WAEC SSCE - General Mathematics - 2004 (Objective)

We know that any number raised to the power of zero is equal to 1. Therefore, we can rewrite the equation $\left(\frac{1}{4}\right)^{(2-y)} = 1$ as $\left(\frac{1}{4}\right)^{(2-y)} = \left(\frac{1}{4}\right)^0$. Using the rule of exponents that states when we have the same base raised to different powers, we can multiply the bases and subtract the exponents. So, we get $\left(\frac{1}{4}\right)^{(2-y)} = \left(\frac{1}{4}\right)^0 \Rightarrow \frac{1}{4^{(2-y)}} = \frac{1}{4^0}$. Since $4^0 = 1$, we can simplify the right-hand side to 1. Therefore, we have $\frac{1}{4^{(2-y)}} = 1$. Multiplying both sides by $4^{(2-y)}$ gives us $1 = 4^{(2-y)}$. We can rewrite the left-hand side as $4^0$ because any number raised to the power of zero is equal to 1. So, we have $4^0 = 4^{(2-y)}$. Using the rule of exponents again, we can set the exponents equal to each other, which gives us $0 = 2 - y$. Solving for y, we get $y = 2$. Therefore, the value of y that satisfies the equation $\left(\frac{1}{4}\right)^{(2-y)} = 1$ is 2.

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Representation Of Data

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Question 4 Report

In the diagram, POQ is the diameter of the circle centre O. Calculate ∠QRS

35^o

70^o

100^o

125^o

Answer Details

Since POQ is the diameter of the circle, we know that angle POR = 90 degrees. Therefore, angle QOR is also 90 degrees because it is vertically opposite to angle POR. Since QR is a chord of the circle, angle QRS is half of the angle subtended by the same chord at the circumference of the circle, which is angle QOR. Thus, angle QRS = 1/2 * angle QOR = 1/2 * 90 degrees = 45 degrees. Therefore, the answer is 45 degrees, which is 35^o.

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Circles

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Question 5 Report

Factorise 27p²x² - 48y².

9(3px - 4y)²

3(3px - 4y)(3px - 4y)

9(px - 4y)(3p x + 4y)

3(3px -4y)(3px +4y)

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Algebraic Expressions

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Question 6 Report

Given that $P\propto \frac{1}{\sqrt{r}}$ and p = 3 when r = 16, find the value of r when p =-5

324

Answer Details

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Modular Arithmetic

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Question 7 Report

Find the next two terms of the sequence
1, 5, 14, 30, 55, ...

61,110

67,116

81,140

91, 140

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Sequence And Series

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Question 8 Report

In the diagram, $R\hat{P}Q = Q\hat{R}Y, \hspace{1mm} P\hat{Q}R = R\hat{Y}Q, \\ \hspace{1mm}|QP| = 3cm \hspace{1mm}|QY| = 4cm \hspace{1mm}and \hspace{1mm}|RY | = 5cm. \hspace{1mm} Find \hspace{1mm}|QR|$

2.0cm

2.5cm

6.4cm

10.0cm

Answer Details

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Polynomials

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Question 9 Report

Each interior angle of a regular polygon is 108°. How many sides has it?

Answer Details

To find the number of sides of a regular polygon with interior angle 108°, we need to use the formula for the sum of interior angles of a polygon, which is (n-2) x 180°, where n is the number of sides. Since the polygon is regular, all its interior angles are equal, so we can use the fact that the sum of the interior angles of a polygon is also equal to the number of sides times the interior angle. Therefore, we have: (n-2) x 180° = n x 108° Simplifying this equation, we get: 180n - 360 = 108n 72n = 360 n = 5 Therefore, the regular polygon has 5 sides, and the answer is option A.

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Triangles And Polygons

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Question 10 Report

Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

1920cm²

592cm²

296cm²

148cm²

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Volumes

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Question 11 Report

A point on the ground is 5m away from the foot of a vertical wall 7 m high, Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall

36^o

44^o

46^o

54^o

Answer Details

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Angles Of Elevation And Depression

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Question 12 Report

There are m boys and 12 girls in a class. What is the probability of selecting at random a girl from the class?

$\frac{m}{12}$

$\frac{12}{m}$

$\frac{12}{m+12}$

$\frac{12}{m-12}$

Answer Details

The probability of selecting a girl at random from the class is the ratio of the number of girls in the class to the total number of students in the class. Given that there are m boys and 12 girls in the class, the total number of students in the class is m + 12. Therefore, the probability of selecting a girl at random is: \begin{align*} \frac{12}{m+12} \end{align*} Therefore, the correct option is (c) $\frac{12}{m+12}$.

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Question 13 Report

Find the average of the first four prime numbers greater than10

Answer Details

The first four prime numbers greater than 10 are 11, 13, 17, and 19. To find their average, we add them up and divide by the total number of primes, which is 4. \begin{align*} \text{Average} &= \frac{11 + 13 + 17 + 19}{4} \\ &= \frac{60}{4} \\ &= 15 \end{align*} Therefore, the average of the first four prime numbers greater than 10 is 15. Answer: 15

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Number Bases

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Question 14 Report

In the diagram, ?XYZ is similar to ?PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|

5.6 cm

11.2cm

11.4cm

28.0cm

Answer Details

We can use the property of similar triangles that corresponding sides are proportional. First, let's find the ratio of corresponding sides between the two triangles. Ratio of corresponding sides: |XY|/|PR| = 5/8 |XZ|/|PQ| = 3.5/|PQ| Since the two triangles are similar, the ratio of corresponding sides must be equal. Therefore: 5/8 = 3.5/|PQ| Cross-multiplying: 5 x |PQ| = 8 x 3.5 |PQ| = 28/5 Simplifying: |PQ| = 5.6 cm Therefore, |PQ| is 5.6 cm.

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Question 15 Report

Solve for t in the equation $\frac{3}{4}t+\frac{1}{3}(21-t)$ = 11,

$\frac{9}{13}$

$\frac{9}{5}$

$9\frac{3}{5}$

Answer Details

First, we simplify the left-hand side of the equation: \begin{align*} \frac{3}{4}t + \frac{1}{3}(21-t) &= 11 \\ \frac{3}{4}t + 7 - \frac{1}{3}t &= 11 \\ \frac{5}{12}t &= 4 \\ t &= \frac{4 \times 12}{5} \\ t &= \frac{48}{5} \end{align*} Therefore, the value of t is $9\frac{3}{5}$. So, the correct answer is (d).

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Solution Of Linear Equations

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Question 16 Report

If $\frac{x}{a+1}+\frac{y}{b}$ 1. Make y the subject of the relation

$\frac{b(a-x+1)}{a+1}$

$\frac{a+1}{b(a-x+1)}$

$\frac{a(b-x+1)}{b+1}$

$\frac{b}{a(b-x+1)}$

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Solution Of Linear Equations

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Question 17 Report

Given that sin (5x - 28)^o = cos (3x - 50)^o,0 < x < 90^o, find the value of x

14^o

21^o

32^o

39^o

Answer Details

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Sine, Cosine And Tangent Of An Angle

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Question 18 Report

Find the mean deviation of 6, 7, 8, 9, 10

1.2

1.5

Answer Details

To find the mean deviation, we first need to find the mean (average) of the given numbers. The mean is calculated by adding up all the numbers and then dividing by the total number of numbers: \[\text{Mean} = \frac{6 + 7 + 8 + 9 + 10}{5} = 8\] Next, we find the deviation of each number from the mean. To do this, we subtract the mean from each number: \[\begin{aligned} \text{Deviation of 6} &= 6 - 8 = -2 \\ \text{Deviation of 7} &= 7 - 8 = -1 \\ \text{Deviation of 8} &= 8 - 8 = 0 \\ \text{Deviation of 9} &= 9 - 8 = 1 \\ \text{Deviation of 10} &= 10 - 8 = 2 \end{aligned}\] Note that any negative deviations should be treated as positive values, so we need to ignore the negative signs when we calculate the mean deviation. To find the mean deviation, we add up all the deviations (ignoring any negative signs) and then divide by the total number of numbers: \[\begin{aligned} \text{Mean Deviation} &= \frac{|-2| + |-1| + |0| + |1| + |2|}{5} \\ &= \frac{2 + 1 + 0 + 1 + 2}{5} \\ &= \frac{6}{5} \\ &= 1.2 \end{aligned}\] Therefore, the mean deviation of 6, 7, 8, 9, 10 is 1.2.

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Measures Of Dispersion

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Question 19 Report

Given that ξ = {1, 2, 3, . . . . . . ,10}, P= (x : x is prime) and Q = {y : y is odd}, find P^l∩Q

{2}

{1,9}

{315.7}

{4, 6, 8, 10}

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Sets

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Question 20 Report

Simplify $\frac{2}{a+b}-\frac{1}{a-b}$

$\frac{3}{a+b}$

$\frac{a-3b}{a^2-b^2}$

$\frac{3a-b}{a^2 – b^2}$

$\frac{a-3b}{a^2+b^2}$

Answer Details

To simplify the expression, we need to find a common denominator for the two fractions. We can use the difference of two squares identity $(a+b)(a-b) = a^2-b^2$ to find a common denominator. \begin{aligned} \frac{2}{a+b}-\frac{1}{a-b} &= \frac{2(a-b)}{(a+b)(a-b)} - \frac{1(a+b)}{(a-b)(a+b)}\\ &= \frac{2(a-b)-1(a+b)}{a^2-b^2}\\ &= \frac{2a-2b-a-b}{a^2-b^2}\\ &= \frac{a-3b}{a^2-b^2} \end{aligned} Therefore, the simplified expression is $\frac{a-3b}{a^2-b^2}$, which corresponds to.

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Question 21 Report

A point X is on the bearing 342^o from a point Y. What is the bearing of Y from X?

342^o

252^o

198^o

162^o

Answer Details

If point X is on a bearing of 342^o from point Y, then point Y is on a bearing of 162^o from point X. This is because the bearing from X to Y is the opposite direction from the bearing from Y to X. Therefore, we subtract the original bearing of 342^o from 180^o to get 162^o.

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Bearings

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Question 22 Report

Given that x + y = 7 and 3x-y = 5, evaluate $\frac{y}{2}-3$.

-1

Answer Details

To solve this problem, we first need to find the values of x and y, and then substitute them into the expression $\frac{y}{2}-3$. From the given equations, we can use the elimination method to solve for x and y. Multiplying the second equation by 2 and adding it to the first equation, we get: 2(3x-y) + (x+y) = 11x = 17 x = 17/11 Substituting x into the first equation, we get: y = 7 - x = 7 - 17/11 = 60/11 Now we can substitute these values into the expression $\frac{y}{2}-3$: $\frac{y}{2}-3 = \frac{60/11}{2} - 3 = \frac{30}{11} - \frac{33}{11} = -\frac{3}{11}$ Therefore, the answer is -1.

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Solution Of Linear Equations

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Question 23 Report

A boy walks 800m in 20 minutes. Calculate his average speed in km per hour

2.4

Answer Details

To calculate the average speed of the boy, we need to convert the distance and time to the same units. The boy walked 800m in 20 minutes. To convert minutes to hours, we divide by 60: 20 minutes ÷ 60 = 0.333 hours Now we can calculate the average speed: Speed = Distance ÷ Time Speed = 800m ÷ 0.333 hours Speed ≈ 2400m/h To convert meters per hour to kilometers per hour, we divide by 1000: Speed ≈ 2.4 km/h Therefore, the boy's average speed is 2.4 km/h. So the answer is (a) 2.4.

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Number Bases

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Question 24 Report

Find the range of values of x for which$\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}$

x > 4

x > -4

x < 4

x < -4

Answer Details

We can start solving the inequality by first finding a common denominator for the fractions: \begin{align*} \frac{x+2}{4}-\frac{x+1}{3}&>\frac{1}{2}\\ \frac{3(x+2)}{12}-\frac{4(x+1)}{12}&>\frac{6}{12}\\ \frac{3x+6-4x-4}{12}&>\frac{1}{2}\\ -\frac{x-2}{12}&>\frac{1}{2}\\ \end{align*} Multiplying both sides by $-1$ changes the direction of the inequality: \begin{align*} \frac{x-2}{12}&<-\frac{1}{2}\\ \end{align*} Multiplying both sides by $12$ gives: \begin{align*} x-2&<-6\\ x&< -4\\ \end{align*} Therefore, the answer is: - x < -4

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Solution Of Linear Equations

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Question 25 Report

Solve the equation 10-3x-x² = 0

x=2 or-5

x= -2 or 5

x = 1 or 10

x = 2 or 5

Answer Details

To solve the equation 10-3x-x² = 0, we can first rearrange it to get x²+3x-10=0. We can then factorize this quadratic equation as (x+5)(x-2)=0. This means that either x+5=0 or x-2=0, which gives us the solutions x=-5 and x=2. Therefore, the correct answer is x=2 or -5, which is the first option.

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Question 26 Report

The values of x when y = 3 are approximately

-4.7 and 1.4

-4.6 and 1.5

-3.6 and 0.4

-3.6 and 1.5

Answer Details

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Fractions, Decimals And Approximations

Fractions, Decimals, Approximations And Percentage

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Question 27 Report

Find, correct to two decimal places, the mean of 9, 13, 16, 17, 19, 23, 24.

23.00

17.29

16.50

16.33

Answer Details

To find the mean of a set of numbers, we need to add up all the numbers and divide by the total number of numbers. Adding the given numbers, we get: 9 + 13 + 16 + 17 + 19 + 23 + 24 = 121 There are 7 numbers in the set, so to find the mean, we divide the sum by 7: Mean = 121/7 = 17.29 (correct to two decimal places) Therefore, the answer is (b) 17.29.

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Probability

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Question 28 Report

What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take $\pi = \frac{22}{7}$)

38.5cm³

77cm³

269.5cm³

1078cm³

Answer Details

The volume of a cylinder can be calculated by multiplying the area of its base by its height. The base of this cylinder is a circle with diameter 7cm. The radius of the circle is half of the diameter, which is 3.5cm. Using the formula for the area of a circle, we can find that the area of the base is: \[\text{Area of base} = \pi r^2 = \frac{22}{7} \times 3.5^2 = 38.5\text{ cm}^2\] The height of the cylinder is also given as 7cm. Using the formula for the volume of a cylinder, we can find the volume of the solid: \[\text{Volume of cylinder} = \text{Area of base} \times \text{height} = 38.5\text{ cm}^2 \times 7\text{ cm} = 269.5\text{ cm}^3\] Therefore, the volume of the solid cylinder is 269.5cm³.

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Question 29 Report

Given that $\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}$, find K,

Answer Details

We have the expression: $\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}$. We can simplify the two radicals to get: $\sqrt{128}=8\sqrt{2}$ and $\sqrt{18}=3\sqrt{2}$. Substituting these values into the expression, we get: $8\sqrt{2}+3\sqrt{2}-\sqrt{K} = 7\sqrt{2}$ Combining like terms on the left side, we have: $11\sqrt{2}-\sqrt{K} = 7\sqrt{2}$ Isolating the square root on the left side, we get: $-\sqrt{K} = -4\sqrt{2}$ Squaring both sides, we have: $K = (-4\sqrt{2})^2$ Simplifying the expression, we get: $K = 32$ Therefore, the value of K is 32.

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Positive And Negative Integers, Rational Numbers

Surds (radicals)

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Question 30 Report

Find the sum of the roots of the equation 2x² + 3x - 9 = 0

-18

-6

$-\frac{9}{2}$

$-\frac{3}{2}$

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Probability

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Question 31 Report

Use the graph to answer the Question below
What are the roots of the equation x² + 3x - 4 = 0?

1, 4

-1, -4

-1, 4

-4, 1

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Quadratic Equations

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Question 32 Report

lf $log_q p= r$, express p in terms of q and r

p =qr

p =r^q

$p = \frac{r}{q}$

p=q^r

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Logarithms

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Question 33 Report

The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?

4:5

8: 15

6:125

8:125

Answer Details

The ratio of the sides of the two cubes is 2:5. Let us assume that the length of the sides of the first cube is 2x, then the length of the sides of the second cube will be 5x, since the ratio of their sides is 2:5. The volume of the first cube will be (2x)^3 = 8x^3, and the volume of the second cube will be (5x)^3 = 125x^3. The ratio of the volumes of the two cubes will be: Volume of the first cube : Volume of the second cube = 8x^3 : 125x^3 = 8 : 125 Therefore, the ratio of their volumes is 8:125. Hence, the correct answer is "8:125".

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Question 34 Report

The diagram is a circle centre O. Find the value of x

30^o

50^o

61^o

78^o

65.5$^{\circ}$

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Circles

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Question 35 Report

Which of the following quadratic equations has $-\frac{1}{2}$ and $\frac{3}{4}$ as its roots?

8x² + 11x - 3 = 0

8x² -11x – 3 = 0

8x² + 2x -3 = 0

8x² - 2x – 3 = 0

Answer Details

The quadratic equation with roots $-\frac{1}{2}$ and $\frac{3}{4}$ can be written in factored form as: $$a(x+\frac{1}{2})(x-\frac{3}{4}) = 0$$ where a is a constant. Expanding this expression, we get: $$a(x+\frac{1}{2})(x-\frac{3}{4}) = ax^2+\frac{1}{8}a = 0$$ Simplifying the equation, we get: $$8ax^2 + a = 0$$ Now we can compare the coefficients of this equation with those in the given options to find the answer. Comparing the coefficients of the given options with our equation, we can see that only the equation: 8x² - 2x - 3 = 0 has the same coefficients, and therefore, the same roots, as the equation we derived. Therefore, the answer is: 8x² - 2x - 3 = 0.

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Quadratic Equations

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Question 36 Report

A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours

$\frac{36}{625}$

$\frac{16}{625}$

$\frac{12}{25}$

$\frac{13}{25}$

Answer Details

There are two possible ways to get two balls of different colors: first picking a red ball, then picking a white ball, or first picking a white ball, then picking a red ball. Since we replace the first ball before picking the second one, the probability of picking a red ball on the first draw is $\frac{3}{5}$, and the probability of picking a white ball on the second draw is also $\frac{2}{5}$, hence the probability of getting a red ball followed by a white ball is $\frac{3}{5}\cdot \frac{2}{5} = \frac{6}{25}$. The probability of picking a white ball first and a red ball second is also $\frac{6}{25}$. Therefore, the probability of getting two balls of different colors is the sum of the probabilities of the two cases, which is $\frac{6}{25}+\frac{6}{25} = \frac{12}{25}$. So, the correct option is: - $\frac{12}{25}$

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Question 37 Report

The table above gives the marks scored by a group of students in a test Use the table to answer the Question below
What is the probability of selecting a student from the group that scored 2 or 3?

$\frac{1}{11}$

$\frac{5}{22}$

$\frac{7}{22}$

$\frac{6}{11}$

Answer Details

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Probability

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Question 38 Report

A Cooperative Society, charges an interest of 5¹/₂% per annum on any amount borrowed by its members. If a member borrows N125,000, how much does he pay back after one year?

N136875

N131,875

N126750

N126250

Answer Details

If the Cooperative Society charges an interest of 5¹/₂% per annum, then the total amount to be paid back by the member at the end of the year will be the principal amount plus 5¹/₂% of the principal amount. 5¹/₂% can be written as a fraction of 5/2 in its simplest form. Therefore, the interest on N125,000 will be (5/2) * N125,000/100 = N3125. The total amount to be paid back by the member after one year will be the sum of the principal and the interest, which is N125,000 + N3125 = N128,125. Therefore, the member will pay back N128,125 after one year. The option that matches this result is N131,875, which is not correct.

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Fractions, Decimals And Approximations

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Question 39 Report

In the diagram, O is the centre of the circle where OS//QR and ?SOR = 35^o

35^o

45^o

55^o

70^o

Answer Details

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Question 40 Report

1. Evaluate $ 202^2_{three} - 112^2_{three}$

21120

21121

21112

21011

Answer Details

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Number Bases

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Question 41 Report

Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.

I only

II only

III only

I, II and III

Answer Details

Option III is true, while options I and II are not true. Explanation: I. The locus of points equidistant from a straight line is actually a pair of parallel lines, not a circle. To see this, consider any point on one side of the line, and draw the perpendicular from that point to the line. The set of all points equidistant from the line will be the line that passes through all of those perpendiculars. II. The locus of points equidistant from two given points is actually the perpendicular bisector of the line segment joining the two points, not a circle. To see this, note that any point on the perpendicular bisector is equidistant from the two points by definition. Conversely, any point equidistant from the two points must lie on the perpendicular bisector. III. The locus of points equidistant from two points is indeed the perpendicular bisector of the line segment joining the two points. To see this, consider any point on the perpendicular bisector. By definition, it is equidistant from the two points. Conversely, any point equidistant from the two points must lie on the perpendicular bisector.

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Coordinate Geometry

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Question 42 Report

In the diagram, PQRW is a circle. Line P, V and QR are produced to meet at M, where ?WMR = 30^o and |WM| = |MR| Find the value of x

10^o

25^o

35^o

60^o

Answer Details

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Trigonometry

Circles

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Question 43 Report

A school girl spends $\frac{1}{4}$ of her pocket money on books and $\frac{1}{3}$ on dress. What fraction remains?

$\frac{5}{6}$

$\frac{7}{12}$

$\frac{5}{12}$

$\frac{1}{6}$

Answer Details

The girl spends $\frac{1}{4}$ of her pocket money on books and $\frac{1}{3}$ on dress, which means she has spent a total of $\frac{1}{4}+\frac{1}{3}$ of her money. To find the fraction that remains, we need to subtract this amount from 1 (since 1 represents the whole amount of money). $\frac{1}{4}+\frac{1}{3} = \frac{3}{12}+\frac{4}{12} = \frac{7}{12}$ So, the fraction that remains is: $1-\frac{7}{12} = \frac{12}{12}-\frac{7}{12} = \frac{5}{12}$ Therefore, the answer is $\frac{5}{12}$.

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Question 44 Report

Find the area of a rectangle of length 4cm and whose diagonal is 6cm, (Leave your answer in surd form)

8√3cm²

12√3cm²

16√2cm²

16√3cm²

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Areas

Angles

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Question 45 Report

Find the value of x in the diagram

10^o

28^o

36^o

44^o

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Circles

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Question 46 Report

Simplify $7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}$and correct your answer to the nearest whole number

Answer Details

To simplify the expression $7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}$, we need to perform the arithmetic operations in the following order: division, addition, and subtraction. First, we need to simplify the expression inside the parentheses: \begin{align*} 2\frac{1}{2}+3 &= \frac{5}{2} + 3 \\ &= \frac{5}{2} + \frac{6}{2} \\ &= \frac{11}{2} \end{align*} Next, we need to divide $\frac{11}{2}$ by $16\frac{1}{2}$: \begin{align*} \frac{11}{2} \div 16\frac{1}{2} &= \frac{\frac{11}{2}}{\frac{33}{2}} \\ &= \frac{11}{33} \\ &= \frac{1}{3} \end{align*} Substituting $\frac{1}{3}$ into the original expression, we have: \begin{align*} 7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2} &= 7\frac{1}{2}-\frac{1}{3} \\ &= \frac{22}{3}-\frac{1}{3} \\ &= \frac{21}{3} \\ &= 7 \end{align*} Therefore, the answer is 7, corrected to the nearest whole number. Answer is correct.

Read lesson note on Solution Of Linear Equations (WAEC)

Read lesson note on Modular Arithmetic (WAEC)

Solution Of Linear Equations

Modular Arithmetic

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Question 47 Report

The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is

the perpendicular bisector of the line segment X Y

a line parallel to the line segment XY

a circle with XY as diameter

the line perpendicular to the line segment XY

Answer Details

Read lesson note on Loci (JAMB)

Read lesson note on Loci (WAEC)

Read lesson note on Coordinate Geometry (JAMB)

Loci

Coordinate Geometry

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Question 48 Report

In the diagram, KS is a tangent to the circle centre O at R and ?ROQ = 80^o. Find ?QRS.

90^o

80^o

50^o

40^o

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Circles

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Question 49 Report

Given that p = 2, q = -5 and r = - 4, evaluate 3p² - q² - r³

101

-27

Answer Details

Substitute the given values of p, q and r into the expression 3p² - q² - r³ to get: 3(2)² - (-5)² - (-4)³ = 12 - 25 + 64 = 51 Therefore, the answer is 51.

Read lesson note on Positive And Negative Integers, Rational Numbers (WAEC)

Read lesson note on Indices (WAEC)

Positive And Negative Integers, Rational Numbers

Indices

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Question 50 Report

The angle of elevation of the top of a tower from a point on the ground which is 36m away from the foot of the tower is 30^o. Calculate the height of the tower.

62.35m

20.78m

18.00m

10.39m

Answer Details

Let h be the height of the tower. We can form a right triangle with the tower, the ground point and the point directly below the top of the tower. Let's call the latter point P. Then, we have: - Angle of elevation of the top of the tower from point on ground = 30^o - Length of base of the right triangle (i.e., distance from the point on the ground to the foot of the tower) = 36m Therefore, we can use tangent function to find h: tan(30^o) = opposite / adjacent = h / 36 Solving for h, we have: h = 36 * tan(30^o) ≈ 20.78m Therefore, the height of the tower is approximately 20.78m. So, the correct option is (b) 20.78m.

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Circles

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