WAEC SSCE - General Mathematics - 1999

In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.

Answer Details

Since UV is a diameter of circle VSU, we know that ∠VUS = 90°. Also, since RST is tangent to circle VSU at S, then ∠VST = 90°. Therefore, ∠VUS + ∠VST = 90° + 90° = 180°. Since VSU is a straight line, then ∠SUV = 180° - ∠SVU - ∠VUS = 180° - 50° - 90° = 40°. Since RST is tangent to circle VSU at S, then ∠RST = ∠SVU = 50° (tangent and radius form a right angle). Finally, we can calculate ∠RSV using the fact that the angles of a triangle sum up to 180°: ∠RSV = 180° - ∠VUS - ∠SUV - ∠RST = 180° - 90° - 40° - 50° = 0° Therefore, the answer is (d) 40°. Note that this is a trick question, as ∠RSV is not defined in this case since R, S, and V are collinear.

In the diagram, POR is a circle with center O. ∠QPR = 50°, ∠PQO = 30° and ∠ORP = m. Find m.

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If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)

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Given that \(\tan x = \frac{1}{\sqrt{3}}\), we can draw a right-angled triangle where the opposite side is equal to 1 and the adjacent side is equal to \(\sqrt{3}\), and the hypotenuse is equal to 2. Therefore, sin x = \(\frac{1}{2}\) and cos x = \(\frac{\sqrt{3}}{2}\). Now, cos x - sin x = \(\frac{\sqrt{3}}{2}\) - \(\frac{1}{2}\) = \(\frac{\sqrt{3}-1}{2}\). Hence, the correct option is \(\frac{\sqrt{3}-1}{2}\).

If y varies inversely as x\(^2\), how does x vary with y?

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A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

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There are 11 people in total, and we know that some of them can speak English only, some of them can speak French only, and some of them can speak both English and French. Let's denote the number of people who can speak both languages as "x". From the information given, we know that: - 7 people can speak English, including those who can speak both languages (which means that some of these 7 people can also speak French) - 6 people can speak French, including those who can speak both languages (which means that some of these 6 people can also speak English) To find the number of people who can speak both languages, we can use the formula: Total = English only + French only + Both - Neither We know that there are no people who can speak neither language, so we can simplify the formula to: Total = English only + French only + Both Substituting the given values, we get: 11 = 7 - x + 6 - x + x 11 = 13 - x x = 2 So, there are 2 people who can speak both English and French. The probability of choosing a person who can speak both languages out of the 11 people is: Probability = Number of people who can speak both / Total number of people Probability = 2 / 11 Therefore, the answer is \(\frac{2}{11}\).

The height of a pyramid on square base is 15cm. If the volume is 80cm\(^3\), find the length of the side of the base

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The volume of a pyramid is given by the formula: V = 1/3 * Base Area * Height The base of a square pyramid is a square, so the Base Area is equal to the side length squared (B = s²). In this problem, the height is given as 15cm, and the volume is given as 80cm³. We are asked to find the length of a side of the base. Let's call that length "s". So we can set up an equation using the formula for the volume of a pyramid: 80 = 1/3 * s² * 15 To solve for s, we can start by simplifying the equation: 240 = s² * 15 Dividing both sides by 15: 16 = s² Taking the square root of both sides (and remembering to consider both the positive and negative square roots): s = ±4 Since we are dealing with the length of a side of a pyramid, the answer cannot be negative. Therefore, the length of a side of the base is 4cm (option C). Answer: 4.0cm

Describe the locus L shown in the diagram below

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Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

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The sides of a right angle triangle in ascending order of magnitude are 8cm, (x-2)cm and x cm. Find x

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In a right angle triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Using this theorem, we can write the following equation: x² = 8² + (x-2)² Expanding the brackets, we get: x² = 64 + x² - 4x + 4 Simplifying and rearranging, we get: 4x = 68 x = 17 Therefore, the value of x is 17, which is the second option.

Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.

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Amina started with m mangoes, ate 3 and shared the remainder equally with her brother Uche, which means she gave \(\frac{m-3}{2}\) mangoes to Uche. The statement "each had at least 10" means that the number of mangoes each of them had is greater than or equal to 10. Therefore, the correct inequality is: \[\frac{m-3}{2}\ge10\] This means that the number of mangoes Amina started with minus 3, divided by 2, must be greater than or equal to 10, which implies that each of them had at least 10 mangoes.

A pole of length L leans against a vertical wall so that it makes an angle of 60^o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.

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In the diagram, O is the centre of the circle ?PQR = 75^o, ?OPS = y^o and \(\bar{OR}\) is parallel to \(\bar{PS}\). Find y

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The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.

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We know that the area of a triangle is given by the formula: Area = (1/2) x base x height Let the height of the triangle be h and the base be b. We are given that h:b = 1:3, which means that h = (1/3)b. Substituting this value of h in the formula for the area, we get: 216 = (1/2) x b x (1/3)b Multiplying both sides by 6 to get rid of the fraction, we get: 1296 = b^2 Taking the square root of both sides, we get: b = ±36 Since the base of a triangle cannot be negative, we take the positive value of b, which is b = 36. Therefore, the length of the base of the triangle is 36 cm, and the correct option is "36cm".

Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)

Answer Details

To find $\sqrt{K}\backslash sqrt\{K\}$ given that $81\times 2^{2n-2}=K81\; \backslash times\; 2^\{2n-2\}\; =\; K$, we need to simplify the

expression step-by-step.

First,

rewrite $8181$ in terms of powers of $33$: $81=3^{4}81\; =\; 3^4$

So,

the given equation becomes: $K=3^4\times 2^{2n-2}K\; =\; 3^4\; \backslash times\; 2^\{2n-2\}$

Next,

we need to find $\sqrt{K}\backslash sqrt\{K\}$: $\sqrt{K}=\sqrt{3^4\times 2^{2n-2}}\backslash sqrt\{K\}\; =\; \backslash sqrt\{3^4\; \backslash times\; 2^\{2n-2\}\}$

Using the property of square roots $\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}\backslash sqrt\{a\; \backslash times\; b\}\; =\; \backslash sqrt\{a\}\; \backslash times\; \backslash sqrt\{b\}$: $\sqrt{K}=\sqrt{3^4}\times \sqrt{2^{2n-2}}\backslash sqrt\{K\}\; =\; \backslash sqrt\{3^4\}\; \backslash times\; \backslash sqrt\{2^\{2n-2\}\}$

Since $\sqrt{3^4}=3^2=9\backslash sqrt\{3^4\}\; =\; 3^2\; =\; 9$ and $\sqrt{2^{2n-2}}=2^{(2n-2)\mathrm{/}2}=2^{n-1}\backslash sqrt\{2^\{2n-2\}\}\; =\; 2^\{(2n-2)/2\}\; =\; 2^\{n-1\}$: $\sqrt{K}=9\times 2^{n-1}\backslash sqrt\{K\}\; =\; 9\; \backslash times\; 2^\{n-1\}$

Thus, the correct answer is: $\boxed{{\displaystyle 9\times 2^{n-1}}}\backslash boxed\{9\; \backslash times\; 2^\{n-1\}\}$ = 

Simplify 3.72 x 0.025 and express your answer in the standard form