WAEC SSCE - General Mathematics - 2008
Question 1 Report
Factorize 5y2 + 2ay - 3a2
Answer Details
To factorize 5y^2 + 2ay - 3a^2, we need to find two numbers that multiply to give -15a^2 and add up to 2a. These numbers are 5a and -3a. We can then rewrite the expression as: 5y^2 + 5ay - 3ay - 3a^2 Factorising by grouping: (5y^2 + 5ay) - (3ay + 3a^2) Factorising out the common factor in each group: 5y(y + a) - 3a(y + a) Factorising out the common factor (y + a): (5y - 3a)(y + a) Therefore, the answer is (5y - 3a)(y + a).
Question 2 Report
If tan x = 1, evaluate sin x + cos x, leaving your answer in the surd form
Answer Details
If \(\tan x = 1\), then we can find the values of sin x and cos x using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\). Since \(\tan x = \frac{\sin x}{\cos x} = 1\), we can say that \(\sin x = \cos x\). So we have, \[\sin^2 x + \cos^2 x = 2\cos^2 x = 1 \implies \cos x = \pm\frac{1}{\sqrt{2}}\] Using \(\sin x = \cos x\), we can say that \(\sin x = \pm\frac{1}{\sqrt{2}}\) Now, \[\sin x + \cos x = \pm\frac{1}{\sqrt{2}} \pm \frac{1}{\sqrt{2}} = \pm\sqrt{2}\] Since \(\tan x = 1\), x must be in the first quadrant, where both \(\sin x\) and \(\cos x\) are positive. Therefore, we have \[\sin x + \cos x = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}} = \sqrt{2}\] Hence, the answer is \(\sqrt{2}\). Therefore, the option that represents this answer is: $\sqrt{2}$.
Question 4 Report
In the diagram, < QPR = 60o
< PQR = 50o
< QRS = 2xo
< SRP = 3xo
< UQP = yo and RS//TU
calculate y
Question 5 Report
Find the mean deviation of these numbers 10, 12, 14, 15, 17, 19.
Answer Details
To find the mean deviation of a set of numbers, we first find the mean (average) of the numbers. The mean of the numbers 10, 12, 14, 15, 17, and 19 is: (mean) = (10 + 12 + 14 + 15 + 17 + 19) / 6 = 87 / 6 = 14.5 Next, we find the deviation of each number from the mean by subtracting the mean from each number: 10 - 14.5 = -4.5 12 - 14.5 = -2.5 14 - 14.5 = -0.5 15 - 14.5 = 0.5 17 - 14.5 = 2.5 19 - 14.5 = 4.5 We take the absolute value of each deviation to ensure that they are all positive: |-4.5| = 4.5 |-2.5| = 2.5 |-0.5| = 0.5 |0.5| = 0.5 |2.5| = 2.5 |4.5| = 4.5 Then we find the mean of the absolute deviations: (mean deviation) = (4.5 + 2.5 + 0.5 + 0.5 + 2.5 + 4.5) / 6 = 2.5 Therefore, the mean deviation of the numbers is 2.5. Therefore, the correct option is (a) 2.5.
Question 6 Report
If the volume of a cube is 343cm3, find the length of its side
Answer Details
To find the length of a side of a cube, we need to take the cube root of its volume. In this case, the volume is given as 343cm3. Taking the cube root of 343, we get: ∛343 = 7 Therefore, the length of the side of the cube is 7cm. So the correct answer is 7cm.
Question 7 Report
Find the quadratic equation whose roots are c and -c
Answer Details
If the roots of the quadratic equation are c and -c, then the equation can be expressed in the factored form as: (x - c)(x + c) = 0 Expanding the above expression: x^2 - c^2 = 0 Therefore, the quadratic equation whose roots are c and -c is x^2 - c^2 = 0. Hence, the correct option is: x2 - c2 = 0.
Question 11 Report
Given that x = 2 and y = -\(\frac{1}{4}\), evaluate \(\frac{x^2y - 2xy}{5}\)
Answer Details
Question 12 Report
A trader bought 100 tubers at 5 for N350.00. She sold them in sets of 4 for N290.00. Find her gain percent.
Answer Details
Question 13 Report
If x \(\alpha\) (45 + \(\frac{1}{2}y\)), which of the following is true>?
Question 14 Report
Simplify: \(\frac{2x^2 - 5x - 12}{4x^2 - 9}\)
Answer Details
To simplify the given expression, we need to factor the numerator and the denominator and then simplify the fraction by canceling out any common factors. The numerator can be factored as follows: \begin{align*} 2x^2 - 5x - 12 &= 2x^2 - 8x + 3x - 12 \\ &= 2x(x - 4) + 3(x - 4) \\ &= (2x + 3)(x - 4) \end{align*} The denominator can be factored using the difference of squares formula as: \begin{align*} 4x^2 - 9 &= (2x)^2 - 3^2 \\ &= (2x - 3)(2x + 3) \end{align*} Now we can simplify the fraction as follows: \begin{align*} \frac{2x^2 - 5x - 12}{4x^2 - 9} &= \frac{(2x + 3)(x - 4)}{(2x - 3)(2x + 3)} \\ &= \frac{x - 4}{2x - 3} \end{align*} Therefore, the simplified form of the expression is \(\frac{x - 4}{2x - 3}\). So, option (B) is the correct answer.
Question 16 Report
If x% of 240 equals 12, find x
Answer Details
We can start solving the problem by setting up an equation based on the information given. The problem states that "x% of 240 equals 12". In other words, we can translate this into an equation: x/100 * 240 = 12 To solve for x, we can isolate it by dividing both sides of the equation by 240/100, which simplifies to 2.4: x/100 * 240 = 12 x = 12 / 2.4 x = 5 Therefore, the value of x that satisfies the given equation is 5.
Question 17 Report
A train travels 60km in M minutes. If its average speed is 400km per hour, find the value of M
Answer Details
The average speed of the train is given as 400km/hr. This means that in one hour, the train travels 400km. We can convert this to km/minute by dividing by 60 (the number of minutes in an hour). Therefore, the speed of the train in km/minute is: 400km/hr ÷ 60 = 6.67km/min (rounded to two decimal places) We are given that the train travels 60km in M minutes. We can use the formula: speed = distance/time to find the value of M. Rearranging the formula gives: time = distance/speed Substituting the given values, we get: M = 60km ÷ 6.67km/min M = 9 minutes (rounded to the nearest minute) Therefore, the value of M is 9.
Question 18 Report
In the diagram, PQRS is a rhombus. /PR/ = 10cm and /QS/ = 24cm. Calculate the perimeter of the rhombus
Answer Details
Question 19 Report
If xo is obtuse, which of the following is true?
Question 20 Report
Solve the inequality 1 - 2x < - \(\frac{1}{3}\)
Answer Details
The given inequality is: 1 - 2x < -\(\frac{1}{3}\) To solve this inequality, we need to isolate the variable, which in this case is x. First, we can simplify the inequality by adding \(\frac{1}{3}\) to both sides: 1 - 2x + \(\frac{1}{3}\) < 0 Next, we can combine like terms: \(\frac{4}{3}\) - 2x < 0 Now, we can isolate x by subtracting \(\frac{4}{3}\) from both sides: -2x < -\(\frac{4}{3}\) Finally, we can solve for x by dividing both sides by -2, remembering to flip the inequality because we are dividing by a negative number: x > \(\frac{2}{3}\) Therefore, the solution to the inequality is x > \(\frac{2}{3}\).
Question 21 Report
If p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), express q in terms of p and r
Answer Details
Given that p = \(\frac{3}{5} \sqrt{\frac{q}{r}}\), we need to express q in terms of p and r. Let's first isolate the term containing q on one side of the equation: \begin{align*} p &= \frac{3}{5} \sqrt{\frac{q}{r}} \\ \frac{5}{3}p &= \sqrt{\frac{q}{r}} \\ \left(\frac{5}{3}p\right)^2 &= \frac{q}{r} \\ \frac{25}{9} p^2r &= q \\ \end{align*} Therefore, q is equal to \(\frac{25}{9} p^2r\). So the correct option is: \(\frac{25}{9} p^2r\)
Question 22 Report
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their difference is 6 or 7?
Answer Details
Question 23 Report
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is picked at random from each of the two sets, what is the probability that their difference is odd?
Answer Details
Question 25 Report
XY is a chord of circle centre O and radius 7cm. The chord XY which is 8cm long subtends an angle of 120o at the centre of the circle. Calculate the perimeter of the minor segment. [Take \(\pi = \frac{22}{7}\)]
Answer Details
Question 26 Report
In the figure /PX/ = /XQ/, PQ//YZ and XV//QR. What is the ratio of the area of XYZQ to te area of \(\bigtriangleup\)YZR?
Answer Details
Question 27 Report
What is the length of an edge of a cube whose total surface area is X cm2 and whose total surface area is \(\frac{X}{2}\)cm3?
Question 28 Report
The angles of a quadrilateral are (x + 10)o, 2yo, 90o and (100 - y)o, Find y in terms of x
Answer Details
The sum of the angles of a quadrilateral is 360o. Therefore, (x + 10)o + 2yo + 90o + (100 - y)o = 360o. Simplifying the equation, we have: x + 10 + 2y + 90 + 100 - y = 360 x + 200 + y = 360 y = 160 - x Therefore, y is equal to 160 subtracted by x. Hence, the correct option is y = 160 - x.
Question 29 Report
P naira invested for 4 years invested for 4 years at r% simple interest per annum yields 0.36 p naira interest. Find the value of r
Answer Details
We can use the formula for simple interest, which is: I = P * r * t Where I is the interest earned, P is the principal (initial amount invested), r is the annual interest rate, and t is the time in years. In this problem, we know that the interest earned is 0.36P, the principal is P, and the time is 4 years. Substituting these values into the formula, we get: 0.36P = P * r * 4 Simplifying the equation, we can divide both sides by P * 4: 0.36 = r * 4 r = 0.36 / 4 r = 0.09 or 9% Therefore, the answer is option (C) 9.
Question 30 Report
In the diagram, /PQ/ = /QR/ and /PR/ = /RS/ = /SP/, calculate the side of < QRS
Answer Details
Question 31 Report
In the figure shown, PQs is a straight line. What is the value of < PRQ?
Question 32 Report
Every staff in an office owns either a Mercedes and/or a Toyota car. 20 own Mercedes, 15 own Toyota and 5 own both. How many staff are there in the office?
Answer Details
To find the total number of staff in the office, we need to add the number of staff who own a Mercedes and the number of staff who own a Toyota, but we must subtract the number of staff who own both cars to avoid counting them twice. Using the given information, we know that there are 20 staff who own a Mercedes, 15 staff who own a Toyota, and 5 staff who own both. Therefore, the number of staff who own either a Mercedes or a Toyota is: 20 + 15 - 5 = 30 Therefore, there are 30 staff in the office who own either a Mercedes or a Toyota.
Question 33 Report
If p-2g + 1 = g + 3p and p - 2 = 0, find g
Answer Details
Substitute p = 2 in the equation p - 2g + 1 = g + 3p to get: 2 - 2g + 1 = g + 3(2) -2g = 3 - 2 -2g = 1 g = -1/2 Therefore, the answer is -1.
Question 34 Report
PQR is a sector of a circle centre O, radius 4cm. If PQR = 30o, find, correct to 3 significant figures, the area of sector PQR. [Take \(\pi = \frac{22}{7}\)]
Answer Details
To find the area of the sector PQR, we need to know the angle at the center of the circle that the sector subtends. Since the radius of the circle is 4 cm and PQR = 30o, the circumference of the circle is 2πr = 8π cm. The fraction of the circle that the sector PQR subtends is 30/360, or 1/12. Therefore, the area of the sector PQR is 1/12 of the total area of the circle: Area of sector PQR = (1/12) × πr2 = (1/12) × π × (4 cm)2 ≈ 3.347 cm2 Rounded to 3 significant figures, the area of sector PQR is approximately 3.35 cm2, which corresponds to the first option: 4.19 cm2.
Question 35 Report
If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x
Answer Details
Given that p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), we want to find the value of x. We can start by substituting the value of p in the second equation: \begin{aligned} \frac{1}{p - 1} &= \frac{2}{p + x} \\ \\ \frac{1}{\frac{1}{2} - 1} &= \frac{2}{\frac{1}{2} + x} && \text{(Substitute } p = \frac{1}{2} \text{)}\\ \\ \frac{1}{-\frac{1}{2}} &= \frac{2}{\frac{1}{2} + x} && \text{(Simplify)}\\ \\ -2 &= \frac{2}{\frac{1}{2} + x} && \text{(Simplify)}\\ \\ -2\left(\frac{1}{2} + x\right) &= 2 && \text{(Cross-multiply)}\\ \\ -1 - 2x &= 1 && \text{(Simplify)}\\ \\ -2x &= 2 \\ \\ x &= -1 \end{aligned} Therefore, the value of x is -1.5, which corresponds to option B: -1\(\frac{1}{2}\).
Question 36 Report
Simplify \(\frac{\log \sqrt{8}}{\log 4 - \log 2}\)
Answer Details
We can start by simplifying the numerator first: \begin{align*} \log \sqrt{8} &= \log \left(\sqrt{4}\cdot\sqrt{2}\right) \\ &= \log 4 + \log \sqrt{2} \\ &= 2 + \frac{1}{2} \log 2 \end{align*} Similarly, we can simplify the denominator: \begin{align*} \log 4 - \log 2 &= \log\frac{4}{2} \\ &= \log 2 \end{align*} Now we can substitute these simplified expressions back into the original expression: \begin{align*} \frac{\log \sqrt{8}}{\log 4 - \log 2} &= \frac{2 + \frac{1}{2} \log 2}{\log 2} \\ &= \frac{2}{\log 2} + \frac{1}{2} \\ &= \boxed{\frac{3}{2}} \end{align*} Therefore, the correct option is (c) \(\frac{3}{2}\).
Question 37 Report
In the diagram, O is the centre of the circle and PQRS is a cyclic quadrilateral. Find the value of x.
Question 38 Report
An arc of a circle, radius 14cm, is 18.33cm long. Calculate to the nearest degree, the angle which the arc subtends at the centre of the circle. [T = \(\frac{22}{7}\)]
Answer Details
The formula for the length of an arc is L = rθ where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the centre of the circle in radians. To find the angle in degrees, we need to convert radians to degrees by multiplying by 180/π. In this problem, the radius of the circle is 14cm and the length of the arc is 18.33cm. Plugging these values into the formula, we get: 18.33 = 14θ Solving for θ, we get: θ = 18.33/14 θ = 1.3093 radians To convert to degrees, we multiply by 180/π: θ = 1.3093 × 180/π θ ≈ 75 degrees Therefore, the angle which the arc subtends at the centre of the circle is approximately 75 degrees. Answer: 75o
Question 39 Report
Simplify \(\frac{\frac{1}{x} + \frac{1}{y}}{x + y}\)
Answer Details
To simplify the expression, we can start by getting a common denominator for the two fractions in the numerator. The common denominator is xy. So, we can write: \begin{align*} \frac{\frac{1}{x} + \frac{1}{y}}{x + y} &= \frac{\frac{y}{xy} + \frac{x}{xy}}{x + y} \\ &= \frac{\frac{x + y}{xy}}{x + y} \\ &= \frac{1}{xy} \end{align*} Therefore, the simplified expression is \(\frac{1}{xy}\).
Question 40 Report
In the diagram, PX is a tangent to the circle and RST is an equilateral triangle. Calculate < PTS
Question 41 Report
Given the sets A = [2, 4, 6, 8] and B = [2, 3, 5, 9]. If a number is selected at random from set B, what is the probability that the number is prime?
Question 42 Report
If 4y is 9 greater than the sum of y and 3x, by how much is greater than x?
Answer Details
Let's start by translating the sentence into an equation: 4y = 9 + y + 3x We can simplify this equation by subtracting y from both sides: 3y = 9 + 3x Now, let's isolate x by subtracting 9 from both sides and then dividing by 3: x = (3y - 9)/3 = y - 3 So we see that x is 3 less than y. Therefore, the answer is (A) 3.
Question 43 Report
If the perimeter of \(\bigtriangleup\)PQR in thr diagram is 24cm, what is the area of \(\bigtriangleup\)PRS?
Answer Details
Question 44 Report