WAEC SSCE - General Mathematics - 1998
Question 1 Rapport
Find the angle x in the diagram above
Détails de la réponse
In the given diagram, there is a straight line that intersects two parallel lines, forming several angles. By the properties of parallel lines, we know that the alternate interior angles are equal. Thus, angle x is equal to the alternate interior angle formed by the transversal and the parallel line. We can see that angle x is adjacent to the angle of 130o, which is one of the interior angles of the triangle formed by the intersecting lines. Therefore, the sum of angle x and 130o should be equal to 180o (the sum of angles in a triangle). Thus, we have: angle x + 130o = 180o angle x = 180o - 130o angle x = 50o Therefore, the answer is (E) 100o.
Question 3 Rapport
The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x
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Question 4 Rapport
A ladder 5cm long long rest against a wall such that its foot makes an angle 30o with the horizontal. How far is the foot of the ladder from the wall?
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Question 6 Rapport
A chord of circle of radius 26cm is 10cm from the center of the circle. calculate the length of the chord
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Question 7 Rapport
Evaluate \(\sqrt{20}\times (\sqrt{5})^3\)
Détails de la réponse
We can simplify the expression as follows: \begin{align*} \sqrt{20}\times (\sqrt{5})^3 &= \sqrt{(2\times2\times5)\times(5\times5\times5)} \\ &= \sqrt{(2\times5\times5\times2\times5\times5)} \\ &= \sqrt{(2^2\times5^2)\times(5^2)} \\ &= \sqrt{(2^2\times5^2\times5^2)} \\ &= \sqrt{(2^2\times5^4)} \\ &= 2\times5^2 \\ &= 50. \end{align*} Therefore, the answer is 50.
Question 8 Rapport
A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 4?
Détails de la réponse
Question 9 Rapport
Find the value of X if \(cos x = \frac{5}{8}for 0^o\le X\le 180^o\)
Détails de la réponse
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 51.3o.
Question 10 Rapport
A piece of cloth was measured as 6.10m. If the actual length of the cloth is 6.35, find the percentage error, correct to 2 decimal places
Détails de la réponse
Question 11 Rapport
The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
What percentage, to the nearest whole number, of tghe students travelled to school on foot?
Détails de la réponse
Question 12 Rapport
Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35o,find ∠PQS
Détails de la réponse
Question 13 Rapport
If h(m+n) = m(h+r) find h in terms of m, n and r
Détails de la réponse
We are given the equation: h(m+n) = m(h+r). Expanding the left-hand side of the equation, we get: hm + hn = hm + mr Subtracting hm from both sides, we get: hn = mr Dividing both sides by n, we get: h = mr/n Therefore, the answer is: h = mr/n. Option D is the correct answer.
Question 14 Rapport
Arrange in ascending order of magnitude \(26_8, 36_7, and 25_9\)
Détails de la réponse
Question 15 Rapport
Evaluate \(3.0\times 10^1 - 2.8\times 10^{-1}\)leaving the answer in standard form
Détails de la réponse
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 \(2.972 \times 10^1\).
Question 16 Rapport
It is observed that \(1 + 3 = 2^2, 1 + 3 + 5 = 3^2, 1 + 3 + 5 + 7 = 4^2. \\If \hspace{1mm}1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = P^2 find\hspace{1mm}P\)
Détails de la réponse
Question 18 Rapport
If the exterior angles of quadrilateral are yo, (y + 5)o, (y + 10)o and (y + 25)o, find y
Détails de la réponse
The sum of the exterior angles of any polygon is always equal to 360 degrees. Therefore, we can write an equation as: y + (y + 5) + (y + 10) + (y + 25) = 360 Simplifying the equation, we get: 4y + 40 = 360 Subtracting 40 from both sides, we get: 4y = 320 Dividing both sides by 4, we get: y = 80° Therefore, the value of y is 80o.
Question 19 Rapport
Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
Détails de la réponse
Question 20 Rapport
Find the root of the equation 2x\(^2\) - 3x - 2 = 0
Détails de la réponse
To find the root(s) of the quadratic equation 2x\(^2\) - 3x - 2 = 0, we can use the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ where a, b, and c are the coefficients of the quadratic equation ax\(^2\) + bx + c = 0. In this case, a = 2, b = -3, and c = -2. Substituting these values into the formula, we get: $$x = \frac{-(-3) \pm \sqrt{(-3)^2-4(2)(-2)}}{2(2)}$$ Simplifying: $$x = \frac{3 \pm \sqrt{9+16}}{4}$$ $$x = \frac{3 \pm \sqrt{25}}{4}$$ We can simplify the square root to get: $$x = \frac{3 \pm 5}{4}$$ So the roots are: $$x = \frac{3 + 5}{4} = 2$$ $$x = \frac{3 - 5}{4} = -\frac{1}{2}$$ Therefore, the answer is x = -1/2 or 2.
Question 21 Rapport
What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0
Détails de la réponse
Question 23 Rapport
Find the curved surface area of a cone of radius 3cm and slant height 7cm (\(take \pi = \frac{22}{7}\)
Détails de la réponse
The curved surface area of a cone can be calculated using the formula: `Curved surface area = πrl` where r is the radius of the base, l is the slant height, and π is the constant pi. In this case, the radius is given as 3cm, and the slant height is given as 7cm. So, the curved surface area of the cone is: `Curved surface area = πrl` `Curved surface area = (22/7) x 3 x 7` `Curved surface area = 66 cm^2` Therefore, the curved surface area of the given cone is 66 cm^2. Answer is the correct answer.
Question 24 Rapport
Cos x is negative and sin x is negative.Which of the following is true of x?
Détails de la réponse
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: - 180o < x < 270o
Question 25 Rapport
In \(\triangle PQR\). T is a point on QR such that \(\angle QPT = 39^o and \angle PTR = 83^o. Calculate \angle PQT\)
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Question 26 Rapport
Make S the subject of the formula: \(V = \frac{K}{\sqrt{T-S}}\)
Détails de la réponse
To make S the subject of the formula, we need to isolate S on one side of the equation by performing operations on both sides of the equation. We begin by multiplying both sides by \(\sqrt{T-S}\), then we multiply both sides by \(\frac{V^2}{K}\) to obtain: \begin{align*} V &= \frac{K}{\sqrt{T-S}} \\ V\sqrt{T-S} &= K \\ T-S &= \left(\frac{K}{V}\right)^2 \\ S &= T-\left(\frac{K}{V}\right)^2 \\ \end{align*} Therefore, the answer is \(T-\left(\frac{K}{V}\right)^2 = S\).
Question 27 Rapport
p and q are two positive numbers such that p > 2q. Which one of the following statements is not true?
Détails de la réponse
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`.
Question 28 Rapport
In the diagram PQ is a diameter of circle PMQN center O, if ?PQM = 63o, find ?MNQ
Détails de la réponse
Question 29 Rapport
In the diagram above, |PQ| = |PR| = |RS| and ?RSP = 35o. Find ?QPR
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Question 30 Rapport
A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?
Détails de la réponse
The probability of picking two balls of different colours is the probability of picking one white ball and one blue ball, because there are no other colours in the box. The probability of picking a white ball on the first draw is 2/5, since there are 2 white balls out of 5 total balls. After one white ball has been removed, there are 4 balls left, including 2 blue balls. Therefore, the probability of picking a blue ball on the second draw is 2/4 or 1/2. The probability of picking a white ball on the first draw and a blue ball on the second draw is thus: \(\frac{2}{5} * \frac{1}{2} = \frac{1}{5}\) There is also a probability of picking a blue ball on the first draw and a white ball on the second draw, which is: \(\frac{3}{5} * \frac{2}{4} = \frac{3}{10}\) Therefore, the total probability of picking two balls of different colours is: \(\frac{1}{5} + \frac{3}{10} = \frac{1}{5} + \frac{2}{5} = \frac{3}{5}\) So the answer is \(\frac{3}{5}\).
Question 31 Rapport
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?
Détails de la réponse
Question 32 Rapport
The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
If a hundred students travelled by bus, find the total number of students in the school
Détails de la réponse
Question 33 Rapport
If log\(_{10}\) a = 4; what is a?
Détails de la réponse
The expression log\(_{10}\) a = 4 can be read as "logarithm of a to base 10 is 4". This means that 10 raised to the power of 4 is equal to a, or simply a = 10\(^4\). Therefore, the value of a is 10,000. The correct option is (e) 10,000.
Question 34 Rapport
In ?PQR. ?PQR is a right angle. |QR| = 2cm and ?PRQ = 60o. Find |PR|
Détails de la réponse
Question 35 Rapport
The diagram above is a rectangle. If the perimeter is 36m, find the area of the rectangle
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Question 36 Rapport
The length of an arc of a circle of radius 5cm is 4cm. Find the area of the sector
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Question 37 Rapport
When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight?
Détails de la réponse
Question 39 Rapport
Convert 35 to a number in base two
Détails de la réponse
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 100011two.
Question 40 Rapport
The radius of a geographical globe is 60cm. Find the length of the parallel of latitude 60oN
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Question 41 Rapport
Three of the angles of a hexagon are each Xo. The others are each 3Xo. Find X
Détails de la réponse
The sum of the interior angles of a hexagon is given by the formula (n-2)×180o, 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)×180o = 4×180o = 720o. Let's assume that three angles of the hexagon are each Xo. Therefore, the sum of these three angles is 3Xo. The other three angles are each 3Xo, so their sum is 9Xo. Thus, the total sum of the six angles is: 3Xo + 9Xo = 12Xo But we also know that the sum of the interior angles of a hexagon is 720o. Therefore, we can equate the two expressions: 12Xo = 720o Dividing both sides by 12, we get: Xo = 60o Therefore, the answer is X = 60o.
Question 42 Rapport
Détails de la réponse
Find the value of x in the diagram aboveQuestion 44 Rapport
The following numbers represent at a set of scores for a class of 32 students, where the maximum score possible was 12, 6, 5, 9, 4, 4, 8, 7, 5, 6, 3, 2, 5, 4, 6, 9, 10, 4, 3, 2, 3, 4, 6, 8, 7, 4, 2, 1, 8, 7, 7, 6, 11. What is the percentage of the class, correct to the nearest whole number, scored above 6?
Détails de la réponse
To find the percentage of the class that scored above 6, we need to first count the number of students who scored above 6, and then divide that number by the total number of students and multiply by 100 to get the percentage. We can start by counting the number of students who scored above 6. From the given set of scores, we can see that the following students scored above 6: 9, 9, 8, 7, 8, 7, 7, 11. Counting these students, we get a total of 8 students who scored above 6. To find the percentage of the class that scored above 6, we divide the number of students who scored above 6 (8) by the total number of students (32), and then multiply by 100: 8/32 * 100 = 25% So, the percentage of the class that scored above 6 is 25%, which is closest to 34% when rounded to the nearest whole number. Therefore, the answer is (a) 34%.
Question 45 Rapport
Find the number whose logarithm to base 10 is 2.6025
Détails de la réponse
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 = 10y. In this case, the logarithm to base 10 is given as 2.6025. Therefore, the number is x = 102.6025. Using a calculator, we get x ≈ 400.4. Therefore, the number whose logarithm to base 10 is 2.6025 is approximately 400.4.
Question 46 Rapport
In the diagram above, the area of triangle ABC is 35cm2, find the value of y
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Question 47 Rapport
Simplify \(\frac{8^{\frac{2}{3}}*27^{\frac{-1}{3}}}{64^{\frac{1}{3}}}\)
Détails de la réponse
Question 49 Rapport
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ?POQ = 50o. Use the diagram to answer question below. (take ? = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ
Détails de la réponse
The area of sector OPQ is a fraction of the area of the whole circle. The whole circle has an area of πr2, where r is the radius. In this case, r = 3.5 cm, so the area of the whole circle is: A = π(3.5 cm)2 = 38.465 cm2 The sector OPQ makes up a fraction of the whole circle. The fraction is equal to the central angle of the sector divided by 360 degrees. In this case, the central angle is 50 degrees, so the fraction is: 50/360 = 5/36 So the area of sector OPQ is: A = (5/36)×38.465 cm2 ≈ 5.350 cm2 Therefore, the correct option is (b) 5.350cm2.
Question 50 Rapport
The nth term of a sequence is represented by 3 x 2(2-n). Write down the first three terms of the sequence
Détails de la réponse
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.
Question 51 Rapport
If log\(_{10}\) q = 2.7078, what is q?
Détails de la réponse
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.
Question 52 Rapport
Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3}\)
Détails de la réponse
Question 53 Rapport
Given that \(\frac{6x-y}{x+2y}=2\), find the value of \(\frac{x}{y}\)
Détails de la réponse
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 \(\frac{5}{4}\).
Question 55 Rapport
If P = {3, 7, 11, 13} and Q = {2, 4, 8, 16}, which of the following is correct
Détails de la réponse
To answer this question, we need to understand some basic set theory notation and concepts: - The intersection of two sets is the set of elements that are in both sets. - The union of two sets is the set of elements that are in either set (or both). - The complement of a set is the set of elements that are not in that set. - The cardinality of a set is the number of elements in that set. (a) \((P\cap Q)^l={2, 3, 4, 13}\) is not correct. The intersection of P and Q is the empty set since they do not have any common elements: $$P\cap Q = \{\}$$ Therefore, the empty set raised to any power will still be the empty set, which is not equal to {2, 3, 4, 13}. (b) \(n(P\cup Q)=4\) is correct. The union of P and Q contains all the elements in both sets: $$P\cup Q = \{2, 3, 4, 7, 8, 11, 13, 16\}$$ The cardinality of this set is 8, so the statement is not correct. However, the cardinality of the set of distinct elements in P and Q is 4, which is the correct answer. Therefore, the statement is correct. (c) \(P\cup Q = \emptyset\) is not correct. As shown above, the union of P and Q is not empty. Therefore, the statement is not correct. (d) \(P\cap Q = \emptyset\) is correct. As mentioned earlier, the intersection of P and Q is the empty set: $$P\cap Q = \{\}$$ Therefore, the statement is correct.
Question 56 Rapport
A trader makes a loss of 15% when selling an article. Find the ratio, selling price : cost price
Détails de la réponse
Let's assume the cost price of the article is $100. Since the trader incurred a loss of 15%, the selling price will be 85% of the cost price. Therefore, Selling price = 85/100 * cost price = 85/100 * 100 = $85. The ratio of the selling price to the cost price is: Selling price : Cost price = $85 : $100 To simplify the ratio, we can divide both sides by the highest common factor, which is 5. This gives: Selling price : Cost price = 17 : 20 Therefore, the ratio of selling price to cost price is 17 : 20. Option C, 17:20, is the correct answer.
Question 57 Rapport
Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures
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Question 58 Rapport
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?
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Question 59 Rapport
The side of a square is increased from 20cm to 21cm. Calculate the percentage increase in its area
Détails de la réponse
The area of a square is given by the formula: A = s^2, where s is the length of a side of the square. Initially, the length of the side of the square is 20cm, so its area is A1 = 20^2 = 400 cm^2. When the length of the side is increased to 21cm, the new area becomes A2 = 21^2 = 441 cm^2. The difference in area between the two squares is: A2 - A1 = 441 - 400 = 41 cm^2 To find the percentage increase in area, we need to divide the difference in area by the original area, and then multiply by 100: percentage increase = (difference in area / original area) x 100% = (41 / 400) x 100% = 0.1025 x 100% = 10.25% Therefore, the percentage increase in area is 10.25%. So, the correct answer is 10.25%.
Question 60 Rapport
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ?POQ = 50o. Use the diagram to answer question below. (take ? = 3.142)
Calculate correct to one decimal place, the length of arc PQ.
Détails de la réponse
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.
Question 61 Rapport
In the diagram above, O is the center if the two concentric circle of radii 13cm and 10cm respectively. Find the area of the shaded portion in the sector with angle 1200 at the center
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Question 62 Rapport
In the diagram, O is the center of the circle and the reflex angle ROS is 264o. Find ?RTS
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Question 64 Rapport
(a) Copy and complete the table of values for the relation \(y = 5 - 7x - 6x^{2}\) for \(-3 \leq x \leq 2\).
| x | -3 | -2 | -1 | -0.5 | 0 | 1 | 2 |
| y | -28 | 6 | 5 |
(b) Using a scale of 2cm to 1 unit on the x- axis and 2cm to 5 units on the y- axis, draw the :
(i) graph of \(y = 5 - 7x - 6x^{2}\) ; (ii) line \(y = 3\) on the same axis.
(c) Use your graph to find the : (i) roots of the equation \(2 - 7x - 6x^{2} = 0\) ; (ii) maximum value of \(y = 5 - 7x - 6x^{2}\).
Question 65 Rapport
Using a ruler and a pair of compasses only, construct (a) triangle QRT with |QR| = 8cm, |RT| = 6cm and |QT| = 4.5cm.
(b) a quadrilateral QRSP which has a common base QR with \(\Delta\)QRT such that QTP is a straight line, PQ || SR, |QP| = 9cm and |RS| = 4.5cm.
(i) Measure |PS| ; (ii) Find the perpendicular distance between RS and PQ ; (iii) What is QRSP?
Détails de la réponse
None
Question 66 Rapport
A surveyor standing at a point X sights a pole Y due east of him and a tower Z of a building on a bearing of 046°. After walking to a point W, a distance of 180m in the South- East direction, he observes the bearing of Z and Y to be 337° and 050° respectively.
(a) Calculate, correct to the nearest metre : (i) |XY| ; (ii) |ZW|
(b) If N is on XY such that XZ = ZN, find the bearing of Z from N.
None
Détails de la réponse
None
Question 67 Rapport
The third term of a Geometric Progression (G.P) is 360 and the sixth term is 1215. Find the
(a) common ratio;
(b) first term ;
(c) sum of the first four terms.
Question 68 Rapport
(a) A number is selected at random from each of the sets {2, 3, 4} and {1, 3, 5}. What is the probability that the sum of the two numbers will be less than 7 but greater than 3?
(b) 
In the diagram, ABCD is a circle. DAE, CBE, ABF and DCF are straight lines. If y + m = 90°, find the value of x.
None
Détails de la réponse
None
Question 69 Rapport
(a) Given that \(\log_{10} 2 = 0.3010, \log_{10} 7 = 0.8451\) and \(\log_{10} 5 = 0.6990\), evaluate without using logarithm tables:
(i) \(\log_{10} 35\); (ii) \(\log_{10} 2.8\).
(b) Given that \(N^{0.8942} = 2.8\), use your result in (a)(ii) to find the value of N.
Question 70 Rapport
(a) A radio which a dealer bought for N6,000.00 and marked to give a profit of 30% was reduced in a sales by 10%. Find : (i) the final sales price ; (ii) the percentage profit.
(b) Solve the equation : \(2^{(2x + 1)} - 9(2^{x}) + 4 = 0\).
Détails de la réponse
None
Question 71 Rapport
(a) The value of the expression \(2Ax - Kx^{2}\) is 7 when x = 1 and 4 when x = 2. Find the values of the constants A and K.
(b) Solve the equation \(x^{2} - 3x - 1 = 0\), giving your answers correct to 1 decimal place.
Question 72 Rapport
In the diagram, ASRTB represents a piece of string passing over a pulley of radius 10cm in a vertical plane. O is the centre of the pulley and AMB is a horizontal straight line touching the pulley at M. Angle SAB = 90° and angle TBA = 60°.
(a) Calculate (i) the obtuse angle SOT ; (ii) arc SRT ; (iii) |BT|
(b) Find, correct to the nearest cm, the length of the string. (Take \(\pi = \frac{22}{7}\)).
None
Détails de la réponse
None
Question 73 Rapport
The area of a rectangular floor is 13.5m\(^{2}\). One side is 1.5m longer than the other.
(a) Calculate the dimensions of the floor ;
(b) If it costs N250.00 per square metre to carpet the floor and only N2,000.00 is available, what area of the floor can be covered with carpet?
Question 74 Rapport
The table below shows the number of eggs laid by the chickens in a man's farm in a year.
| No of eggs per year | No of chickens |
| 45 - 49 | 10 |
| 50 - 54 | 36 |
| 55 - 59 | 64 |
| 60 - 64 | 52 |
| 65 - 69 | 28 |
| 70 - 74 | 10 |
(a) Draw a cumulative frequency curve for the distribution.
(b) Use your graph to find the interquartile range.
(c) If a woman buys a chicken from the farm, what is the probability that the chicken lays at least 60 eggs in a year?
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Détails de la réponse
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Question 75 Rapport
A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,..., 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), where y is a prime number.
(a) Draw a venn diagram to illustrate the information given above;
(b) Find: (i) \((B \cup C)'\); (ii) \(A' \cap B \cap C\).
Détails de la réponse
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