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**Question 1**
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Express 2.7864 x 10^{-3} to 2 significant figures

**Answer Details**

To express 2.7864 x 10^{-3} to 2 significant figures, we need to round off the number to the second significant digit from the left. Since the first significant digit is 2, and the second significant digit is 7, we will look at the third digit, which is 8. Since 8 is greater than or equal to 5, we round up the second significant digit (7) by 1. Therefore, the number becomes 0.0028. So, the answer is 0.0028.

**Question 2**
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If M and N are two fixed points in a plane. Find the locus L = [P : PM = PN]

**Question 3**
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In the diagram, /TP/ = 12cm and it is 6cm from O, the centre of the circle, Calculate < TOP

**Question 4**
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Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest

**Answer Details**

Simple interest is calculated as the product of the principal, the rate of interest, and the time duration. From the question, we have a principal of N3000.00, an interest rate of 6%, and a duration of 5 years. Using the formula for simple interest, we can find the interest accrued over the 5 years as: Interest = (P * R * T) / 100 = (3000 * 6 * 5) / 100 = N900.00 The total value to which N3000.00 will amount to after 5 years is the sum of the principal and the interest, which is: Total = Principal + Interest = 3000 + 900 = N3900.00 Therefore, N3000.00 will amount to N3900.00 after 5 years at 6% per annum simple interest. So the correct answer is option A, N3,900.00.

**Question 5**
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If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x

**Question 8**
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Simplify: (3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\))

**Answer Details**

We will start by simplifying the expression inside the parenthesis first. 3\(\frac{1}{2}\) + 4\(\frac{1}{3}\) = (7/2) + (13/3) To add these two fractions, we need a common denominator. Multiplying the denominators together gives us 6, so: (7/2) + (13/3) = (21/6) + (26/6) = 47/6 Now, let's simplify the expression in the denominator: \(\frac{5}{6} - \frac{2}{3}\) = \(\frac{5}{6} - \frac{4}{6}\) = \(\frac{1}{6}\) Finally, we can substitute these values into the original expression: (3\(\frac{1}{2}\) + 4\(\frac{1}{3}\)) ÷ (\(\frac{5}{6}\) - \(\frac{2}{3}\)) = (47/6) ÷ (1/6) When dividing fractions, we can multiply the first fraction by the reciprocal of the second: (47/6) ÷ (1/6) = (47/6) x (6/1) = 47 Therefore, the answer is 47.

**Question 10**
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In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x

**Question 11**
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Arrange the following numbers in descending orders of magnitude: 22_{three}, 34_{five}, 21_{six}

**Answer Details**

To compare these numbers, we need to convert all of them to the same base. Let's convert them all to base 10 for simplicity: - 22_{three} = 2\*3^{1} + 2\*3^{0} = 6 + 2 = 8 - 34_{five} = 3\*5^{1} + 4\*5^{0} = 15 + 4 = 19 - 21_{six} = 2\*6^{1} + 1\*6^{0} = 12 + 1 = 13 So, in base 10, the numbers are 8, 19, and 13. To arrange them in descending order of magnitude, we simply sort them from largest to smallest: - 19, 13, 8 Therefore, the correct answer is: 34_{five}, 21_{six}, 22_{three}

**Question 12**
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A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red?

**Answer Details**

The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). Let's assume that there are x red balls in the box. Since there are a total of 30 balls, we can write: number of black balls + number of white balls + number of red balls = total number of balls \(\frac{3}{10}(30) + \frac{2}{5}(30) + x = 30\) Simplifying the above equation gives: 9 + 12 + x = 30 x = 30 - 9 - 12 x = 9 Therefore, there are 9 red balls in the box.

**Question 13**
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Each of the interior angles of a regular polygon is 140^{o}. Calculate the sum of all the interior angles of the polygon

**Answer Details**

In a regular polygon with n sides, each interior angle measures: \begin{align*} 180^\circ - \frac{360^\circ}{n} \end{align*} Since each interior angle of this polygon is 140^{o}, we can equate the above formula to 140^{o}: \begin{align*} 180^\circ - \frac{360^\circ}{n} &= 140^\circ\\ \frac{360^\circ}{n} &= 40^\circ\\ n &= \frac{360^\circ}{40^\circ}\\ n &= 9 \end{align*} Therefore, the given polygon is a nonagon (a polygon with nine sides). The sum of the interior angles of a polygon with n sides can be calculated using the formula: \begin{align*} S &= (n-2)180^\circ \end{align*} Substituting n=9 into this formula, we get: \begin{align*} S &= (9-2)180^\circ\\ &= 7\cdot180^\circ\\ &= 1260^\circ \end{align*} Therefore, the sum of all the interior angles of the given polygon is 1260^{o}. Hence, the correct option is: - 1260^{o}

**Question 14**
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If 85% of x is N3230, what is the value of x?

**Answer Details**

We can solve this problem using a proportion. If 85% of x is N3230, that means we can write: 0.85x = N3230 To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides by 0.85: x = N3230 ÷ 0.85 Using a calculator, we get: x ≈ N3800.00 Therefore, the value of x is N3800.00.

**Question 15**
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The following is the graph of a quadratic friction, find the co-ordinates of point P

**Question 16**
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in the diagram, angle 20^{o} is subtended at the centre of the circle, find the value of x

**Answer Details**

In the given diagram, we have a circle with center O and angle 20^{o} subtended at the center. We need to find the value of x. Firstly, we know that the angle subtended at the center of a circle is twice the angle subtended at the circumference by the same arc. Therefore, angle AOB = 2 × 20^{o} = 40^{o} Also, we know that angle in a semicircle is a right angle. So, angle AOC = 90^{o}. Using the fact that the angles in a triangle add up to 180^{o}, we can find angle BOC as follows: angle BOC = 180^{o} - angle AOB - angle AOC = 180^{o} - 40^{o} - 90^{o} = 50^{o} Since angle BOC is an angle at the circumference that subtends the arc BC, which is equal to x degrees, we have: x = angle BOC = 50^{o} Therefore, the value of x is 50^{o}. Answer is correct.

**Question 17**
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The following is the graph of a quadratic friction, find the value of x when y = 0

**Question 18**
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Two sets are disjoint if

**Answer Details**

Two sets are said to be disjoint if their intersection is an empty set. In other words, if there are no common elements between the sets, they are said to be disjoint. For example, the sets {1,2,3} and {4,5,6} are disjoint since their intersection is an empty set {} or ∅. On the other hand, the sets {1,2,3} and {2,3,4} are not disjoint since they have elements in common, namely 2 and 3.

**Question 19**
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Find the quadratic equation whose roots are -\(\frac{1}{2}\) and 3

**Answer Details**

To find the quadratic equation given its roots, we use the fact that for a quadratic equation of the form ax^{2} + bx + c = 0, the roots are given by the formula: x = (-b ± √(b^{2} - 4ac)) / 2a If the roots are given as α and β, then the quadratic equation can be written as: (x - α)(x - β) = 0 Expanding the above equation gives: x^{2} - (α + β)x + αβ = 0 Therefore, to find the quadratic equation whose roots are -\(\frac{1}{2}\) and 3, we substitute α = -\(\frac{1}{2}\) and β = 3 into the equation: x^{2} - (α + β)x + αβ = 0 x^{2} - (-\(\frac{1}{2}\) + 3)x + (-\(\frac{1}{2}\) × 3) = 0 Simplifying the above equation, we get: 2x^{2} - 5x - 3 = 0 Therefore, the quadratic equation whose roots are -\(\frac{1}{2}\) and 3 is 2x^{2} - 5x - 3 = 0. The correct option is (C) 2x^{2} - 5x - 3 = 0.

**Question 20**
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If 9^{2x} = \(\frac{1}{3}\)(27^{x}), find x

**Question 21**
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Find the value of x in the diagram

**Question 22**
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The pie chart shows the distribution of 4320 students who graduated from four departments in a university. If a student is picked at random from the four departments, what id the probability that he is not from the education department?

**Answer Details**

To find the probability that a student picked at random is not from the education department, we need to find the total number of students who are not from the education department and divide it by the total number of students in all departments. From the pie chart, we can see that the education department has 30% of the total students. Therefore, the remaining three departments have a total of 70% of the total students. To find the probability of picking a student who is not from the education department, we divide the percentage of students who are not in the education department by 100%: Probability = \(\frac{70}{100}\) = \(\frac{7}{10}\) Therefore, the probability that a student picked at random is not from the education department is \(\frac{7}{10}\). The correct option is: \(\frac{7}{10}\).

**Question 23**
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The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take \(\pi \frac{22}{7}\)

**Answer Details**

The distance covered by the wheel is equal to the circumference of the wheel multiplied by the number of revolutions made. The circumference of the wheel can be calculated using the formula: circumference = diameter x pi circumference = 42cm x 22/7 circumference = 132cm Therefore, the distance covered by the wheel in 16 complete revolutions is: distance = circumference x number of revolutions distance = 132cm x 16 distance = 2112cm So, the answer is (c) 2112cm.

**Question 24**
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PQRS is a trapezuim. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42^{o}. Calculate the perpendicular distance between the parallel sides

**Question 25**
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Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} \sqrt{2}\)

**Question 26**
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PQRS is a trapezium. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42^{o}. Calculate, correct to the nearest cm^{2}, the area of the trapezium (h = 3.35cm^{2} )

**Question 27**
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The pie chart shows the distribution of 4320 students who graduated from four departments in a university. How many students graduated from the science department?

**Answer Details**

To find the number of students who graduated from the science department, we need to look at the pie chart and determine the percentage of students that belong to that department. From the pie chart, we can see that the science department occupies 20% of the entire circle. To find the number of students in the science department, we need to calculate 20% of 4320, which can be done by multiplying 4320 by 0.20. 20% of 4320 = 0.20 x 4320 = 864 Therefore, the number of students who graduated from the science department is 864. So, the correct answer is option B: 864.

**Question 28**
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solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

**Answer Details**

To solve the equation \(\frac{2x + 1}{6} - \frac{3x - 1}{4} = 0\), we need to simplify the left-hand side and solve for x. First, we need to find a common denominator for the two fractions. The smallest common multiple of 6 and 4 is 12, so we can rewrite the equation as: \[\frac{2x+1}{6}\cdot \frac{2}{2} - \frac{3x-1}{4}\cdot \frac{3}{3} = 0\] Simplifying, we get: \[\frac{4x+2}{12} - \frac{9x-3}{12} = 0\] Combining the fractions, we get: \[\frac{4x+2-(9x-3)}{12} = 0\] Simplifying further, we get: \[\frac{-5x+5}{12} = 0\] Multiplying both sides by 12, we get: \[-5x+5=0\] Adding 5 to both sides, we get: \[-5x=-5\] Dividing both sides by -5, we get: \[x=1\] Therefore, the solution to the equation is x = 1.

**Question 29**
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Simplify (x - 3y)^{2} - (x + 3y)^{2}

**Question 30**
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A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm^{3})`

**Answer Details**

The volume of the reservoir can be found by multiplying its dimensions: 8m x 7m x 5m = 280 m^3 Since 1 liter is equal to 1000 cubic centimeters (cm^3), 1 cubic meter is equal to 1,000,000 cubic centimeters. Therefore, the reservoir has a volume of: 280 m^3 x 1,000,000 cm^3/m^3 = 280,000,000 cm^3 Each bucket can hold 10 liters of water or 10,000 cubic centimeters (cm^3) of water since 1 liter is equal to 1000 cm^3. Therefore, the number of buckets needed to fill the reservoir is: 280,000,000 cm^3 ÷ 10,000 cm^3/bucket = 28,000 buckets Therefore, the answer is 28,000.

**Question 31**
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What is the median of the following scores: 22 35 41 63 74 82

**Answer Details**

To find the median of a set of numbers, we first need to arrange them in ascending or descending order. In this case, arranging the numbers in ascending order gives us: 22, 35, 41, 63, 74, 82 The median is the middle number in the set when the numbers are arranged in order. Since we have an even number of numbers in this set, there are two middle numbers: 41 and 63. To find the median, we take the average of these two numbers: Median = (41 + 63) / 2 = 104 / 2 = 52 Therefore, the median of the scores is 52.

**Question 32**
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If c and k are the roots of 6 - x - x^{2} = 0, find c + k

**Question 33**
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In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x

**Answer Details**

Kofi's mean score for the three subjects was 55%, so the total percentage score for the three subjects is 3 x 55 = 165%. Let's assume that Kofi scored x% in Physics. Then, the total percentage score for Physics, Chemistry and Biology would be: x + 50 + 70 = 165 Simplifying the equation, we get: x = 165 - 50 - 70 x = 45 Therefore, Kofi scored 45% in Physics. So the correct option is (B) 45.

**Question 34**
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The angles of triangle are (x + 10)^{o}, (2x - 40)^{o} and (3x - 90)^{o}. Which of the following accurately describes the triangle?

**Question 36**
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The capacity of a water tank is 1,800 litres. If the tank is in form of a cuboid with base 600cm by 150 cm. Find the height of the tank

**Question 37**
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If (2x + 3)^{3} = 125, find the value of x