WAEC SSCE - General Mathematics - 2015 (Objective)

Question 1 Report

Find the equation whose roots are $\frac{3}{4}$ and -4

4x² - 13x + 12 = 0

4x² - 13x - 12 = 0

4x² + 13x - 12 = 0 Correct answer

4x² + 13x + 12 = 0

Answer Details

If a quadratic equation has roots p and q, then it can be expressed in the factored form as:

(x - p)(x - q) = 0

Expanding this equation, we get:

x² - (p + q)x + pq = 0

In this case, the roots are given as $\frac{3}{4}$ and -4. Thus, the equation can be expressed as:

(x - \(\frac{3}{4}\))(x + 4) = 0

Expanding this equation, we get:

x² + (4 - \(\frac{3}{4}\))x - 3 = 0

Multiplying throughout by 4 to eliminate fractions, we get:

4x² + 13x - 12 = 0

Therefore, the equation whose roots are $\frac{3}{4}$ and -4 is 4x² + 13x - 12 = 0.

Hence, the answer is 4x² + 13x - 12 = 0.

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Question 2 Report

Find the 7^th term of the sequence: 2, 5, 10, 17, 6,...

50 Correct answer

Answer Details

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Sequence And Series

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Question 3 Report

The scores of twenty students in a test are as follows: 44, 47, 48, 49, 50, 51, 52, 53, 53, 54, 58, 59, 60, 61, 63, 65, 67, 70, 73, 75. Find the third quartile.

64 Correct answer

Answer Details

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Measures Of Dispersion

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Question 4 Report

In the diagram, $\bar{OX}$ bisects < YXZ and $\bar{OZ}$ bisects < YZX. If < XYZ = 68^o, calculate the value of < XOZ

68^o

72^o

112^o

124^o Correct answer

Answer Details

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Angles And Intercepts On Parallel Lines

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Question 5 Report

The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 7 students

32^o Correct answer

45^o

60^o

75^o

Answer Details

To find the sectoral angle for a class of 7 students, we first need to calculate what percentage of the total population they represent: Percentage of class of 7 students = (Number of students in the class / Total population) x 100% Percentage of class of 7 students = (7 / 810) x 100% Percentage of class of 7 students = 0.864% (rounded to three decimal places) Next, we need to convert this percentage to an angle of the pie chart. We know that a full circle is 360 degrees, and the percentage of the class of 7 students represents a certain portion of this circle. We can use the following formula to calculate the sectoral angle: Sectoral angle = Percentage of class of 7 students x 360 degrees Plugging in the percentage we calculated earlier, we get: Sectoral angle = 0.864% x 360 degrees Sectoral angle ≈ 3.11 degrees (rounded to two decimal places) Therefore, the sectoral angle for a class of 7 students in the pie chart is approximately 3.11 degrees. So, the correct option is (a) 32^o.

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Representation Of Data

Sets

Mensuration

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Question 6 Report

Factorize completely: 6ax - 12by - 9ay + 8bx

(2a - 3b)(4x + 3y)

(3a + 4b)(2x - 3y) Correct answer

(3a - 4b)(2x + 3y)

(2a + 3b)(4x -3y)

Answer Details

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Algebraic Expressions

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Question 7 Report

The volume of a cone of height 3cm is 38$\frac{1}{2}$cm³. Find the radius of its base. [Take $\pi = \frac{22}{7}$]

3.0cm

3.5cm Correct answer

4.0cm

4.5cm

Answer Details

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Question 8 Report

Adding 42 to a given positive number gives the same result as squaring the number. Find the number

7 Correct answer

Answer Details

Let's call the unknown number "x". According to the problem, adding 42 to x gives the same result as squaring x. We can write this as an equation: x + 42 = x^2 To solve for x, we can rearrange this equation to get it in standard quadratic form: x^2 - x - 42 = 0 Now we can factor this quadratic equation: (x - 7)(x + 6) = 0 This gives us two possible solutions: x = 7 and x = -6. However, we were given that x is a positive number, so we can discard the negative solution. Therefore, the answer is x = 7. To check our answer, we can substitute x = 7 into the original equation: 7 + 42 = 49 7^2 = 49 So adding 42 to 7 does indeed give the same result as squaring 7.

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Question 9 Report

If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x

15 Correct answer

Answer Details

To solve this problem, we need to use the given conditions to find the possible values of x and then determine the highest value among them. From the first condition, we know that x is an integer between 2 and 19 (inclusive) and can be represented as {X: 2 d- x d- 19; X integer}. This means that x can take on any of the following values: 2, 3, 4, ..., 18, 19. The second condition tells us that 7 + x is congruent to 4 modulo 9, which can be written as: 7 + x ≡ 4 (mod 9) To solve for x, we can subtract 7 from both sides of the congruence: x ≡ -3 (mod 9) Since we want x to be between 2 and 19, we can add or subtract multiples of 9 to -3 until we get a value within the range of possible values for x. Doing so, we obtain: x ≡ -3 (mod 9) x ≡ 15 (mod 9) Since 15 is the largest value of x that satisfies both conditions, our answer is 15.

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Positive And Negative Integers, Rational Numbers

Modular Arithmetic

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Question 10 Report

If $\frac{\sqrt{2} + \sqrt{3}}{\sqrt{3}}$ is simplified as m + n$\sqrt{6}$, find the value of (m + n)

$\frac{1}{3}$

$\frac{2}{3}$

1$\frac{1}{3}$ Correct answer

1$\frac{2}{3}$

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Surds (radicals)

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Question 11 Report

In a circle radius rcm, a chord 16$\sqrt{3}cm$ long is 10cmfrom the centre of the circle. Find, correct to the nearest cm, the value of r

22cm

17cm Correct answer

16cm

15cm

Answer Details

In a circle, a radius is a line segment that connects the center of the circle to any point on the circle. A chord is a line segment that connects two points on a circle. Given that a chord of length 16$\sqrt{3}cm$ is 10cm from the center of the circle, we can use the Pythagorean theorem to find the length of the radius. First, we draw a line from the center of the circle perpendicular to the chord, creating a right triangle with the radius, the perpendicular line, and half the chord length (which is $8\sqrt{3}$ cm). Using the Pythagorean theorem: \begin{align*} r^2 &= (8\sqrt{3})^2 + 10^2 \\ r^2 &= 192 + 100 \\ r^2 &= 292 \\ r &\approx \sqrt{292} \\ r &\approx 17 \text{ cm} \end{align*} Rounding to the nearest whole number, we get the answer of 17cm. Therefore, the correct option is (b) 17cm.

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Circles

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Question 12 Report

If m = 4, n = 9 and r = 16., evaluate $\frac{m}{n}$ - 1$\frac{7}{9}$ + $\frac{n}{r}$

1$\frac{5}{16}$

1$\frac{1}{16}$

$\frac{5}{16}$

- 1$\frac{37}{48}$ Correct answer

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Fractions, Decimals And Approximations

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Question 13 Report

Simplify: $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2}$

$\frac{4x + 5y - xy}{2xy}$

$\frac{5y - 4x + xy}{2xy}$

$\frac{5x + 4y - xy}{2xy}$

$\frac{4x - 5y + xy}{2xy}$ Correct answer

Answer Details

To simplify the expression, we first need to find a common denominator for the fractions. The lowest common multiple of the denominators xy and 2xy is 2xy. $\frac{3x - y}{xy} - \frac{2x + 3y}{2xy} + \frac{1}{2} = \frac{3x\cdot2 - y\cdot2}{xy\cdot2} - \frac{2x\cdot1 + 3y\cdot1}{2xy\cdot1} + \frac{1\cdot xy}{2\cdot xy}$ Simplifying further, we get: $\frac{6x - 2y}{2xy} - \frac{2x + 3y}{2xy} + \frac{xy}{2xy}$ Combining like terms, we get: $\frac{4x - 5y + xy}{2xy}$ Therefore, the answer is option D: $\frac{4x - 5y + xy}{2xy}$.

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Question 14 Report

PQRT is square. If x is the midpoint of PQ, Calculate correct to the nearest degree, LPXS

53^o

55^o

63^o Correct answer

65^o

Answer Details

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Question 15 Report

The dimension of a rectangular tank are 2m by 7m by 11m. If its volume is equal to that of a cylindrical tank of height 4cm, calculate the base radius of the cylindrical tank. [Take $\pi = \frac{22}{7}$]

14cm

3$\frac{1}{2}$m Correct answer

1$\frac{3}{4}$m

Answer Details

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Volumes

Fractions, Decimals And Approximations

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Question 16 Report

Find the value of p if $\frac{1}{4}$p + 3q = 10 and 2p - q = 7

4 Correct answer

-3

-4

Answer Details

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Solution Of Linear Equations

Algebraic Expressions

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Question 17 Report

Which of the following is used to determine the mode of a grouped data?

Bar chart

Frequency polygon

Ogive

Histogram Correct answer

Answer Details

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Representation Of Data

Integration

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Question 18 Report

In the diagram, PQ//RT, QR//Su,

134^o

132^o Correct answer

96^o

48^o

Answer Details

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Angles And Intercepts On Parallel Lines

Triangles And Polygons

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Question 19 Report

A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira?

N250,000.00

N200,000.00 Correct answer

N150,000.00

N100,000.00

Answer Details

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Positive And Negative Integers, Rational Numbers

Modular Arithmetic

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Question 20 Report

If 2ⁿ = y, Find 2$^{(2 + \frac{n}{3})}$

4y$^\frac{1}{3}$ Correct answer

4y$^-3$

2y$^\frac{1}{3}$

2y$^-3$

Answer Details

We know that 2$^n$ = y. Therefore, 2$^{(2 + \frac{n}{3})}$ can be written as 2$^2$ × 2$^{\frac{n}{3}}$ = 4 × 2$^{\frac{n}{3}}$. Substituting 2$^n$ = y in the above equation, we get: 2$^{(2 + \frac{n}{3})}$ = 4y$^\frac{1}{3}$ Therefore, the answer is (a) 4y$^\frac{1}{3}$.

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Indices

Logarithms

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Question 21 Report

Describe the shaded portion in the diagram

P' $\cap$ Q $\cap$ R' Correct answer

(P' $\cap$ R)' $\cap$ R

P' $\cap$ Q $\cap$ R

(P $\cap$ Q)' $\cap$ R

Answer Details

The shaded portion in the diagram represents the set of elements that belong to the complement of P and the intersection of Q and R. In other words, it represents the set of elements that are not in P, but are in both Q and R. Therefore, the correct answer is P' $\cap$ Q $\cap$ R'.

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Logical Reasoning

Sets

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Question 22 Report

In the given diagram, $\bar{QT}$ and $\bar{PR}$ are straight lines, < ROS = (3n - 20), < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.

35^o Correct answer

40^o

55^o

60^o

Answer Details

Since < QOL is a right angle, we have: < QOT + < SOT = 90^o Since < QOT = 180^o - < POL, we have: < QOT = 180^o - m Substituting into the first equation, we get: 180^o - m + n = 90^o n - m = 90^o - 180^o = -90^o Also, from the diagram, we have: < QOT + < ROS + < SOT = 180^o Substituting < QOT = 180^o - < POL and simplifying, we get: 180^o - m + (3n - 20) + n = 180^o 4n - m = 20 We now have a system of two equations: n - m = -90^o 4n - m = 20 Solving simultaneously, we get: n = 35^o

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Algebraic Expressions

Angles And Intercepts On Parallel Lines

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Question 23 Report

If $\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1$, find the value of x.

$\frac{1}{2}$ Correct answer

-$\frac{1}{2}$

-1

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Number Bases

Indices

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Question 24 Report

The rate of consumption of petrol by a vehicle varies directly as the square of the distance covered. If 4 litres of petrol is consumed on a distance of 15km. how far would the vehicle go on 9 litres of petrol?

22$\frac{1}{2}$km Correct answer

30km

33$\frac{1}{2}$km

45km

Answer Details

Since the rate of consumption of petrol varies directly as the square of the distance covered, let's assume that the rate is k$\frac{\text{litres}}{\text{km}^2}$. Then we can write the relationship as: rate of consumption = k(distance covered)$^2$ We are given that when the distance covered is 15 km, the rate of consumption is 4 litres. Substituting these values in the above equation, we get: 4 = k(15)$^2$ k = $\frac{4}{15^2}$ Now, we need to find how far the vehicle can go on 9 litres of petrol. Let's assume that the vehicle can travel a distance of x km on 9 litres of petrol. Using the same equation as before, we get: 9 = $\frac{4}{15^2}$(x)$^2$ Simplifying this equation, we get: x$^2$ = $\frac{9}{\frac{4}{15^2}}$ x$^2$ = 506.25 x = 22.5 Therefore, the vehicle can travel 22.5 km on 9 litres of petrol. So the answer is 22$\frac{1}{2}$km.

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Sequence And Series

Ratio, Proportions And Rates

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Question 25 Report

In the diagram, O is the centre, $\bar{RT}$ is a diameter, < PQT = 33$^o$ and < TOS = 76$^o$. Using the diagram, find the size of angle PRS.

76^o

71^o Correct answer

38^o

33^o

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Circles

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Question 26 Report

The angle of elevation of an aircraft from a point K on the horizontal ground 30$\alpha$. If the aircraft is 800m above the ground, how far is it from K?

400.00m

692.82m

923.76m

1,600.99m Correct answer

Answer Details

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Introductory Calculus

Coordinate Geometry

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Question 27 Report

A letter is selected from the letters of the English alphabet. What is the probability that the letter selected is from the word MATHEMATICS?

$\frac{9}{13}$

$\frac{11}{26}$

$\frac{4}{13}$ Correct answer

$\frac{1}{26}$

Answer Details

The word MATHEMATICS contains the letters A, C, E, H, I, M, S, and T. Since there are 26 letters in the English alphabet, the probability of selecting any letter from the alphabet is 1 out of 26. Out of the letters in the word MATHEMATICS, there are 8 letters, so the probability of selecting a letter from the word MATHEMATICS is 8 out of 26. Therefore, the probability of selecting a letter from the word MATHEMATICS is: $$\frac{8}{26}=\frac{4}{13}$$ Therefore, the correct answer is option (C).

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Probability

Surds (radicals)

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Question 28 Report

Given that logx 64 = 3, evaluate x log$_2$8

12 Correct answer

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Modular Arithmetic

Logarithms

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Question 29 Report

Tom will be 25 years old in n years' time. If he is 5 years younger than Bade's present age.

(30 - n)years Correct answer

(20 - n)years

(25 - n)years

(30 + n)years

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Solution Of Linear Equations

Circles

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Question 30 Report

Two angles of a pentagon are in the ratio 2:3. The others are 60^o each. Calculate the smaller of the two angles

72^o

100^o

120^o

144^o Correct answer

Answer Details

Let's call the two angles that are in the ratio 2:3 as "2x" and "3x". The sum of the interior angles of a pentagon is given by the formula (5-2) x 180 degrees = 540 degrees. Since the other three angles are all 60 degrees each, we can find the sum of those angles by multiplying 60 by 3, which gives us 180 degrees. Now we can set up an equation to solve for the unknown angle, which is 2x + 3x. 2x + 3x + 180 = 540 Simplifying this equation, we get: 5x + 180 = 540 Subtracting 180 from both sides, we get: 5x = 360 Dividing both sides by 5, we get: x = 72 So the smaller angle, which is 2x, is equal to 2 times 72, which is 144 degrees. Therefore, the correct answer is 144 degrees.

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Angles

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Question 31 Report

A farmer uses $\frac{2}{5}$ of his land to grow cassava, $\frac{1}{3}$ of the remaining for yam and the rest for maize. Find the part of the land used for maize

$\frac{2}{15}$

$\frac{2}{5}$ Correct answer

$\frac{2}{3}$

$\frac{4}{5}$

Answer Details

Let's assume the farmer has 15 parts of land. The fraction of land used for cassava is $\frac{2}{5}$ of 15, which is 6 parts. The remaining land is 15 - 6 = 9 parts. The fraction of the remaining land used for yam is $\frac{1}{3}$ of 9, which is 3 parts. Therefore, the part of the land used for maize is the remaining land after cassava and yam are planted, which is 9 - 3 = 6 parts. So the fraction of the land used for maize is $\frac{6}{15}$, which simplifies to $\frac{2}{5}$. Therefore, the answer is option (B) $\frac{2}{5}$.

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Fractions, Decimals And Approximations

Number Bases

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Question 32 Report

The area of a rhombus is 110 cm$^2$. If the diagonals are 20 cm and (2x + 1) cm long, find the value of x.

5.0 Correct answer

4.0

3.0

2.5

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Areas

Angles

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Question 33 Report

In the diagram, O is the centre, $\bar{RT}$ is a diameter, < PQT = 33$^o$ and <TOS = 76$^o$. Using the diagram, calculate the value of angle PTR.

73^o

67^o

57^o Correct answer

37^o

Answer Details

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Number Bases

Coordinate Geometry

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Question 34 Report

In the diagram, PTR is a tangent to the centre O. If angles TON = 108°, Calculate the size of angle PTN

132^o

126^o Correct answer

108^o

102^o

Answer Details

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Circles

Algebraic Expressions

Euclidean Geometry

Triangles And Polygons

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Question 35 Report

Ada draws the graph of y = x² - x - 2 and y = 2x - 1 on the same axes. Which of these equations is she solving?

x² - x - 3 = 0

x² - 3x - 1 = 0 Correct answer

x² - 3x - 3 = 0

x² + 3x - 1 = 0

Answer Details

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Quadratic Equations

Graphs Of Linear And Quadratic Functions

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Question 36 Report

Calculate the mean deviation of 5, 3, 0, 7, 2, 1

0.0

2.0 Correct answer

2.5

3.0

Answer Details

To find the mean deviation, we need to first calculate the mean of the given set of numbers: Mean = (5 + 3 + 0 + 7 + 2 + 1) / 6 = 18 / 6 = 3 Next, we need to find the absolute deviation of each number from the mean: |5 - 3| = 2 |3 - 3| = 0 |0 - 3| = 3 |7 - 3| = 4 |2 - 3| = 1 |1 - 3| = 2 To calculate the mean deviation, we add up these absolute deviations and divide by the number of numbers: Mean deviation = (2 + 0 + 3 + 4 + 1 + 2) / 6 = 12 / 6 = 2 Therefore, the answer is option (B) 2.0.

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Measures Of Location

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Question 37 Report

Make K the subject of the relation T = $\sqrt{\frac{TK - H}{K - H}}$

K = $\frac{H(T^2 - 1)}{T^2 - T}$ Correct answer

K = $\frac{HT}{(T - 1)^2}$

K = $\frac{H(T^2 + 1)}{T}$

K = $\frac{H(T - 1)}{T}$

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Algebraic Fractions

Quadratic Equations

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Question 38 Report

$\begin{array}{c|c}
x & 0 & 1\frac{1}{4} & 2 & 4\\
\hline
y & 3 & 5\frac{1}{2} & &
\end{array}$
The table given shows some values for a linear graph. Find the gradient of the line

2 Correct answer

Answer Details

To find the gradient of a line, we need to calculate the change in y divided by the change in x between two points on the line. Let's choose two points on the line from the given table. We can select the points (0,3) and (2,y), where y is the value of y for x = 2. The change in y is y - 3, and the change in x is 2 - 0 = 2. Therefore, the gradient of the line is: gradient = change in y / change in x = (y - 3) / 2 We don't know the value of y yet, but we can use the other point on the line to find it. Using the points (1.25, 5.5) and (2, y), we get: gradient = (y - 5.5) / (2 - 1.25) = (y - 5.5) / 0.75 Setting the two expressions for the gradient equal to each other, we get: (y - 3) / 2 = (y - 5.5) / 0.75 Solving for y gives: y = 7 Therefore, the value of y for x = 2 is 7, and the gradient of the line is: gradient = (y - 3) / 2 = (7 - 3) / 2 = 2 So the answer is 2, and the gradient of the line is 2. In simple terms, the gradient of a line tells us how steep the line is. If the gradient is positive, the line is sloping upwards from left to right. If the gradient is negative, the line is sloping downwards from left to right. The larger the absolute value of the gradient, the steeper the line.

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Graphs Of Linear And Quadratic Functions

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Question 39 Report

In the diagram, O is the centre. If PQ//RS and ∠ONS = 140°, find the size of ∠POM.

40^o Correct answer

50^o

60^o

80^o

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Euclidean Geometry

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Question 40 Report

A trader bought 100 oranges at 5 for N40.00 and 20 for N120.00. Find the profit or loss percent

20% profit

20% loss

25% profit

25% loss Correct answer

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Number Bases

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Question 41 Report

In the diagram, VW//YZ, |WX| = 6cm, |XY| = 16cm, |YZ| = 20cm and |ZX| = 12cm. Calculate |VX|

3cm

4cm

6cm

8cm Correct answer

Answer Details

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Question 42 Report

In the diagram, the shaded part is carpet laid in a room with dimensions 3.5m by 2.2m leaving a margin of 0.5m round it. Find area of the margin

4.7m² Correct answer

4.9m²

5.7m²

5.9m²

Answer Details

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Lengths And Perimeters

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Question 43 Report

$\begin{array}{c|c}
Scores & 0 - 4 & 5 - 9 & 10 - 14\\
\hline Frequency & 2 & 1 & 2\end{array}$

The table shows the distribution of the scores of some students in a test. Calculate the mean scores.

5.6

6.2

6.6

7.0 Correct answer

Answer Details

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Integration

Statistics

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Question 44 Report

The probability that kebba, Ebou and Omar will hit a target are $\frac{2}{3}$, $\frac{3}{4}$ and $\frac{4}{5}$ respectively. Find the probability that only Kebba will hit the target.

$\frac{2}{5}$

$\frac{7}{60}$

$\frac{1}{30}$ Correct answer

$\frac{1}{60}$

Answer Details

The probability that only Kebba will hit the target means that Kebba hits the target and the other two miss the target. We can find this probability by multiplying the probability of Kebba hitting the target with the probability of Ebou missing the target and the probability of Omar missing the target. Probability that only Kebba hits the target = Probability of Kebba hitting the target × Probability of Ebou missing the target × Probability of Omar missing the target = $\frac{2}{3}$ × $\frac{1}{4}$ × $\frac{1}{5}$ = $\frac{2}{3\times4\times5}$ = $\frac{1}{30}$ Therefore, the probability that only Kebba will hit the target is $\frac{1}{30}$.

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Probability

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Question 45 Report

The sum 11011₂, 1111₂ and 10_m10_n0₂. Find the value of m and n.

m = 0, n = 0

m = 1, n = 0

m = 0, n = 1 Correct answer

m = 1, n = 1

Answer Details

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Number Bases

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