WAEC SSCE - General Mathematics - 1990 (Objective)
Question 2 Report
An arc of length 22cm subtends an angle of θ at the center of the circle. What is the value of θ if the radius of the circle is 15cm?[Take π = 22/7]
Answer Details
To find the value of θ, we can use the formula: θ = (arc length / radius) In this case, the arc length is given as 22cm, and the radius is given as 15cm. So we have: θ = (22 / 15) θ = 1.47 (approx) However, the answer options are in degrees, so we need to convert radians to degrees. We can use the formula: degrees = (radians × 180) / π Substituting θ = 1.47 and π = 22/7, we get: degrees = (1.47 × 180) / (22/7) degrees = 89.14 (approx) Therefore, the answer is closest to option (B) 84o.
Question 3 Report
If 3\(^{2x}\) = 27, what is x?
Answer Details
We can solve for x by using the laws of exponents and taking the logarithm of both sides. First, we can rewrite 3²x as (3²)ⁿ, where n = 2x. So, we have: (3²)ⁿ = 27 3ⁿ² = 27 Now, we can take the logarithm of both sides of the equation. Let's use the natural logarithm, denoted as ln, which is the logarithm to the base e: ln(3ⁿ²) = ln(27) Using the power rule of logarithms, we can simplify the left-hand side: n² ln(3) = ln(27) Now, we can solve for n: n² = ln(27) / ln(3) n² = 3 Taking the square root of both sides, we get: n = ± √3 But we know that n = 2x, so we can substitute back: 2x = ± √3 Solving for x, we get: x = ± (1/2) √3 Since the question is asking for a real value of x, we can take the positive square root: x = (1/2) √3 ≈ 0.866 Therefore, x is approximately 0.866, which is option (B) 1.5 rounded to one decimal place.
Question 4 Report
The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart
How much money did he invest in agriculture?
Answer Details
Question 5 Report
Use mathematical table to evaluate (cos40° - sin30°)
Answer Details
To evaluate (cos40° - sin30°), we first need to find the values of cos40° and sin30°. Using a mathematical table (such as a trigonometric table), we can look up the values of cos40° and sin30°: - cos40° = 0.7660 - sin30° = 0.5000 Now we can substitute these values into the expression: (cos40° - sin30°) = (0.7660 - 0.5000) = 0.2660 Therefore, the answer is option (D) 0.2660.
Question 6 Report
The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school. What is the mode?
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Question 9 Report
In the diagram above, |PQ| = |PR| = |RS| and ?RPS = 32°. Find the value of ?QPR
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Question 10 Report
If log x = \(\bar{2}.3675\) and log y = 0.9750, what is the value of x + y? Correct to three significant figures
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Question 11 Report
calculate the surface area of a sphere of radius 7cm [Take π = 22/7]
Answer Details
The surface area of a sphere can be calculated using the formula: Surface area = 4πr2 where r is the radius of the sphere. Substituting r=7cm and π = 22/7, we get: Surface area = 4 x (22/7) x 72 cm2 Surface area = 4 x (22/7) x 49 cm2 Surface area = 616 cm2 Therefore, the surface area of the sphere is 616cm2. So the answer is 616cm2.
Question 12 Report
The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school.
What is the median of distributionAnswer Details
To find the median of a distribution, we first need to arrange the values in order from smallest to largest. In this case, the data is already presented in order, so we can simply identify the middle value of the data set. Since there are 5 values, the middle value will be the 3rd value. So, the median of the distribution is N12.00, which is the value in the middle of the data set. Therefore, the answer is (c) N12.00.
Question 13 Report
Solve the equation 7y\(^2\) = 3y
Answer Details
To solve the equation 7y\(^2\) = 3y, we can start by rearranging it to get 7y\(^2\) - 3y = 0. We can then factor out y to get y(7y - 3) = 0. From here, we have two solutions: y = 0 or 7y - 3 = 0, which gives us y = 3/7. Therefore, the solutions to the equation 7y\(^2\) = 3y are y = 0 or y = 3/7. Therefore, the answer is: y = 0 or 3/7.
Question 14 Report
If the shadow of a pole 7m high is 1/2 its length what is the angle of elevation of the sun, correct to the nearest degree?
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Question 15 Report
In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ?BTO. Find x.
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Question 17 Report
If the radius of the parallel of latitude 30°N is equal to the radius of the parallel of latitude θ°S, what is the value of θ?
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Question 18 Report
In the diagram above, PQRS s a cyclic quadrilateral, ?PSR = 86o and ?QPR = 38o. Calculate PRQ
Answer Details
In a cyclic quadrilateral, the opposite angles add up to 180 degrees. Therefore, we can find the value of angle PQR as follows: angle PSR + angle PQR = 180 (since PQRS is a cyclic quadrilateral) 86 + angle PQR = 180 angle PQR = 180 - 86 = 94 degrees We are given angle QPR as 38 degrees, and since angles in a triangle add up to 180 degrees, we can find angle PRQ as: angle PRQ = 180 - angle PQR - angle QPR angle PRQ = 180 - 94 - 38 angle PRQ = 48 degrees Therefore, the answer is option (C) 48o.
Question 19 Report
In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR
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Question 20 Report
In the diagram above, WXYZ is a rhombus and ?WYX = 20°. What is the value of ?XZY
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Question 21 Report
Two groups of male students cast their votes on a particular proposal. The result are as follows:
| In favor | Against | |
| Group A | 128 | 32 |
| Group B | 96 | 48 |
If a student in favor of the proposal is selected for a post, what is the probability that he is from group A?
Answer Details
Question 22 Report
Which angle is equal to ?VWZ?
Question 23 Report
The area shaded with horizontal lines is the solution set of the inequalities;
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Question 24 Report
Let J be the set of positive integers, If H = {x: x∈J, x\(^2\) < 3 and x ≠ 0}, then
Answer Details
The set H consists of all positive integers x such that x² is less than 3 and x is not equal to zero. The only positive integer that satisfies this condition is 1, because 1²=1 which is less than 3. Therefore, the set H contains only one element which is 1, so the answer is H = {1}. Option (a) is correct, and options (b), (c), (d), and (e) are incorrect. It is important to note that the symbol ∈ means "is an element of", and the symbol ≠ means "is not equal to". The symbol J ≤ H is not a valid statement because J is not a subset of H.
Question 25 Report
In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?
Answer Details
To find out how many students studied both economics and geography, we need to use the principle of inclusion-exclusion. First, we add the number of students who studied economics and geography, as some students could have studied both subjects. Let's call this number "x." Then, we subtract x from the total number of students (80), which gives us the number of students who studied only economics or only geography. We know that 65 students studied economics, so the number of students who studied only economics is 65 - x. Similarly, the number of students who studied only geography is 50 - x. Since every student had to study at least one subject, the total number of students who studied only economics or only geography is equal to the sum of the students who studied only economics and the students who studied only geography: (65 - x) + (50 - x) Simplifying this expression, we get: 115 - 2x But we know that this number is equal to the total number of students who studied only economics or only geography, which is 80 minus the number of students who studied both subjects: 80 - x Therefore, we can set up an equation: 115 - 2x = 80 - x Solving for x, we get: x = 35 So 35 students studied both economics and geography.
Question 26 Report
From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69o. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building
Question 27 Report
Given that 1/3log10 P = 1, find the value of P
Answer Details
We can solve for P by isolating it on one side of the equation. Starting with: 1/3log10 P = 1 We can multiply both sides by 3 to get rid of the 1/3: log10 P = 3 Now, we can rewrite this equation in exponential form: 103 = P Simplifying: P = 1000 Therefore, the value of P is 1000.
Question 29 Report
In the diagram above, O is the center of the circle with radius 10cm, and ?ABC = 30°. Calculate, correct to 1 decimal place, the length of arc AC [Take ? = 22/7]
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Question 30 Report
Express 0.00562 in standard form
Answer Details
To convert a decimal number to standard form, we need to express it in the form of a x 10n, where a is a number between 1 and 10 and n is an integer. Starting with 0.00562, we need to move the decimal point to the right until we obtain a number between 1 and 10. This means moving the decimal point four places to the right: 0.00562 = 5.62 x 10-3 Therefore, the answer is option A: 5.62 x 10-3.
Question 31 Report
A sector of a circle of radius 7cm has an area of 44cm2. Calculate the angle of the sector correct to the nearest degree [Take π = 22/7]
Answer Details
The formula for the area of a sector is: A = (θ/360)πr2 where A is the area of the sector, θ is the angle of the sector in degrees, r is the radius of the circle, and π is the mathematical constant pi. We are given that the radius of the circle is 7cm and the area of the sector is 44cm2. Substituting these values into the formula above, we get: 44 = (θ/360) × (22/7) × 72 Simplifying this equation, we get: 44 = (θ/360) × 22 × 7 44 = (θ/360) × 154 Multiplying both sides by 360, we get: θ = (44 × 360) / 154 θ = 102.597 Rounding to the nearest degree, we get: θ ≈ 103o Therefore, the angle of the sector correct to the nearest degree is 103o. Answer is correct.
Question 32 Report
the area shaded with vertical lines is the solution set of the inequalities;
Answer Details
Question 33 Report
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]
Find the total surface area of the container
Answer Details
The total surface area of the cylindrical container is the sum of the areas of its top, bottom, and lateral surface. The top and bottom of the container are both circles, each with an area of πr², where r is the radius of the container. So the total area of the top and bottom is 2πr². The lateral surface of the container is a rectangle that has been rolled into a cylinder. The length of the rectangle is the circumference of the circle, which is 2πr. The height of the rectangle is the height of the container, which is given as 5cm. So the area of the lateral surface is 2πrh. Therefore, the total surface area of the container is: 2πr² + 2πrh Substituting the given values for r and h, we get: 2 × (22/7) × 7² + 2 × (22/7) × 7 × 5 = 2 × (22/7) × 49 + 2 × (22/7) × 35 = (22/7) × 2 × (49 + 35) = (22/7) × 168 = 528 cm² Therefore, the total surface area of the container is 528 cm². So, the correct option is (D) 528cm².
Question 34 Report
Two groups of male students cast their vote on a particular proposal. The results are as follows:
| In favor | Against | |
| Group A | 128 | 32 |
| Group B | 96 | 48 |
If a student is chosen at random, what is probability that he is against the proposal?
Answer Details
To find the probability that a student chosen at random is against the proposal, we need to add up the number of students from Group A and Group B who are against the proposal, and divide that by the total number of students. The number of students against the proposal in Group A is 32, and in Group B it is 48. So the total number of students against the proposal is: 32 + 48 = 80 The total number of students in both groups is: 128 + 32 + 96 + 48 = 304 So the probability that a student chosen at random is against the proposal is: 80 / 304 = 5/19 Therefore, the answer is option (C) 5/19.
Question 35 Report
Factorize 2e\(^2\) - 3e + 1
Answer Details
To factorize 2e\(^2\) - 3e + 1, we can use the quadratic formula: e = (-b ± √(b² - 4ac)) / 2a where a = 2, b = -3, and c = 1. Plugging in the values, we get: e = (3 ± √(9 - 8)) / 4 e = (3 ± 1) / 4 So the roots are e = 1 and e = 1/2. Therefore, we can factorize 2e\(^2\) - 3e + 1 as: 2e\(^2\) - 3e + 1 = 2(e - 1)(e - 1/2) Simplifying this expression, we get: 2(e - 1)(2e - 1) Therefore, the factorization of 2e\(^2\) - 3e + 1 is (2e-1) (e-1), which corresponds to option (A).
Question 36 Report
Which of the sketches above gives a correct method for constructed an angle of 120o at the point P?
Answer Details
Question 37 Report
The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart
How much did he spend on food items?
Answer Details
Question 38 Report
The bearing of a point X from a point Y is 074°. What is the bearing of Y from X?
Answer Details
If the bearing of point X from point Y is 074°, then the bearing of Y from X is the opposite direction, which is 180° away from 074°. To find the bearing of Y from X, we can add 180° to 74°, which gives us 254°. Therefore, the correct answer is 254°.
Question 40 Report
Simplify \(\frac{\log \sqrt{8}}{\log 8}\)
Answer Details
We can simplify the expression using the laws of logarithms. First, we can simplify the numerator by using the fact that the square root of 8 is equal to 8 raised to the power of 1/2: log√8 = log(81/2) = 1/2 log 8 Now, we can substitute this into the original expression: \(\frac{\log \sqrt{8}}{\log 8} = \frac{1/2 \log 8}{\log 8}\) We can simplify this by canceling out the factor of log 8 in the numerator and denominator: \(\frac{1/2 \log 8}{\log 8} = \frac{1}{2}\) Therefore, the simplified expression is 1/2, which corresponds to option (B).
Question 41 Report
Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5
Answer Details
In an arithmetic progression (A.P.), the terms increase or decrease by a constant difference called the common difference. In this problem, the first term is 2, and the common difference is 0.5. Therefore, the second term would be 2 + 0.5 = 2.5, the third term would be 2.5 + 0.5 = 3, and the fourth term would be 3 + 0.5 = 3.5. Therefore, the answer is option (C) 3.5.
Question 42 Report
A cylindrical container closed at both ends, has a radius of 7cm and height 5cm [Take π = 22/7]. What is the volume of the container?
Answer Details
To find the volume of a cylindrical container, we use the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder. In this problem, the radius of the container is given as 7cm, and the height is given as 5cm. Substituting these values into the formula, we get: V = πr^2h V = (22/7)(7^2)(5) V = (22/7)(49)(5) V = 22(5)(7) V = 770 Therefore, the volume of the container is 770 cm^3. So, the correct answer is option (E) 770cm^3.
Question 43 Report
From the graph determine the roots of the equation y = 2x2 + x - 6
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Question 44 Report
While doing his physics practical, Idowu recorded a reading as 1.12cm instead of 1.21cm. Calculate his percentage error
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Question 46 Report
Solve the equation 2a\(^2\) - 3a - 27 = 0
Answer Details
To solve the equation 2a\(^2\) - 3a - 27 = 0, we can use the quadratic formula which is: a = (-b ± sqrt(b\(^2\) - 4ac)) / 2a In this case, we have a = 2, b = -3, and c = -27. Substituting these values into the formula, we get: a = (-(-3) ± sqrt((-3)\(^2\) - 4(2)(-27))) / 2(2) Simplifying the expression under the square root, we get: a = (-(-3) ± sqrt(225)) / 4 which gives us: a = (3 ± 15) / 4 Therefore, we have two solutions: a = 3 and a = -6/2 = -3/2 Hence, the correct option is -3, 9/2.
Question 47 Report
In the diagram below, O is the center of the circle if ?QOR = 290o, find the size ?QPR
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