WAEC SSCE - General Mathematics - 1993…

Vraag 1 Verslag

Cos 75^o has the same value as

cos 115^o

cos 255^o

cos 285^o Juist antwoord

-sin165^o

-sin 255^o

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Vraag 2 Verslag

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% Juist antwoord

27⁷/₉%

28⁴/₇%.

Antwoorddetails

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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Vraag 3 Verslag

How many students scored less than 7 marks?

15 Juist antwoord

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Vraag 4 Verslag

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

¹/₄

2 Juist antwoord

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Vraag 5 Verslag

How many student took the examination

24 Juist antwoord

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Vraag 6 Verslag

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 Juist antwoord

66cm

115.5cm

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Circles

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Vraag 7 Verslag

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

15^o

25^o Juist antwoord

40^o

50^o

55^o

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Vraag 8 Verslag

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 Juist antwoord

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Fractions, Decimals And Approximations

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Vraag 9 Verslag

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 Juist antwoord

0.2

Antwoorddetails

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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Vraag 10 Verslag

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

(-3, 1)

(-1, -3)

(3,1)

(43, 0)

(-1, 3). Juist antwoord

Antwoorddetails

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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Vraag 11 Verslag

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

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

(2s + t)(s - 2t) Juist antwoord

(s + t)(2s - 1)

(2s + t)(s -t)

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

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Vraag 12 Verslag

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

\(-\frac{81}{8}, -\frac{729}{32}\) Juist antwoord

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

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

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

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

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Vraag 13 Verslag

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

28°

40° Juist antwoord

44°

84°

124°

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Vraag 14 Verslag

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 Juist antwoord

5.0

5.2

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Vraag 15 Verslag

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

1/6

3/8 Juist antwoord

1/2

3/4

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Surds (radicals)

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Vraag 16 Verslag

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 Juist antwoord

8/13

Antwoorddetails

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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Vraag 17 Verslag

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

r/12

12/r

1/6r

r/6

1/12r

Juist antwoord

Antwoorddetails

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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Vraag 18 Verslag

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 Juist antwoord

18/25

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Vraag 19 Verslag

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

5/36

1/6 Juist antwoord

7/36

5/6

Antwoorddetails

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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Vraag 20 Verslag

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 Juist antwoord

361 3/7cm²

Antwoorddetails

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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Vraag 21 Verslag

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

2/11 Juist antwoord

5/11

6/11

9/11

2/3

Antwoorddetails

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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Vraag 22 Verslag

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 Juist antwoord

0.500

0.725

Antwoorddetails

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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Vraag 23 Verslag

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} Juist antwoord

{2, 3, 4, 5}

{1, 2, 3, 4, 5}

Antwoorddetails

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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Vraag 24 Verslag

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

29.5

28.5 Juist antwoord

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Vraag 25 Verslag

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 Juist antwoord

31km

84km

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Vraag 26 Verslag

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

40^o Juist antwoord

45^o

50^o

90^o

130^o

Antwoorddetails

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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Vraag 27 Verslag

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

Juist antwoord

20√3m

40√3m

60cm

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Vraag 28 Verslag

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 Juist antwoord

86cm²

95cm²

Antwoorddetails

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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Vraag 29 Verslag

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) Juist antwoord

(5,6)

(6,5)

(9,4)

(9,5)

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Vraag 30 Verslag

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 Juist antwoord

12cm

15cm

Antwoorddetails

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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Vraag 31 Verslag

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 Juist antwoord

138^o

149^o

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Vraag 32 Verslag

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

1/6

1/3 Juist antwoord

2/3

1/2

5/6

Antwoorddetails

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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Vraag 33 Verslag

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 Juist antwoord

15 sides

Antwoorddetails

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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Vraag 34 Verslag

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 Juist antwoord

(150 + 45√3)km

240km

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Vraag 35 Verslag

What is A?B in the diagram above?

(2,3)

(2,3,4) Juist antwoord

(1,2,3)

(2,3,8)

(6,4,7)

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Vraag 36 Verslag

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

(2x - 9)(x - 5)

(2x-15)(x + 3)

(2x +15)(x - 3)

(2x -15(x - 3) Juist antwoord

(2x - 9)(x + 5)

Antwoorddetails

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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Vraag 37 Verslag

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

1101001

1011001 Juist antwoord

1001101

101101

11001

Antwoorddetails

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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Vraag 38 Verslag

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 Juist antwoord

5cm

5.5cm

6.6cm

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Vraag 39 Verslag

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 Juist antwoord

Antwoorddetails

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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Vraag 40 Verslag

Solve the inequality: 3m + 3 > 9

m > 2 Juist antwoord

m > 3

m>4

m>6

m>12

Antwoorddetails

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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Vraag 41 Verslag

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 Juist antwoord

68^o

73^o

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Vraag 42 Verslag

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 Juist antwoord

297cm³

445.5cm³

Antwoorddetails

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

Lees lesnotitie op Volumes (WAEC)

Volumes

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Vraag 43 Verslag

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

1/6

1/3

1/2 Juist antwoord

2/3

5/6

Antwoorddetails

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.

Lees lesnotitie op Probability (WAEC)

Probability

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Vraag 44 Verslag

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

5/13

7/13

12/13

17/13 Juist antwoord

5/12

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Lees lesnotitie op Introductory Calculus (WAEC)

Lees lesnotitie op Trigonometry (JAMB)

Introductory Calculus

Trigonometry

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Vraag 45 Verslag

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 Juist antwoord

Antwoorddetails

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.

Lees lesnotitie op Circles (WAEC)

Lees lesnotitie op Coordinate Geometry (WAEC)

Circles

Coordinate Geometry

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Vraag 46 Verslag

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

12.5 Juist antwoord

13.5

Antwoorddetails

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.

Lees lesnotitie op Sets (JAMB)

Lees lesnotitie op Measures Of Dispersion (JAMB)

Sets

Measures Of Dispersion

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Vraag 47 Verslag

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

.-2,-6

2,6 Juist antwoord

2,-6

-2,6

-1,-3

Antwoorddetails

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.

Lees lesnotitie op Solution Of Linear Equations (WAEC)

Lees lesnotitie op Quadratic Equations (WAEC)

Solution Of Linear Equations

Quadratic Equations

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Vraag 48 Verslag

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 Juist antwoord

Antwoorddetails

Lees lesnotitie op Sequence And Series (WAEC)

Sequence And Series

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WAEC SSCE - General Mathematics - 1993 (Objective)