area of the rhombus is given as 60 cm\(^2\). We can write the formula for the area of a rhombus as: Area = (1/2) x (diagonal 1) x (diagonal 2) Substituting the values we know, we get: 60 = (1/2) x 12 x d Simplifying this equation, we get: 60 = 6d Dividing both sides by 6, we get: d = 10 Therefore, the length of the other diagonal is 10 cm. So, the answer is option C - 10cm.

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Integration

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Question 4 Report

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

22cm

33.5cm

43cm Correct answer

66cm

115.5cm

Answer Details

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Circles

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Question 5 Report

A die is rolled 200 times the outcomes obtained are shown in the table below.

Find the probability of obtaining 2.

0.002

0.015

0.15 Correct answer

0.2

Answer Details

To find the probability of obtaining 2, we need to look at the frequency of occurrence of 2 in the outcomes. From the table, we see that 2 appears 30 times out of 200. Therefore, the probability of obtaining 2 on a single roll of the die is: Probability of obtaining 2 = (number of times 2 appears) / (total number of rolls) Probability of obtaining 2 = 30 / 200 Probability of obtaining 2 = 0.15 Therefore, the probability of obtaining 2 is 0.15, which is.

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Probability

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Question 6 Report

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

1/6

1/3 Correct answer

2/3

1/2

5/6

Answer Details

A fair die has six possible outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Since we want to find the probability of obtaining a number less than 3, we need to count how many of these outcomes satisfy this condition. There are only two possible outcomes that satisfy this condition: 1 and 2. Therefore, the probability of obtaining a number less than 3 is 2 out of 6 possible outcomes or 2/6, which simplifies to 1/3. So, the answer is: - Probability = 1/3

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Question 7 Report

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

36^o

42^o

45^o

48^o

54^o Correct answer

Answer Details

To find the angle subtended by Ondo in the pie chart, we need to first calculate the total number of students in the Faculty of Science. Total number of students = 45 + 410 + 105 + 126 + 154 = 840 Next, we need to find the percentage of students from Ondo: Percentage of students from Ondo = (Number of students from Ondo / Total number of students) x 100 = (126/840) x 100 = 15 Since there are five states in total, and the pie chart represents 360 degrees, we can find the angle subtended by Ondo as follows: Angle subtended by Ondo = (Percentage of students from Ondo / 100) x 360 = (15/100) x 360 = 54 degrees Therefore, the answer is (e) 54^o.

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Question 8 Report

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

2⁷/₉%

2⁶/₇% Correct answer

27⁷/₉%

28⁴/₇%.

Answer Details

To find the percentage error, we need to first calculate the absolute error which is the difference between the measured value and the actual value. Absolute error = |1.80 - 1.75| = 0.05m Then, we can calculate the percentage error using the formula: Percentage error = (Absolute error / Actual value) x 100% Percentage error = (0.05 / 1.75) x 100% = 2.86% Therefore, the percentage error in the boy's measurement is approximately 2.86%. The closest option to this value is 2⁶/₇%.

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Percentages

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Question 9 Report

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

\(-\frac{81}{8}, -\frac{729}{32}\) Correct answer

\(\frac{8}{81}, \frac{72}{39}\)

\(\frac{27}{729}, \frac{718}{39}\)

\(-\frac{27}{16}, -\frac{79}{81}\)

\(-\frac{21}{8}, \frac{32}{618}\)

Answer Details

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Sequence And Series

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Question 10 Report

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

2/11 Correct answer

5/11

6/11

9/11

2/3

Answer Details

The set of integers from 20 to 30 is {20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30}. We need to find the probability of selecting a prime number from this set. Prime numbers are the numbers that are only divisible by 1 and themselves. The prime numbers in this set are 23 and 29. So, out of the 11 numbers in the set, only 2 are prime. Therefore, the probability of selecting a prime number from the set is 2/11. Hence, the answer is (a) 2/11.

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Probability

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Question 11 Report

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

(2s - t)(s + 2t)

(2s + t)(s - 2t) Correct answer

(s + t)(2s - 1)

(2s + t)(s -t)

(2s + t)(s + 2t)

Answer Details

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Algebraic Expressions

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Question 12 Report

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

(-3, 1)

(-1, -3)

(3,1)

(43, 0)

(-1, 3). Correct answer

Answer Details

To solve the equation x\(^2\) - 2x - 3 = 0, we can use the quadratic formula, which is given by: x = (-b ± sqrt(b\^2 - 4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation ax\^2 + bx + c = 0. Using the coefficients of the given equation, a=1, b=-2, and c=-3, we get: x = (-(-2) ± sqrt((-2)\^2 - 4(1)(-3))) / 2(1) x = (2 ± sqrt(16)) / 2 x = (2 ± 4) / 2 So the solutions of the equation are: x = 3 or x = -1 Therefore, the correct answer is: (-1, 3).

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Quadratic Equations

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Question 13 Report

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]

75cm²

84cm²

85cm² Correct answer

86cm²

95cm²

Answer Details

To find the area of a sector, we need to use the formula: Area of sector = (θ/360) x πr² where θ is the angle subtended at the centre of the circle, r is the radius of the circle, and π is a mathematical constant approximately equal to 22/7. In this case, the radius is given as 9cm and the angle is given as 120°. So, substituting these values into the formula, we get: Area of sector = (120/360) x (22/7) x 9² = (1/3) x (22/7) x 81 = 754/7 ≈ 107.71 cm² (rounded to the nearest cm²) Therefore, the correct answer is: 85 cm² (option C).

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Question 14 Report

Number	1	2	3	4	5	6
No of times	25	30	45	28	40	32

A die rolled 200 times. The outcome obtained are shown in the table above.

What is the probability of obtaining a number less than 3 ?

0.125

0.150

0.275 Correct answer

0.500

0.725

Answer Details

To find the probability of obtaining a number less than 3, we need to add up the number of times the die rolled a 1 or a 2, since these are the numbers less than 3. From the table, we see that the number of times the die rolled a 1 is 25 and the number of times it rolled a 2 is 30. So the total number of times the die rolled a number less than 3 is: 25 + 30 = 55 Therefore, the probability of obtaining a number less than 3 is: 55/200 = 0.275 So the answer is option C: 0.275.

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Question 15 Report

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

{1, 4, 5}

{2, 4, 5}

{1, 2, 4, 5} Correct answer

{2, 3, 4, 5}

{1, 2, 3, 4, 5}

Answer Details

The given problem involves set theory and requires finding the union and intersection of sets. We are given three sets: S, T, and R. Set S contains six elements, {1, 2, 3, 4, 5, 6}, set T contains four elements, {2, 4, 5, 7}, and set R contains three elements, {1, 4, 5}. First, we need to find the intersection of sets S and T, denoted as S∩T, which represents the elements that are common to both sets. The elements common to sets S and T are 2, 4, and 5. Next, we need to find the union of the intersection of sets S and T with set R, denoted as (S∩T) ∪ R, which represents all the elements that are in either set. The elements in (S∩T) ∪ R are {1, 2, 4, 5}. Therefore, the answer is {1, 2, 4, 5}.

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Positive And Negative Integers, Rational Numbers

Sets

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Question 16 Report

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,

250m

353m

354m

433m

500m Correct answer

Answer Details

We can use the trigonometric ratio tangent to solve this problem. Let h be the height of the tank. Then, we have: tan(45°) = h/500 Since tan(45°) = 1, we can simplify to: h/500 = 1 h = 500 Therefore, the height of the tank is 500 meters. Note that the answer is not in the options provided.

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Question 17 Report

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

1.5 x 10^-4

1.5 x 10^-2

1.5 x 10^-3

1.5 x 10¹

1.5 x 10² Correct answer

Answer Details

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Fractions, Decimals And Approximations

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Question 18 Report

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

1101001

1011001 Correct answer

1001101

101101

11001

Answer Details

To convert a decimal number to a binary number, we need to repeatedly divide the decimal number by 2 and take note of the remainder. The binary number is obtained by arranging the remainders in the reverse order. Here's the process for converting 89\(_{10}\) to binary: 1. Divide 89 by 2. The quotient is 44 and the remainder is 1. 2. Divide 44 by 2. The quotient is 22 and the remainder is 0. 3. Divide 22 by 2. The quotient is 11 and the remainder is 0. 4. Divide 11 by 2. The quotient is 5 and the remainder is 1. 5. Divide 5 by 2. The quotient is 2 and the remainder is 1. 6. Divide 2 by 2. The quotient is 1 and the remainder is 0. 7. Divide 1 by 2. The quotient is 0 and the remainder is 1. The remainders, taken in reverse order, are 1011001, which is the binary equivalent of 89\(_{10}\). Therefore, the correct answer is option (B) 1011001.

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Number Bases

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Question 19 Report

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

5/13

7/13

12/13

17/13 Correct answer

5/12

Answer Details

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Introductory Calculus

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Question 20 Report

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

120km

165km

195km Correct answer

(150 + 45√3)km

240km

Answer Details

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Circles

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Question 21 Report

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

34 sides

30 sides

26 sides

17 sides Correct answer

15 sides

Answer Details

The sum of the interior angles of a polygon with n sides is given by the formula (n - 2) x 180 degrees. Since a right angle is equal to 90 degrees, 30 right angles is equal to 30 x 90 = 2700 degrees. Thus, we can set up the equation: (n - 2) x 180 = 2700 Solving for n: n - 2 = 15 n = 17 Therefore, the polygon has 17 sides, so the answer is (d) 17 sides.

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Question 22 Report

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

(2x - 9)(x - 5)

(2x-15)(x + 3)

(2x +15)(x - 3)

(2x -15(x - 3) Correct answer

(2x - 9)(x + 5)

Answer Details

To factorize 2x\(^2\) - 21x + 45, we need to find two numbers that multiply to give 2\(\times\)45 = 90 and add to give -21. Let's factorize 90 to find such numbers: 90 = 1\(\times\)90 = 2\(\times\)45 = 3\(\times\)30 = 5\(\times\)18 = 6\(\times\)15 Out of these, the pair that adds up to -21 is 6 and 15. So, we can rewrite the expression as: 2x\(^2\) - 21x + 45 = 2x\(^2\) - 6x - 15x + 45 Now, we can group the first two terms and the last two terms separately and factorize them using the distributive law. That gives us: 2x\(^2\) - 6x - 15x + 45 = 2x(x - 3) - 15(x - 3) Notice that we have a common factor of (x - 3) in both terms. We can factor it out to get the final answer: 2x\(^2\) - 21x + 45 = (x - 3)(2x - 15) Therefore, the correct answer is (x - 3)(2x - 15).

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Question 23 Report

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

40^o Correct answer

45^o

50^o

90^o

130^o

Answer Details

Since sin x = cos 90 - x for any angle x, we can write: sin x = cos (90 - x) Given sin x = cos 50°, we can substitute to get: cos (90 - x) = cos 50° Taking the inverse cosine of both sides, we get: 90 - x = 50° Solving for x, we get: x = 40° Therefore, the answer is option A: 40°.

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Question 24 Report

How many student took the examination

24 Correct answer

Answer Details

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Question 25 Report

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

11^o

73^o

107^o Correct answer

138^o

149^o

Answer Details

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Circles

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Question 26 Report

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

r/12

12/r

1/6r

r/6

1/12r

Correct answer

Answer Details

To add or subtract fractions, we need to have a common denominator. Here, we have denominators of 6r and 4r. The least common multiple (LCM) of 6r and 4r is 12r. So, we need to convert each fraction so that it has a denominator of 12r. \(\frac{5}{6r} - \frac{3}{4r} = \frac{5 \cdot 4}{6r \cdot 4} - \frac{3 \cdot 3}{4r \cdot 3}\) Simplifying the resulting fractions, we get: \(\frac{20}{24r} - \frac{9}{12r} = \frac{20}{24r} - \frac{18}{24r}\) Now, we can combine the fractions by subtracting the numerators and keeping the same denominator: \(\frac{20}{24r} - \frac{18}{24r} = \frac{2}{24r}\) Finally, we can simplify the resulting fraction by dividing the numerator and the denominator by 2: \(\frac{2}{24r} = \frac{1}{12r}\) Therefore, the answer is:

1/12r

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Algebraic Fractions

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Question 27 Report

A cone is 14cm deep and the base radius is 41/2cm. Calculate the volume of water that is exactly half the volume of the cone.[Take π = 22/7]

49.5cm³

99cm³

148.5cm³ Correct answer

297cm³

445.5cm³

Answer Details

The volume of a cone is given by the formula: V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. The cone in the question has height 14 cm and base radius 4.5 cm. Therefore, its volume is: V = (1/3) × (22/7) × (4.5)² × 14 = 346.5 cm³ Half of this volume is: V/2 = 346.5/2 = 173.25 cm³ Therefore, the volume of water that is exactly half the volume of the cone is 173.25 cm³. The answer closest to this value is 148.5 cm³, so the correct option is: - 148.5cm³

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Volumes

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Question 28 Report

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

28°

40° Correct answer

44°

84°

124°

Answer Details

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Question 29 Report

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.

-2 Correct answer

Answer Details

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Sequence And Series

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Question 30 Report

What is the probability that the total sum of seven would appear in toss of a fair die?

5/36

1/6 Correct answer

7/36

5/6

Answer Details

When a fair die is rolled, there are 6 possible outcomes, each with an equal probability of 1/6. The only way to obtain a sum of 7 is by rolling a combination of (1,6), (2,5), (3,4), (4,3), (5,2), or (6,1). That means there are 6 possible ways to get a sum of 7 out of 36 possible outcomes. Therefore, the probability of obtaining a sum of 7 is 6/36, which simplifies to 1/6. So the answer is: 1/6.

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Probability

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Question 31 Report

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

29.5

28.5 Correct answer

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Surds (radicals)

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Question 32 Report

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?

20km

24km

25km Correct answer

31km

84km

Answer Details

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Question 33 Report

What is A?B in the diagram above?

(2,3)

(2,3,4) Correct answer

(1,2,3)

(2,3,8)

(6,4,7)

Answer Details

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Coordinate Geometry

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Question 34 Report

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

1/6

1/3

1/2 Correct answer

2/3

5/6

Answer Details

In a single toss of a fair die, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Out of these outcomes, three of them (2, 4, and 6) are even numbers. Therefore, the probability of getting an even number in a single toss of a fair die is 3 out of 6 or 1 out of 2. This can be expressed as a fraction of 1/2 or a decimal of 0.5. So, the correct answer is 1/2.

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Probability

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Question 35 Report

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

What is the mean of the distribution?

4.2

4.5

4.8 Correct answer

5.0

5.2

Answer Details

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Loci

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Question 36 Report

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

34^o

48^o

56^o Correct answer

68^o

73^o

Answer Details

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Circles

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Question 37 Report

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

(5,5) Correct answer

(5,6)

(6,5)

(9,4)

(9,5)

Answer Details

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Probability

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Question 38 Report

Cos 75^o has the same value as

cos 115^o

cos 255^o

cos 285^o Correct answer

-sin165^o

-sin 255^o

Answer Details

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Sine, Cosine And Tangent Of An Angle

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Question 39 Report

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

12.5 Correct answer

13.5

Answer Details

To find the median, we need to first arrange the set of numbers in order from least to greatest: 12, 12, 12, 13, 14, 15 The median is the middle number in the set. Since there are six numbers in this set, the middle number will be the average of the two middle numbers. In this case, the two middle numbers are 12 and 13, so their average is: (12 + 13) / 2 = 12.5 Therefore, the median of this set of numbers is 12.5. Option (B) is the correct answer.

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Sets

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Question 40 Report

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

1/6

3/8 Correct answer

1/2

3/4

Answer Details

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Surds (radicals)

Logarithms

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Question 41 Report

How many students scored less than 7 marks?

15 Correct answer

Answer Details

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Percentages

Linear Inequalities

Sets

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Question 42 Report

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

25/169

64/169

105/169

144/169 Correct answer

8/13

Answer Details

We know that sin x = opposite/hypotenuse = 12/13, therefore, the adjacent side of the right-angled triangle is √(13^2 - 12^2) = 5. Now, we need to find the value of 1 - cos^2x. Using the identity sin^2x + cos^2x = 1, we can write: cos^2x = 1 - sin^2x Substituting sin x = 12/13, we get: cos^2x = 1 - (12/13)^2 cos^2x = 1 - 144/169 cos^2x = 25/169 Therefore, 1 - cos^2x = 1 - 25/169 = 144/169. Hence, the answer is (d) 144/169.

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Question 43 Report

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

7/30

7/24

9/25

¹/₂ Correct answer

18/25

Answer Details

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Question 44 Report

Solve the inequality: 3m + 3 > 9

m > 2 Correct answer

m > 3

m>4

m>6

m>12

Answer Details

The inequality 3m + 3 > 9 can be solved by isolating m on one side of the inequality sign. First, subtract 3 from both sides to get 3m > 6. Then, divide both sides by 3 to get m > 2. Therefore, the solution to the inequality is m > 2, which means any value of m that is greater than 2 would make the inequality true. The correct label for the solution is "m > 2".

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Question 45 Report

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

¹/₄

2 Correct answer

Answer Details

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Indices

Logarithms

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Question 46 Report

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

.-2,-6

2,6 Correct answer

2,-6

-2,6

-1,-3

Answer Details

The first equation can be rearranged as x = y/3. Then substituting this value of x into the second equation, we get: 4y - 5(y/3) = 14 Multiplying both sides by 3, we get: 12y - 5y = 42 7y = 42 y = 6 Substituting y = 6 into the first equation, we get: x = y/3 = 2 Therefore, the solution to the simultaneous equations is x = 2 and y = 6. So the answer is 2,6.

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Solution Of Linear Equations

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Question 47 Report

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

15^o

25^o Correct answer

40^o

50^o

55^o

Answer Details

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Circles

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Question 48 Report

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

180 5/7cm²

240 2/7cm²

235 5/7cm²

282 6/7cm² Correct answer

361 3/7cm²

Answer Details

To find the total surface area of a cone, we need to add the area of the base and the curved surface area. Given that the base radius is 5cm, we can find the base area by using the formula for the area of a circle: Area of base = πr² = π(5)² = 25π To find the curved surface area, we need to first find the slant height of the cone. We can use the Pythagorean theorem to find this value: l = √(r² + h²) = √(5² + 12²) = √169 = 13cm Now, we can find the curved surface area using the formula: Curved surface area = πrl Curved surface area = π(5)(13) = 65π Therefore, the total surface area of the cone is: Total surface area = Base area + Curved surface area Total surface area = 25π + 65π = 90π Using the approximation π = 22/7, we get: Total surface area = 90π = 90(22/7) = 282.8571... cm² Rounding off to one decimal place, we get: Total surface area ≈ 282.9 cm² Therefore, the correct option is 4) 282 6/7cm².

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