WAEC SSCE - General Mathematics - 2022

If √24 + √96 - √600 = y√6, find the value of y

Answer Details

To find the value of y in the given expression, let's simplify it step by step: √24 + √96 - √600 = y√6 First, let's simplify the square roots inside the expression: √24 = √(4 * 6) = √4 * √6 = 2√6 √96 = √(16 * 6) = √16 * √6 = 4√6 √600 = √(100 * 6) = √100 * √6 = 10√6 Now, we substitute the simplified values back into the expression: 2√6 + 4√6 - 10√6 = y√6 Combining like terms: (2 + 4 - 10)√6 = y√6 Simplifying further: -4√6 = y√6 Since the coefficient of √6 on both sides of the equation is the same, we can conclude that the value of y must be -4. Therefore, y = -4. So, the correct answer is -4.

Evaluate, correct to four significant figures, (573.06 x 184.25).

Answer Details

573.06 x 184.25 = 105,586.305

1,05600.00 to four significant figure

What are the Rules for significant figures?

Significant Figures

• All non-zero numbers ARE significant.
• Zeros between two non-zero digits ARE significant. 
• Leading zeros are NOT significant.
• Trailing zeros to the right of the decimal ARE significant.
• Trailing zeros in a whole number with the decimal shown ARE significant.

A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?

Answer Details

To find how high up the wall the ladder reaches, we can use trigonometry, specifically the sine function. Given: Length of the ladder = 6m Angle between the ladder and the horizontal = 53º We want to find the height of the ladder on the wall. Using the trigonometric relationship for right triangles, we can use the sine function to relate the angle and the sides of the triangle. sin(angle) = opposite / hypotenuse In this case, the height of the ladder on the wall is the opposite side, and the length of the ladder is the hypotenuse. sin(53º) = height / 6 To find the height, we rearrange the equation: height = sin(53º) * 6 Using a calculator, we can evaluate sin(53º) ≈ 0.7986. height ≈ 0.7986 * 6 ≈ 4.7916 Therefore, the height up the wall that the ladder reaches is approximately 4.7916m. So, the correct answer is 4.792m.

Answer Details

The area of a rectangle = length ✕ width

: Length = area ÷ width → 3 38 $\frac{\mathrm{<br>}}{}$ ÷ 34 $\frac{\mathrm{<br>}}{}$

= 278 $\frac{\mathrm{<br>}}{}$ * 43 $\frac{\mathrm{<br>}}{}$

= 412 $\frac{\mathrm{<br>}}{}$cm

An exterior angle of a regular polygon is 22.5°. Find the number of sides.

Answer Details

For a regular polygon with n sides, each exterior angle is equal to 360°/n. Given that the exterior angle of the regular polygon is 22.5°, we can set up an equation as follows: 360°/n = 22.5° Multiplying both sides by n, we get: 360° = 22.5°n Dividing both sides by 22.5°, we get: n = 360°/22.5° = 16 Therefore, the regular polygon has 16 sides. Hence, the answer is (d) 16.

The age (years) of some members in a singing group are: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41 and 36.

Find the lower quartile

Answer Details

To find the lower quartile, we need to first arrange the ages in ascending order. Here are the ages provided: 12, 47, 49, 15, 43, 41, 13, 39, 43, 41, and 36. Next, we divide the data set into four equal parts, with each part containing an equal number of values. The lower quartile is the median of the first half of the data set. Let's arrange the ages in ascending order: 12, 13, 15, 36, 39, 41, 41, 43, 43, 47, 49 We can see that there are 11 ages in total, which means the first half contains 11/2 = 5.5 ages. Since we can't have a fraction of an age, we round down to the nearest whole number, which is 5. Now, let's look at the five ages in the first half of the data set: 12, 13, 15, 36, 39. To find the lower quartile, we need to find the median of this subset of ages. Since there are an odd number of ages (5), the median is the middle value. In this case, the middle value is 15. Therefore, the lower quartile is 15. So, the correct answer is 15.

Simplify 2−18m21+3m

Answer Details

2−18m21+3m $\frac{\mathrm{<br>}}{}$ =  2[1−9m2]1+3m $\frac{\mathrm{<br>}}{}$

2[1−3m][1+3m]1+3m $\frac{\mathrm{<br>}}{}$

2[1-3m]

Change 432five ${}_{\mathrm{<br>}}$  to a number in base three.

Answer Details

Convert from base 5 to base 10

432five ${}_{\mathrm{<br>}}$ =  (4 x 52 ${}^2$) + (3 x 51 ${}^1$) + (2 x 50 ${}^0$)

= (4 x 25) + (3 x 5) + (2 x 1)

= 100 + 15 + 2

= 117ten ${}_{\mathrm{<br>}}$

Then convert from base 10 to base 3

Selecting the remainders from bottom to top:

117ten ${}_{\mathrm{<br>}}$ = 11100three ${}_{\mathrm{<br>}}$

Hence; 432five ${}_{\mathrm{<br>}}$ =  11100three

Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).

Answer Details

n(AuB) = n(A) + n(B) -  n(AnB)

n(AuB) = 8 + 12 - 3

= 17 

Answer Details

 5b+(a+b)2(a−b)2 $\frac{\mathrm{<br>}}{}$

= 5∗−7+(3+−7)2(3−−7)2 $\frac{\mathrm{<br>}}{}$

=  −35+16102 $\frac{<br>}{}$

=  −19100 $\frac{<br>}{}$ or -0.19

In the diagram, MNR is a tangent to the circle centre O at N and ∠NOS = 108°. Find ∠OSN

Answer Details

The sum of angles in a triangle = 180º

(180 - 108)º = 72º

Isosceles triangle has both two equal sides and two equal angles.

 ∠OSN =  ∠SON = 722 $\frac{\mathrm{<br>}}{}$

= 36º

Consider the statements:

p: Stephen is intelligent

q: Stephen is good at Mathematics

If p⇒q, which of the following is a valid conclusion?

Answer Details

The given statements are: - p: Stephen is intelligent - q: Stephen is good at Mathematics The symbol "⇒" means "implies". So, p⇒q means "if Stephen is intelligent, then he is good at Mathematics". , "If Stephen is good at Mathematics, then he is intelligent", is a valid conclusion because it is the contrapositive of p⇒q. In other words, if the original statement is true, then its contrapositive must also be true. The contrapositive of p⇒q is "if Stephen is not good at Mathematics, then he is not intelligent" However, is also valid because the contrapositive of a true statement is always true. , "If Stephen is not intelligent, then he is not good at Mathematics", is the inverse of the original statement and is not necessarily true. In other words, just because Stephen is not intelligent, it does not mean that he is not good at Mathematics. For example, he may have a natural talent for Mathematics even if he is not generally intelligent. , "If Stephen is not good at Mathematics, then he is intelligent", is the converse of the original statement and is also not necessarily true. In other words, just because Stephen is good at Mathematics, it does not mean that he is intelligent. For example, he may be good at Mathematics but struggle with other subjects. So, the valid conclusion is: "If Stephen is good at Mathematics, then he is intelligent".

Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]

Answer Details

The formula for the volume of a cone is V = 1/3 πr^2h, where r is the radius of the base and h is the height of the cone. Substituting the given values into the formula: V = 1/3 × 22/7 × (3.5cm)^2 × 12cm = 1/3 × 22/7 × 12.25cm^2 × 12cm = 1/3 × 22/7 × 147cm^3 = 22/7 × 49cm^3 = 154cm^3 Therefore, the volume of the cone is 154cm^3. The answer is (d) 154cm3.

Mary has $ 3.00 more than Ben but $ 5.00 less than Jane. If Mary has $ x, how much does Jane and Ben have altogether?

Answer Details

Let's use algebra to solve the problem. Given that Mary has $3.00 more than Ben, we can express Ben's amount of money in terms of x as (x - 3). Also, given that Mary has $5.00 less than Jane, we can express Jane's amount of money in terms of x as (x + 5). Therefore, the sum of Ben and Jane's money would be: Ben + Jane = (x - 3) + (x + 5) Simplifying this expression, we get: Ben + Jane = 2x + 2 So, the correct answer is $(2x+2).

The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm2 ${}^2$, find the perpendicular distance between the parallel sides.

Answer Details

To find the perpendicular distance between the parallel sides of a trapezium, we can use the formula for the area of a trapezium. The formula for the area of a trapezium is given by: Area = (1/2) * (sum of parallel sides) * (perpendicular distance between the parallel sides) In this case, we are given: Length of one parallel side = 9 cm Length of the other parallel side = 12 cm Area of the trapezium = 105 cm² Let's denote the perpendicular distance between the parallel sides as "h." Using the formula for the area of a trapezium, we can rewrite it as: 105 = (1/2) * (9 + 12) * h Simplifying the equation: 105 = (1/2) * 21 * h Multiplying both sides by 2 to eliminate the fraction: 210 = 21h Dividing both sides by 21 to solve for "h": h = 210 / 21 h = 10 cm Therefore, the perpendicular distance between the parallel sides of the trapezium is 10 cm. So, the correct answer is 10 cm.

M varies directly as n and inversely as the square of p. If M= 3 when n = 2 and p = 1, find M in terms of n and p.

Answer Details

The problem tells us that M varies directly as n and inversely as the square of p. This can be written as: M ∝ n/p^2 Where the symbol "∝" means "is proportional to". We can also write this using a constant of proportionality k: M = k(n/p^2) To find the value of k, we can use the values of M, n, and p given in the problem: 3 = k(2/1^2) Simplifying this equation, we get: k = 3/2 Now we can use this value of k to find M in terms of n and p: M = (3/2)(n/p^2) Simplifying further: M = (3n)/(2p^2) Therefore, the answer is: - 3n/(2p^2)

In the diagram, triangle MNR is inscribed in circle MNR and line PQ is a straight line. ∠MRN = 41 and = 141, find ∠QNR

Answer Details

We can use the property that an angle inscribed in a circle is half the measure of the arc it intercepts. Since triangle MNR is inscribed in circle MNR, we know that angle MNR is half the measure of arc MR. Similarly, angle MRN is half the measure of arc MN. We also know that arc PQM and arc QNR add up to a full circle, which has a measure of 360 degrees. Using these facts, we can write two equations: - angle MNR = 1/2(arc MR) = 1/2(360 - arc PQM - arc QNR) - angle MRN = 1/2(arc MN) = 1/2(360 - arc PQM) Substituting the given angle measures, we have: - 41 = 180 - arc PQM/2 - arc QNR/2 - 141 = 180 - arc PQM/2 Solving for arc PQM in the second equation gives us arc PQM = 198. Substituting this into the first equation, we have: 41 = 180 - 99 - arc QNR/2 arc QNR/2 = 40 arc QNR = 80 Therefore, angle QNR is half the measure of arc QNR, which is 80 degrees. So, the answer is 80º.

Solve 6x2 ${}^{\mathrm{<br>}}$ = 5x - 1

Answer Details

To solve the equation 6x^2 = 5x - 1, we first move all the terms to one side to obtain a quadratic equation in standard form, which is 6x^2 - 5x + 1 = 0. Then we can apply the quadratic formula: x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 6, b = -5, and c = 1. Plugging these values into the quadratic formula, we get: x = (-(-5) ± sqrt((-5)^2 - 4(6)(1))) / 2(6) x = (5 ± sqrt(25 - 24)) / 12 x = (5 ± 1) / 12 Therefore, the solutions to the equation are x = 1/2 and x = 1/3. So the answer is x = 1/2, 1/3.

The mean of two numbers x and y is 4. Find the mean of four numbers x, 2x, y and 2y

Answer Details

The mean of two numbers x and y is 4, which means (x + y) / 2 = 4. Solving for x + y, we get x + y = 8. Now we need to find the mean of four numbers x, 2x, y, and 2y. The mean is calculated by adding up all the numbers and dividing by the total number of numbers. So the sum of these four numbers is x + 2x + y + 2y = 3x + 3y, and the total number of numbers is 4. Therefore, the mean is (3x + 3y) / 4. We can substitute 8 for x + y since we know it equals 8, and simplify the expression to get (3x + 3y) / 4 = (3(x+y)) / 4 = (3(8)) / 4 = 6. Therefore, the mean of the four numbers x, 2x, y, and 2y is 6. The answer is option C.

A trader made a loss of 15% when an article was sold. Find the ratio of the selling price  : cost price

Answer Details

Let's assume the cost price of the article to be 100. As per the question, the trader made a loss of 15% when the article was sold. Therefore, the selling price would be: Selling price = Cost price - Loss Selling price = 100 - 15% of 100 Selling price = 100 - 15 Selling price = 85 So, the ratio of selling price to cost price can be calculated as: Selling price : Cost price = 85 : 100 Selling price : Cost price = 17 : 20 Therefore, the ratio of the selling price to cost price is 17:20. Hence, the correct option is (C) 17:20.

A cylinder, opened at one end, has a radius of 3.5cm and height 8cm. calculate the total surface area

Answer Details

The surface area of an open-top cylinder = πr(r + 2h),

where 'r' is the radius and 'h' is the height of the cylinder.

= 227 $\frac{\mathrm{<br>}}{}$ * 3.5 (3.5 + 2 * 8)

= 11 (3.5 + 16) → 11 (19.5)

= 214.5cm2

Given that log3 ${}_3$ 27 = 2x + 1, find the value of x.

Answer Details

Recall that: log3 ${}_3$ 27 → log3 ${}_3$33 ${}^{\mathrm{<br>}}$

3log3 ${}_3$3 → 3 * 1

= 3

Then log3 ${}_3$ 27 = 2x + 1

→ 3 = 2x + 1 

3 - 1 = 2x

2 = 2x

1 = x

Mrs Gabriel is pregnant. The probability that she will give birth to a girl is 1/2 and with  blue eyes is 1/4. What is the probability that she will give birth to a girl with blue eyes? 

Answer Details

To find the probability that Mrs. Gabriel will give birth to a girl with blue eyes, we can multiply the probabilities of each event. Given: Probability of giving birth to a girl = 1/2 Probability of having a baby with blue eyes = 1/4 To find the probability of both events happening, we multiply the individual probabilities: Probability of girl with blue eyes = (Probability of girl) * (Probability of blue eyes) = (1/2) * (1/4) = 1/8 Therefore, the probability that Mrs. Gabriel will give birth to a girl with blue eyes is 1/8. So, the correct answer is 1/8.

A boy 14 m tall, stood 10m away from a tree of height 12 m. Calculate, correct to the nearest degree, the angle of elevation of the top of the tree from the boy's eyes.

Answer Details

The angle of elevation

= Tan θ = oppadj $\frac{\mathrm{<br>}}{}$

Tan θ = 12+1410 $\frac{\mathrm{<br>}}{}$

Tan θ =  2610 $\frac{\mathrm{<br>}}{}$

θ = Tan−1 ${}^{<br>}$(2.6)

θ ≈ 70º

Find the area of the sector OPSQ

Answer Details

θ360
  *π * r2 ${}^{\mathrm{<br>}}$ → 210∗22∗4.2∗4.2360∗7 $\frac{\mathrm{<br>}}{}$

161750 $\frac{\mathrm{<br>}}{}$ = 32.34cm2

In the diagram, ∠POQ = 150 and the radius of the circle PSQR is 4.2cm. [take π = 22/7]

What is the length of the minor arc?

Answer Details

θ360
  * 2 * π * r → 150∗2∗22∗4.2360x7 $\frac{\mathrm{<br>}}{}$

= 11cm

The straight line y = mx - 4 passes through the point(-4,16). Calculate the gradient of the line

Answer Details

To calculate the gradient of the line, we need to find the slope, which is represented by "m" in the equation y = mx - 4. The slope of a line tells us how steep or flat it is. To find the slope, we can use the coordinates of the given point (-4, 16) and the equation of the line. The equation tells us that for any point on the line, the y-coordinate (vertical) is equal to the slope multiplied by the x-coordinate (horizontal) minus 4. Let's substitute the given point's coordinates into the equation: 16 = m(-4) - 4 Now, let's simplify the equation: 16 = -4m - 4 To solve for "m," we need to isolate it on one side of the equation. Let's add 4 to both sides: 16 + 4 = -4m Simplifying further: 20 = -4m To find the value of "m," we divide both sides by -4: 20/-4 = m Simplifying the division: -5 = m Therefore, the gradient or slope of the line is -5.

If 5x + 3y=4 and 5x-3y= 2, what is the value of (25x2 ${}^{\mathrm{<br>}}$ -9y2 ${}^{\mathrm{<br>}}$)?

Answer Details

5x + 3y=4

5x-3y= 2

Using elimination method 

5x + 3y=4 →    5x + 3y=4

-[5x-3y= 2] → -5x +3y= -2

6y = 2 

y → 1/3 and x = 3/5

solving (25x2 ${}^{\mathrm{<br>}}$ -9y2 ${}^{\mathrm{<br>}}$)

25 * [3/5]2 ${}^{\mathrm{<br>}}$ -9 * [1/3]