WAEC SSCE - General Mathematics - 1998

Question 1 Report

It is observed that $1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2. \\If \hspace{1mm}1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P^2 find\hspace{1mm}P$

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Sequence And Series

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Question 2 Report

The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x

$y=\frac{x}{2}$

$y\frac{x}{\sqrt{2}}$

$y=\sqrt{x}$

$y=\sqrt{\frac{x}{2}}$

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Question 3 Report

Convert 35 to a number in base two

1011_two

10011_two

100011_two

110010_two

110001_two

Answer Details

To convert the number 35 to a number in base two, we need to divide 35 by 2 repeatedly until we get a quotient of 0, taking note of the remainder at each step. The remainders, read from bottom to top, will give us the binary equivalent of 35. 35 divided by 2 gives us a quotient of 17 and a remainder of 1. 17 divided by 2 gives us a quotient of 8 and a remainder of 1. 8 divided by 2 gives us a quotient of 4 and a remainder of 0. 4 divided by 2 gives us a quotient of 2 and a remainder of 0. 2 divided by 2 gives us a quotient of 1 and a remainder of 0. 1 divided by 2 gives us a quotient of 0 and a remainder of 1. Reading the remainders from bottom to top, we get 100011 as the binary equivalent of 35. Therefore, we can conclude that 35 in base two is 100011_two.

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Number Bases

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Question 4 Report

Find the equation whose roots are $\frac{2}{3}and \frac{-1}{4}$

$12x^2+11x+2=0$

$12x^2-11x+2=0$

$x^2-\frac{11}{12}x+2=0$

$x^2+\frac{11}{12}x-2=0$

$12x^2+11x+2=0$

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Quadratic Equations

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Question 5 Report

P varies inversely as Q. The table above shows the value of Q for some selected values of P
What is the missing value of Q in the table?

144

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Solution Of Linear Equations

Quadratic Equations

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Question 6 Report

Cos x is negative and sin x is negative.Which of the following is true of x?

0^o < x < 90^o

90^o < x <180^o

180^o < x < 270^o

270^o < x <360^o

-90^o < x <90^o

Answer Details

If both cosine and sine are negative, it means the angle x is in the third quadrant of the unit circle where both coordinates x and y are negative. Therefore, the possible range for x is from 180 degrees to 270 degrees. Hence, the correct option is: - 180^o < x < 270^o

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Sine, Cosine And Tangent Of An Angle

Introductory Calculus

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Question 7 Report

If log$_{10}$ q = 2.7078, what is q?

5102

849.9

510.2

84.99

51.02

Answer Details

The logarithm of a number to a given base is the exponent to which the base must be raised to obtain the number. So, if log$_{10}$ q = 2.7078, then 10$^{2.7078}$ = q. Evaluating this expression, we get q ≈ 510.2. Therefore, the correct option is 510.2.

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Logarithms

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Question 8 Report

In the diagram above, the area of triangle ABC is 35cm², find the value of y

5cm

10cm

17.5cm

28cm

70cm

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Triangles And Polygons

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Question 9 Report

A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 4?

$\frac{1}{36}$

$\frac{1}{6}$

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{2}{3}$

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Question 10 Report

The values of x when y = -1 are approximately

-10 and 2.0

-1.3 and 2.3

-0.6 and 2.6

-0.6 and 1.6

1.6 and 1.6

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Fractions, Decimals, Approximations And Percentage

Quadratic Equations

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Question 11 Report

A chord of circle of radius 26cm is 10cm from the center of the circle. calculate the length of the chord

16cm

27.86cm

32cm

48cm

55.72cm

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Question 12 Report

The nth term of a sequence is represented by 3 x 2^(2-n). Write down the first three terms of the sequence

³/₂, 3, 6

6, 3, ³/₂

³/₂, 3, ¹/₃

²/₃, 3, ⁸/₃

³/₂, 0, 6

Answer Details

The nth term of the sequence is given as 3 x 2^(2-n). To find the first three terms of the sequence, we need to substitute the values of n = 1, 2, 3. When n = 1, the nth term is: 3 x 2^(2-1) = 3 x 2¹ = 3 x 2 = 6 When n = 2, the nth term is: 3 x 2^(2-2) = 3 x 2⁰ = 3 x 1 = 3 When n = 3, the nth term is: 3 x 2^(2-3) = 3 x 2^-1 = 3 x 1/2 = 3/2 = ³/₂ Therefore, the first three terms of the sequence are 6, 3, ³/₂. Hence, the answer is: 6, 3, ³/₂.

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Sequence And Series

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Question 13 Report

A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room?

3.78m

3.80m

4.18m

4.20m

4.788m

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Percentages

Fractions, Decimals, Approximations And Percentage

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Question 14 Report

Three of the angles of a hexagon are each X^o. The others are each 3X^o. Find X

30^o

40^o

60^o

80^o

120^o

Answer Details

The sum of the interior angles of a hexagon is given by the formula (n-2)×180^o, where n is the number of sides/angles in the polygon. Since a hexagon has six sides/angles, the sum of its interior angles is (6-2)×180^o = 4×180^o = 720^o. Let's assume that three angles of the hexagon are each X^o. Therefore, the sum of these three angles is 3X^o. The other three angles are each 3X^o, so their sum is 9X^o. Thus, the total sum of the six angles is: 3X^o + 9X^o = 12X^o But we also know that the sum of the interior angles of a hexagon is 720^o. Therefore, we can equate the two expressions: 12X^o = 720^o Dividing both sides by 12, we get: X^o = 60^o Therefore, the answer is X = 60^o.

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Indices

Triangles And Polygons

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Question 15 Report

In ?PQR. ?PQR is a right angle. |QR| = 2cm and ?PRQ = 60^o. Find |PR|

4?3cm

4cm

2?3cm

$\frac{4}{3}cm$

1cm

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Circles

Angles And Intercepts On Parallel Lines

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Question 16 Report

In the diagram PQ is a diameter of circle PMQN center O, if ?PQM = 63^o, find ?MNQ

58.5^o

44^o

35^o

31.5^o

27^o

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Circles

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Question 17 Report

p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?

-p < -2q

-p > -2q

-q < 2p

q < 1/2p

p² > 2q²

Answer Details

The statement that is not true is: `-p > -2q` Given that `p` is greater than `2q`, we can multiply both sides of the inequality by `-1` to obtain `-p < -2q`. Therefore, the statement `-p < -2q` is true. Similarly, we can multiply both sides of `p > 2q` by `-1` to get `-p < -2q`, and then multiply both sides by `-1` again to obtain `2q < p`. This means that `-q < 1/2p`, making the statement `-q < 1/2p` true. Now, to check the remaining options, we can square both sides of `p > 2q` to get `p^2 > 4q^2`, and since `4q^2 > 2q^2`, we have `p^2 > 2q^2`, making the statement `p^2 > 2q^2` true. Finally, we can divide both sides of `p > 2q` by `2` to get `q < 1/2p`, which means that the statement `q < 1/2p` is also true. Therefore, the only statement that is not true is `-p > -2q`.

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Question 18 Report

A ladder 5cm long long rest against a wall such that its foot makes an angle 30^o with the horizontal. How far is the foot of the ladder from the wall?

$\frac{5\sqrt{2}}{3}m$

$2\frac{1}{2}m$

$\frac{5\sqrt{3}}{2}m$

$\frac{10\sqrt{3}}{3}m$

$10\sqrt{3}m$

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Trigonometry

Coordinate Geometry

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Question 19 Report

Evaluate $3.0\times 10^1 - 2.8\times 10^{-1}$leaving the answer in standard form

$2\times 10^{-1}$

$2\times 10^{2}$

$2.972 \times 10^{1}$

$2.972 \times 10^{2}$

Answer Details

To subtract two numbers in scientific notation, we first need to make sure they have the same power of 10. We can do this by moving the decimal point to the right or left as needed. Starting with $3.0\times 10^1$ and $2.8\times 10^{-1}$, we can move the decimal point one place to the left in the first number to get $3.0$ and two places to the right in the second number to get $0.028$. Now we have: $$ 3.0 - 0.028 = 2.972 $$ To express the answer in standard form, we need to convert it to the form $a \times 10^b$, where $1 \leq a < 10$ and $b$ is an integer. We can do this by moving the decimal point to get a number between 1 and 10, and counting the number of places we moved it. In this case, we moved the decimal point one place to the left, so: $$ 2.972 = 2.972 \times 10^1 $$ Therefore, the answer is $2.972 \times 10^1$.

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Indices

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Question 20 Report

In the diagram, PQ||SR. Find the value of Z

30^o

40^o

45^o

90^o

120^o

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Angles And Intercepts On Parallel Lines

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Question 21 Report

The graph of the quadratic expression

$y=x^2 + x - 2$

$y=x^2 - x + 2$

$y=x^2 - x - 2$

$y=x + x + 2$

$y=x^2 - 2 x - 2$

Answer Details

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Quadratic Equations

Graphs Of Linear And Quadratic Functions

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Question 22 Report

Given that $\frac{6x-y}{x+2y}=2$, find the value of $\frac{x}{y}$

$\frac{3}{8}$

$\frac{5}{8}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{8}{5}$

Answer Details

We are given that: \[\frac{6x-y}{x+2y}=2\] To solve for $\frac{x}{y}$, we can simplify the equation above and isolate $\frac{x}{y}$. We start by cross multiplying both sides of the equation: \[6x-y=2(x+2y)\] Expanding the brackets, we get: \[6x-y=2x+4y\] Simplifying and isolating $x$, we get: \[4x=5y\] Therefore, $\frac{x}{y}=\frac{5}{4}$. Hence, the answer is $\frac{5}{4}$.

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Algebraic Fractions

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Question 23 Report

In $\triangle PQR$. T is a point on QR such that $\angle QPT = 39^o and \angle PTR = 83^o. Calculate \angle PQT$

$34^o$

$44^o$

$45^o$

$97^o$

$107^o$

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Question 24 Report

Find the value of X if $cos x = \frac{5}{8}for 0^o\le X\le 180^o$

141.3^o

128.7^o

51.3^o

48.7^o

38.7^o

Answer Details

To find the value of X, we can use the inverse cosine function (also known as the arccosine function) on both sides of the equation: \begin{align*} \cos x &= \frac{5}{8} \\ \Rightarrow \quad x &= \cos^{-1} \left( \frac{5}{8} \right) \end{align*} Using a calculator, we can find that: \begin{align*} x &\approx 51.32^\circ \end{align*} Therefore, the correct answer is 51.3^o.

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Sine, Cosine And Tangent Of An Angle

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Question 25 Report

In the diagram O is the center of circle PRQ. The radius is 3.5cm and ?POQ = 50^o. Use the diagram to answer question below. (take ? = 3.142)
Calculate correct to one decimal place, the length of arc PQ.

175.0cm

157.1cm

37.7cm

11.0cm

3.1cm

Answer Details

To find the length of arc PQ, we need to first find the circumference of the circle. The circumference of a circle with radius r is given by the formula: C = 2πr Substituting the given values, we get: C = 2 × 3.142 × 3.5 C ≈ 21.991cm Since the angle ?POQ is 50 degrees and the total angle of a circle is 360 degrees, the length of arc PQ is given by: length of arc PQ = (50/360) × C length of arc PQ ≈ 3.054cm ≈ 3.1cm (rounded to one decimal place) Therefore, the correct answer is 3.1cm.

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Circles

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Question 26 Report

Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35^o,find ∠PQS

35^o

45^o

55^o

70^o

90^o

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Circles

Triangles And Polygons

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Question 27 Report

In the diagram above, |PQ| = |PR| = |RS| and ?RSP = 35^o. Find ?QPR

70^o

50^o

45^o

40^o

35^o

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Angles

Triangles And Polygons

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Question 28 Report

Arrange in ascending order of magnitude $26_8, 36_7, and 25_9$

$25_9 26_8 36_7$

$26_8 25_9 36_7$

$36_7 26_8 25_9$

$36_7 25_9 26_8$

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Number Bases

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Question 29 Report

Find the number whose logarithm to base 10 is 2.6025

0.0004

4.004

40.04

400.4

4004

Answer Details

The logarithm of a number to base 10 is the power to which 10 is raised to give the number. Therefore, if log₁₀x = y, then x = 10^y. In this case, the logarithm to base 10 is given as 2.6025. Therefore, the number is x = 10^2.6025. Using a calculator, we get x ≈ 400.4. Therefore, the number whose logarithm to base 10 is 2.6025 is approximately 400.4.

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Logarithms

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Question 30 Report

solve the inequality $(Y-3)<\frac{y}{3}$

y > -9

y < 3

y > 4

y < 9

y > 0

Answer Details

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