WAEC SSCE - General Mathematics - 1989 (Objective)
Pregunta 1 Informe
In the diagram above, O is the center of the circle QRT and PT is a tangent to the circle at T. Calculate the angle x
Detalles de la respuesta
Pregunta 2 Informe
A sector is cut off from a circle radius 8.2cm to form a cone, if the radius of the resulting cone is 3.5cm, calculate the curved surface area of the cone. [take π = 22/7]
Detalles de la respuesta
Pregunta 4 Informe
In the diagram, O is the center of the circle, If ?POQ = 80o and ?PRQ = 5x, find the value of x.
Detalles de la respuesta
In a circle, the angle subtended by an arc at the center is twice the angle subtended by the same arc at any point on the circumference of the circle. Using this property, we can find the value of ?PRQ: ?POQ = 80o (given) Therefore, ?PRQ = 1/2 ?POQ = 1/2 x 80o = 40o Now, we can use the value of ?PRQ to find the value of x: ?PRQ = 5x (given) Substituting the value of ?PRQ, we get: 40o = 5x Simplifying this equation, we get: x = 8 Therefore, the value of x is 8. The answer is option B.
Pregunta 5 Informe
For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;
4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2
What is the median score?
Detalles de la respuesta
Pregunta 6 Informe
If the second and fourth term of a G.P are 8 and 32 respectively,what is the sum of the first four terms?
Detalles de la respuesta
Pregunta 7 Informe
Given that logp = 2 logx + 3logq, which of the following expresses p in terms of x and q?
Detalles de la respuesta
We are given the equation: log p = 2 log x + 3 log q. We know that log a + log b = log(ab) and log a - log b = log(a/b). Using these properties, we can rewrite the given equation as follows: log p = log x^2 + log q^3 log p = log (x^2q^3) Now we can write the exponential form of this equation as: p = x^2q^3 Therefore, the expression for p in terms of x and q is p = x^2q^3. Hence, the correct answer is "p = x^2q^3".
Pregunta 8 Informe
What angle represents grown up girls ? Correct to one decimal place
Detalles de la respuesta
Pregunta 9 Informe
Evaluate, using logarithm tables \(\frac{5.34 \times 67.4}{2.7}\)
Detalles de la respuesta
To evaluate this expression using logarithm tables, we can use the following steps: 1. Take the logarithm (base 10) of each of the numbers in the expression. 2. Add the logarithms of the two factors in the numerator. 3. Subtract the logarithm of the denominator from the result in step 2. 4. Take the antilogarithm (base 10) of the result in step 3. Using these steps, we get: log(5.34) = 0.727 log(67.4) = 1.829 log(2.7) = 0.431 log(5.34 x 67.4) = log(5.34) + log(67.4) = 0.727 + 1.829 = 2.556 log(5.34 x 67.4) - log(2.7) = 2.556 - 0.431 = 2.125 antilog(2.125) = 133.2 Therefore, the value of the expression is 133.2. The answer is option C.
Pregunta 10 Informe
Using the above graph, if 10o < x < 60o, what is the value of x for which sin x = cos x?
Detalles de la respuesta
Since sin x = cos x, we have: sin x = cos x Dividing both sides by cos x, we get: tan x = 1 Taking the inverse tangent (tan-1) of both sides, we get: x = 45o Therefore, the value of x for which sin x = cos x is 45o. Therefore, the correct option is (d) 45o.
Pregunta 11 Informe
An arc of a circle radius 7cm is 14cm long. What angle does the arc subtend at the center of circle?
[Take π = 22/7]
Detalles de la respuesta
Pregunta 12 Informe
The angle of depression of a point on the ground from the top of a building is 20.3o. If the foot of the building is 40m, calculate the height of the building, correct to one decimal place
Detalles de la respuesta
In this problem, we can use trigonometry to determine the height of the building. Let h be the height of the building and d be the distance from the point on the ground to the foot of the building. We can see that the angle of depression is the angle between the line of sight from the top of the building to the point on the ground and the horizontal line. Therefore, we can draw a right-angled triangle with the height of the building, the distance from the point on the ground to the foot of the building, and the line of sight from the top of the building to the point on the ground as the sides. From the triangle, we can use the tangent function since we have the opposite and adjacent sides. Therefore: tan(20.3°) = h/40 h = 40 tan(20.3°) ≈ 14.8m Therefore, the height of the building is approximately 14.8m. The correct answer is 14.8m.
Pregunta 13 Informe
In an A.P the first term is 2, and the sum of the 1st and the 6th term is 161/2. What is the 4th term
Detalles de la respuesta
Pregunta 14 Informe
The angle of elevation of X from Y is 30o. If XY = 40m, how high is X above the level of Y?
Detalles de la respuesta
Pregunta 15 Informe
If twice a certain integer is subtracted from 5 times the integer, the result is 63. Find the integer.
Detalles de la respuesta
Pregunta 16 Informe
The venn diagram below shows the number of students who studied Physics, Chemistry, and Mathematics in a certain school. How many students took at least two of the three subjects?
Detalles de la respuesta
Pregunta 17 Informe
Find the volume of a cone of radius 3.5cm and vertical height 12cm [Take π = 22/7]
Detalles de la respuesta
Pregunta 19 Informe
In the diagram O is the center of the circle, if ?QRS = 62o, find the value of ?SQR.
Detalles de la respuesta
Pregunta 20 Informe
In the diagram above O is the center of the circle, if ∠PAQ = 75o, what is the value of ∠PBQ?
Detalles de la respuesta
Pregunta 21 Informe
In the diagram above, ?SPR = P and ?SQR = 2x. Find x in terms of P
Detalles de la respuesta
Pregunta 22 Informe
Instead of recording the number 1.23cm of the radius of a tube, a student recorded 1.32cm. Find the percentage of error, correct to one decimal place.
Detalles de la respuesta
To find the percentage of error, we first need to find the absolute error, which is the difference between the measured value and the true value. In this case, the true value is 1.23 cm, and the measured value is 1.32 cm. Absolute error = |measured value - true value| = |1.32 - 1.23| = 0.09 cm Next, we can find the relative error, which is the ratio of the absolute error to the true value. Relative error = (absolute error / true value) x 100% Relative error = (0.09 / 1.23) x 100% = 7.32% Therefore, the percentage of error, correct to one decimal place, is 7.3%. The answer is option B.
Pregunta 23 Informe
In the diagram above, O is the center of the circle. Calculate the length of the chord AB if |OA| = 5cm, |OD| = 3cm and ?AOD = ?BOD
Detalles de la respuesta
Pregunta 24 Informe
In the diagram above, O is the center of the circle. If ?POR = 114o, calculate ?PQR
Detalles de la respuesta
Pregunta 25 Informe
Which of the following gives the point of intersection of the graph y = x2 and y = x + 6 shown above?
Detalles de la respuesta
The problem is asking us to find the point of intersection of the two graphs y = x2 and y = x + 6. This can be done by solving the equations simultaneously. We need to find the values of x and y that satisfy both equations. We can do this by substituting y = x + 6 for y in the equation y = x2, giving us: x + 6 = x2 Rearranging this equation gives us: x2 - x - 6 = 0 We can factor this quadratic equation to obtain: (x - 3)(x + 2) = 0 Thus, the solutions are x = 3 or x = -2. To find the corresponding values of y, we can substitute these values of x into either of the original equations. For example, if we use y = x + 6, we get: When x = 3, y = 3 + 6 = 9, giving us the point (3, 9). When x = -2, y = -2 + 6 = 4, giving us the point (-2, 4). Therefore, the point of intersection of the two graphs is (3, 9) and (-2, 4).
Pregunta 26 Informe
If A = {a,b,c}, B = {a,b,c,d,e} and C = {a,b,c,d,e,f}. Find (A∪B)∩(A∪C)
Detalles de la respuesta
The union of sets A and B (A ∪ B) is the set of elements that are in either set A, set B or both. Similarly, the union of sets A and C (A ∪ C) is the set of elements that are in either set A, set C or both. The intersection of these two sets ((A ∪ B) ∩ (A ∪ C)) is the set of elements that are common to both sets. Therefore, we can first find the union of A and B which gives us {a, b, c, d, e}. Then, we can find the union of A and C which gives us {a, b, c, d, e, f}. The intersection of these two sets is the set of elements that are in both sets, which is {a, b, c, d, e}. Therefore, (A∪B)∩(A∪C) = {a, b, c, d, e}. So the correct answer is: {a,b,c,d,e}.
Pregunta 27 Informe
Calculate the surface area of a hallow cylinder which is closed at one end, if the base radius is 3.5cm and the height 8cm.[take π = 22/7]
Detalles de la respuesta
Pregunta 28 Informe
For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;
4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2
What is the range of the distribution?
Detalles de la respuesta
Range of a distribution refers to the difference between the highest and lowest value in a dataset. To find the range of the given Mathematics test scores, we need to determine the highest and lowest values. The lowest score in the test is 2, while the highest score is 9. Therefore, the range of the distribution is 9 - 2 = 7. Hence, the answer is 7.
Pregunta 29 Informe
The graph above is that of a quadratic function y = 2x2 - x - 6
The roots of the equation are
Detalles de la respuesta
To find the roots of a quadratic function, we need to set y to zero and solve for x. Therefore, we have: 2x² - x - 6 = 0 We can factorize this quadratic equation by splitting the middle term: 2x² - 4x + 3x - 6 = 0 2x(x - 2) + 3(x - 2) = 0 (2x + 3)(x - 2) = 0 Setting each factor to zero, we get: 2x + 3 = 0 or x - 2 = 0 Solving for x in each equation, we get: x = -3/2 or x = 2 Therefore, the roots of the equation are -3/2 and 2. So the correct answer is (B) -1.5, 2.
Pregunta 30 Informe
Points X and Y are respectively 20km North and 9km East of a point O. What is the bearing of Y from X? Correct to the nearest degree
Detalles de la respuesta
Pregunta 32 Informe
The table above gives the scores of a group of students in an English Language test
If a student is chosen at random from the group, what is the probability that the scored at least 6 marks?
Detalles de la respuesta
Pregunta 34 Informe
Evaluate \(\frac{0.009}{0.012}\), leaving your answer in standard form.
Detalles de la respuesta
To evaluate \(\frac{0.009}{0.012}\) in standard form, we need to simplify the fraction and express the result in the form of \(a \times 10^b\), where \(1 \leq a < 10\) and \(b\) is an integer. We can simplify the fraction by dividing both the numerator and the denominator by 0.003: \[\frac{0.009}{0.012} = \frac{0.009 \div 0.003}{0.012 \div 0.003} = \frac{3}{4}\] Now we can express 3/4 in standard form: \[\frac{3}{4} = 0.75 = 7.5 \times 10^{-1}\] Therefore, the answer is option (C) 7.5 x 10-1.
Pregunta 35 Informe
In the diagram above, TPS is a straight line, PQRS is a parallelogram with base QR and height 8cm. |QR| = 6cm and the area of triangle QST is 52cm2. Find the area of ?QPT
Detalles de la respuesta
Pregunta 36 Informe
For a class of 30 students, the scores in a Mathematics test out of 10 marks were as follows;
4,5,7,2,3,6,5,5,8,9,5,4,2,3,7,9,8,7,7,7,3,4,5,5,2,3,6,7,7,2
What is the mode of the score
Detalles de la respuesta
The mode of a set of data is the value that appears most frequently. To find the mode of the scores in the Mathematics test, we need to determine which score occurs the most number of times. From the given data, we can see that the score "7" appears 6 times, which is more than any other score. Therefore, the mode of the score is 7. So the answer is (e) 7.
Pregunta 37 Informe
If 3\(^y\) = 243, find the value of y.
Detalles de la respuesta
Since 3 raised to what power gives 243, we need to find the exponent that makes this equation true: 3\(^y\) = 243 We can rewrite 243 as 3\(^5\), so the equation becomes: 3\(^y\) = 3\(^5\) Since the bases are equal, the exponents must also be equal. Therefore: y = 5 So the value of y is 5.
Pregunta 38 Informe
In the diagram above ABDE and FCDE are parallelograms. If |FC| = 12.2cm and the height |PC| = 4.0cm, calculate the area of the parallelogram ABDE.
Detalles de la respuesta
We know that ABDE and FCDE are parallelograms which means their opposite sides are equal and parallel. Therefore, |AB| = |DE| and |AE| = |BD|. We can calculate the area of parallelogram ABDE as follows: Area of ABDE = |AB| x |PC| We need to calculate |AB| and we can do this by finding the length of |DE|. In parallelogram FCDE, the opposite sides |DE| and |FC| are equal. Therefore, |DE| = |FC| = 12.2cm. Also, we know that FCDE is a parallelogram, so the height |PC| is equal to the height of parallelogram ABDE. Now, we can find the length of |AB| using the Pythagorean theorem. |AB|2 = |AE|2 + |DE|2 |AB|2 = (4.0cm)2 + (12.2cm)2 |AB|2 = 149.24cm2 |AB| = 12.2cm Therefore, the area of ABDE is: Area of ABDE = |AB| x |PC| = 12.2cm x 4.0cm = 48.8cm2 Therefore, the answer is 48.8cm2.
Pregunta 39 Informe
With reference to the graph above, which f the following solution sets is represented by ΔOPQ?
Detalles de la respuesta
Pregunta 40 Informe
Solve for x: (x2 + 2x + 1) = 25
Detalles de la respuesta
We are given the equation: x2 + 2x + 1 = 25 To solve for x, we first simplify the left-hand side of the equation by subtracting 24 from both sides: x2 + 2x - 24 = 0 We can then factor this quadratic equation as follows: (x + 6)(x - 4) = 0 Using the zero product property, we know that this equation is true if either (x + 6) = 0 or (x - 4) = 0. Solving for x in each case, we get: x + 6 = 0 or x - 4 = 0 x = -6 or x = 4 Therefore, the solutions to the original equation are x = -6 and x = 4. So the answer is: -6, 4
Pregunta 41 Informe
If logax = p, express x in terms of a and p
Detalles de la respuesta
We know that logax = p This means that ap = x So, we can express x in terms of a and p as x = ap. Therefore, the answer is x = ap.
Pregunta 42 Informe
The angle of a sector of a circle of diameter 8cm [Take x = 22/7].
Detalles de la respuesta
Pregunta 43 Informe
Calculate and correct to three significant figures, the length of an arc subtends an angle of 70o at the center of the circle radius 4cm. [Take π = 22/7]
Detalles de la respuesta
Pregunta 45 Informe
What is the probability that 3 customers waiting in a bank will be served in the sequence of their arrival at the bank
Detalles de la respuesta
The probability that 3 customers waiting in a bank will be served in the sequence of their arrival at the bank can be calculated using the permutation formula. Since there are three customers waiting in line, the total number of possible arrangements is 3! = 6. However, only one arrangement results in the customers being served in the sequence of their arrival at the bank. Therefore, the probability of this happening is 1/6. Hence, the correct answer is 1/6.
Pregunta 46 Informe
Simplify \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}}\)
Detalles de la respuesta
We can simplify this expression using the rules of exponents and radicals. First, we can rewrite 9 as \(3^2\) and 27 as \(3^3\): \(\frac{9^{-\frac{1}{2}}}{27^{\frac{2}{3}}} = \frac{(3^2)^{-\frac{1}{2}}}{(3^3)^{\frac{2}{3}}}\) Next, we can simplify the exponents using the product rule of exponents: \(\frac{(3^2)^{-\frac{1}{2}}}{(3^3)^{\frac{2}{3}}} = \frac{3^{-1}}{3^2} = \frac{1}{3^{1+2}} = \frac{1}{3^3} = \frac{1}{27}\) Therefore, the simplified expression is 1/27. The answer is option E.
Pregunta 47 Informe
What percentage of the population are married? correct to one decimal place
Detalles de la respuesta
Pregunta 48 Informe
sinθ = 1/2 and cosθ = -√3/2, what is the value of θ?
Detalles de la respuesta
We can use the fact that sin2θ + cos2θ = 1, to find the value of sinθ or cosθ given the other one. Since sinθ = 1/2, we know that sin2θ + cos2θ = 1 becomes: (1/2)2 + cos2θ = 1 Simplifying the equation, we get: 1/4 + cos2θ = 1 cos2θ = 3/4 Taking the square root of both sides, we get: cosθ = ±√3/2 Since we know that cosθ = -√3/2, we can conclude that θ = 150o (or 5π/6 radians) as this is the angle in the fourth quadrant that has a cosine of -√3/2. Therefore, the answer is option E: 150o.
