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The volume of a cone of height 18 cm is 8,316 cm3. Find the base radius of the cone. [Take \(\pi = \frac{22}{7}\)]
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A square has diagonal length of 10 cm. Find the perimeter of the square.
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The height of 4 orange seedlings are: 2 cm, 5 cm, 7 cm and 10 cm. Calculate the variance.
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Two towns X and Y are located at points (–2, –5) and (3, 7) respectively. Calculate the distance between the two towns.
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Given that \((x^{-n})^4 = \frac{1}{x^6}\), find the value of \(n\).
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Solve: \(\frac{1}{3}(k - 4) - \frac{1}{2}(k + 1) < \frac{1}{6}\)
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In a class of 42 students, 21 offer History and 28 offer Government. If each student offers at least one of the two subjects, find the probability that a student selected at random from the class offers Government only.
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Consider the following statements:
p: The weather is warm.
q: The sun is shining.
Which of the following correctly represents the statement "The sun is shining if and only if the weather is warm"? -
The bearing of F from G is \(064^\circ\). What is the bearing of G from F?
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Ajoke will be 31 years in \(x\) years time. If Ajoke is 6 years older than Chioma, find an expression for Chioma's present age.
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Simplify: \(\sqrt{200} - \sqrt{72}\)
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Simplify: \(\frac{2\frac{1}{3}+\frac{5}{2}-1}{12-11\frac{3}{4}}\)
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Given that \(x + y = 1\) and \(x + 3y = 5\), find the value of \((x^2 + 4xy + 3y^2)\).
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Write 0.0364891 in three significant figures and express the answer in standard form.
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The radius and height of a circular base cylinder are 8 cm and 14 cm respectively. Find its curved surface area. [Take \(\pi = \frac{22}{7}\)]
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An interior angle of a regular polygon is \(150^\circ\). How many sides has the polygon?
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Solve: \(d^2 - 4d - 96 = 0\)
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The interior angles of a triangle are in the ratio 2 : 5 : 8. Find the difference between the smallest and largest angles.
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The interior angles of a hexagon are \(107^\circ, (2x)^\circ, 150^\circ, 95^\circ, (2x - 15)^\circ\) and \(123^\circ\). Find the value of \(x\).
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Two ball bearings have volumes 1.6 cm3 and 5.4 cm3. Find the ratio of their surface areas.
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Given that \(21_x = 14_5\), find the value of \(x\).
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Two consecutive odd integers are such that the sum of 5 times the smaller and twice the bigger integer is 222. Find the value of the smaller integer.
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Kwakye, Sabina and Owusu shared an amount of $12,000.00. Kwakye had 20% of the amount and the remaining amount was shared between Sabina and Owusu in the ratio 5 : 3 respectively. How much did Sabina receive?
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The third and ninth terms of an Arithmetic Progression (AP) are 9 and 27 respectively. Find the fifth term.
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If \(2\log_{x}({\frac{1-\sqrt{x}}{\sqrt{x}}})=0\), find the value of \(x\).
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A cylinder and a cone have the same volume. If the height of the cone is 24 cm, find the height of the cylinder.
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A variable \(P\) varies inversely as the square of \(Q\). If \(P = 5\) when \(Q = 6\), find \(Q\) when \(P = 1.8\).
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Factorize \(3 - 2x - x^2\).
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Make \(r\) the subject of the relation: \(\frac{1}{p} = \frac{b}{t} + \frac{c}{r}\)
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In \(\triangle PQR\), \(|QR| = 2\) cm, \(\angle PRQ = 60^\circ\) and \(\angle PQR = 90^\circ\). Find \(|PR|\).
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A sector of a circle of radius 21 cm subtends an angle of \(120^\circ\) at the centre. Find the length of the arc of the sector. [Take \(\pi = \frac{22}{7}\)]
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The population of a town increases by 2% every year. After 2 years, its population is 83,232. Calculate, correct to the nearest thousand, the original population.
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A profit of 8% was made when an article was sold for $500.00. At what price should it be sold to make a profit of 16%?
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The sets \(M = \{x : 2 \leq x \leq 6\}\) and \(N = \{x : 4 \leq x \leq 8\}\) are subsets of \(\mu = \{x : 1 \leq x \leq 10, \text{where } x \text{ is an integer}\}\). Find \(M' \cap N'\).
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Given that \(\sin(x - 46)^\circ = \cos 62^\circ\), find the value of \(x\).
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Given that \(\log_4 16 = \log_y 36\), find the value of \(y\).
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In the diagram, \(\angle PMQ = 34^\circ\) and \(\angle NQM = 28^\circ\). Find \(\angle QTN\).
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Find \(\angle MPN\).
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For what value of \(x\) is \(\frac{3x + 2}{2x + 1}\) undefined?
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In the diagram, P, Q, R and S are points on the circle with centre O. \(\angle QRS = (5x)^\circ\) and \(\angle QOS = (6x + 24)^\circ\). Find \(\angle QPS\).
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In the diagram, O, R, S and T are points on the circle with centre O, \(\angle STR = 37^\circ\) and \(\angle QRT = 59^\circ\). Find \(\angle SPR\).
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John sold an article for ₦105,000.00 at a loss of 4%. Find the cost price of the article.
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In the diagram, \(SR \parallel UW\), \(\angle VUT = y\), \(\angle SXT = 45^\circ\) and \(\angle VTU = 20^\circ\). Find the angle marked \(x\).
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Find the angle marked \(y\).
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What is the gradient of the line \(7x - 5y = 3\)?
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The Venn diagram illustrates the information about the sets P = {Primates}, C = {Smart People} and M = {My friends}. Which of the following is a valid conclusion from the diagram?
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The table shows the ages of students in a class. Find, correct to the nearest whole number, the average age of the students.
Age (years) 13 14 15 16 17 Number of Students 3 14 13 8 3 -
What is the median age?
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The angle of elevation of the top P of a ladder PQ from its base Q, 12 m away from a wall is \(36^\circ\). Find correct to the nearest metre, the length of the ladder.
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A fair dice is thrown once. Find the probability of obtaining an odd number or a prime number.
