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**Question 2**
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In the diagram, PQR is straight line, ( m + n) = 120o and ( n + r) = 100o. Find (m + r).

**Question 3**
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In the diagram, the value of x + y = 220^{o}. Find the value of n

**Question 4**
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The volume of a cube is 512cm^{3}. Find the length of its side

**Answer Details**

To find the length of a side of a cube, we need to take the cube root of its volume. Given that the volume of the cube is 512cm³, we have: side³ = volume side³ = 512cm³ Taking the cube root of both sides, we get: side = ∛(512cm³) side = 8cm Therefore, the length of the side of the cube is 8cm. Answer: Option (C) 8cm

**Question 5**
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If one student is selected at random, find the probability that he/she scored at most 2 marks

**Question 6**
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If (x - a) is a factor pf bx - ax + x^{2}, find the other factor.

**Question 7**
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A ship sails x km due east to a point E and continues x km due north to F. Find the bearing the bearing of f from the starting point.

**Answer Details**

Let's draw a diagram to visualize the situation:

N | F | W-------+-------E | | S

The ship starts at the point marked "W", then sails east to reach the point marked "E". The distance between W and E is x km. Then the ship sails north from E to reach the point marked "F". The distance between E and F is also x km.

We want to find the bearing of F from W. This is the angle that the line segment WF makes with the north-south line, measured in a clockwise direction.

Let's call the point where the north-south line intersects the line WE as point G. Then we have a right triangle WGE, where WG is the distance travelled east by the ship, and GE is the distance travelled north. The angle WGE is the bearing we're looking for.

From the right triangle WGE, we can use trigonometry to find the angle WGE:

tan(WGE) = opposite / adjacent = GE / WG = x / x = 1

Taking the arctan of both sides, we get:

WGE = arctan(1) = 45 degrees

Therefore, the bearing of F from W is **045 degrees**. Answer: (a) 045^{o}.

**Question 8**
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If 23_{x} = 32_{5}, find the value of x

**Answer Details**

To find the value of x, we need to determine what base value the number 23_{x} represents. We are told that 23_{x} is equal to 32_{5}. In other words, the value represented by 23_{x} is equal to the value represented by 32_{5}. We can convert 32_{5} to base 10 to get: 32_{5} = (3 x 5^{1}) + (2 x 5^{0}) = 15 + 2 = 17 So, we have: 23_{x} = 17 To find the value of x, we need to determine what base value raised to what power is equal to 17. We can do this by trying different values of x. If x is 2, then 23_{2} = (2 x 2^{1}) + (3 x 2^{0}) = 4 + 3 = 7 If x is 3, then 23_{3} = (2 x 3^{1}) + (3 x 3^{0}) = 6 + 3 = 9 If x is 4, then 23_{4} = (2 x 4^{1}) + (3 x 4^{0}) = 8 + 3 = 11 If x is 5, then 23_{5} = (2 x 5^{1}) + (3 x 5^{0}) = 10 + 3 = 13 If x is 6, then 23_{6} = (2 x 6^{1}) + (3 x 6^{0}) = 12 + 3 = 15 If x is 7, then 23_{7} = (2 x 7^{1}) + (3 x 7^{0}) = 14 + 3 = 17 So, we have found that if x is 7, then 23_{x} = 17, which matches the value of 32_{5}. Therefore, the value of x is 7. Answer: 7

**Question 9**
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If \(\frac{2}{x - 3} - \frac{3}{x - 2}\) is equal to \(\frac{p}{(x - 3)(x - 2)}\), find p

**Question 10**
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Simplify 10\(\frac{2}{5} - 6 \frac{2}{3} + 3\)

**Answer Details**

To simplify the expression 10\(\frac{2}{5} - 6 \frac{2}{3} + 3\), we first need to convert the mixed numbers to improper fractions. 10\(\frac{2}{5}\) can be written as \(\frac{52}{5}\) and 6\(\frac{2}{3}\) can be written as \(\frac{20}{3}\). So, the expression becomes: \begin{align*} 10\frac{2}{5} - 6 \frac{2}{3} + 3 &= \frac{52}{5} - \frac{20}{3} + 3\\ &= \frac{156}{15} - \frac{100}{15} + \frac{45}{15}\\ &= \frac{101}{15} \end{align*} Therefore, the simplified expression is 6\(\frac{11}{15}\). Hence, the correct option is: \boxed{2. 6\frac{11}{15}}

**Question 11**
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approximate 0.0033780 to 3 significant figures

**Answer Details**

To approximate 0.0033780 to 3 significant figures, we need to count the first three non-zero digits, then round off the remaining digits. The first three non-zero digits are 3, 3, and 7, so we keep them. The next digit is 8, which is greater than or equal to 5, so we round up the last digit (0) to 1. Therefore, the answer is 0.00338 (option c).

**Question 12**
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Make u the subject of formula, E = \(\frac{m}{2g}\)(v^{2} - u^{2})

**Answer Details**

The formula we want to solve for `u`

is `E = (m/2g)(v^2 - u^2)`

.

To make `u`

the subject of the formula, we need to isolate `u`

on one side of the equation by performing the necessary algebraic operations.

First, we'll simplify the right side of the equation:

```
E = (m/2g)(v^2 - u^2)
2gE/m = v^2 - u^2 // Multiply both sides by 2g/m
```

Next, we'll isolate `u^2`

by adding it to both sides of the equation:

```
2gE/m + u^2 = v^2
```

Finally, we'll solve for `u`

by taking the square root of both sides of the equation:

```
u = sqrt(v^2 - 2gE/m)
```

Therefore, the value of `u`

as the subject of the formula is:

```
u = sqrt(v^2 - 2gE/m)
```

**Option A** is the correct answer.

**Question 13**
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Each exterior angle of a polygon is 30^{o}. Calculate the sum of the interior angles

**Answer Details**

The sum of the exterior angles of a polygon is always 360 degrees. Therefore, if each exterior angle is 30 degrees, the polygon must have 360/30 = 12 sides. The formula to find the sum of interior angles of a polygon is (n-2) x 180 degrees, where n is the number of sides. Substituting n = 12 into the formula, we get: (12-2) x 180 = 10 x 180 = 1800 degrees Therefore, the sum of the interior angles of this polygon is 1800 degrees. So the correct option is 1800^{o}.

**Question 15**
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The coordinates of points P and Q are (4, 3) and (2, -1) respectively. Find the shortest distance between P and Q.

**Question 16**
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Which of the following is a measure of dispersion?

**Answer Details**

A measure of dispersion describes how spread out or varied a set of data is. Among the options given, only the range is a measure of dispersion. Range is calculated by subtracting the minimum value from the maximum value in a dataset. It provides information about the spread of the data from the lowest to the highest value. Percentile, median, and quartile are measures of central tendency, which describe the typical or central value in a dataset.

**Question 17**
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The graph given is for the relation y = 2x^{2} + x - 1. Find the minimum value of y

**Answer Details**

To find the minimum value of y for the given relation y = 2x^2 + x - 1, we need to locate the vertex of the parabolic graph. The vertex of a parabola with equation y = ax^2 + bx + c is given by the coordinates (-b/2a, c - b^2/4a). In this case, a = 2, b = 1, and c = -1. Substituting these values into the formula, we get: Vertex x-coordinate = -b/2a = -1/(2*2) = -1/4 Vertex y-coordinate = 2(-1/4)^2 + (1/4) - 1 = -1.25 Therefore, the minimum value of y is -1.25. So the correct option is (C) -1.25.

**Question 18**
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The radii of the base of two cylindrical tins, P and Q are r and 2r respectively. If the water level in p is 10cm high, would be the height of the same quantity of water in Q?

**Answer Details**

The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base of the cylinder and h is the height of the cylinder. The volume of the water in tin P is V_{P} = πr²h_{P}, where r is the radius of the base of tin P and h_{P} is the height of the water in tin P. The volume of the same quantity of water in tin Q is V_{Q} = π(2r)²h_{Q} = 4πr²h_{Q}, where 2r is the radius of the base of tin Q and h_{Q} is the height of the water in tin Q. Since the same quantity of water is in both tins, V_{P} = V_{Q}. Substituting the expression for V_{P} and V_{Q} into the equation V_{P} = V_{Q} gives πr²h_{P} = 4πr²h_{Q}, which simplifies to h_{Q} = h_{P}/4. Therefore, the height of the water in tin Q is one-fourth of the height of the water in tin P. Since the height of the water in tin P is 10cm, the height of the water in tin Q would be (10/4) cm = 2.5 cm. Therefore, the height of the same quantity of water in tin Q is 2.5 cm. Answer option (A) is the correct answer.

**Question 19**
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Subtract \(\frac{1}{2}\)(a - b - c) from the sum of \(\frac{1}{2}\)(a - b + c) and \(\frac{1}{2}\)

(a + b - c)

**Answer Details**

We have: \begin{align*} &\frac{1}{2}(a-b+c)+\frac{1}{2}(a+b-c)-\frac{1}{2}(a-b-c)\\ &=\frac{1}{2}(2a)\\ &=a \end{align*} Therefore, the expression simplifies to $a$. So, the answer is: $\frac{1}{2}(a+b+c)$.

**Question 20**
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In the diagram, O is the centre of the circle of the circle, PR is a tangent to the circle at Q < SOQ = 86^{o}. Calculate the value of < SQR.

**Question 21**
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F x varies inversely as y and y varies directly as Z, what is the relationship between x and z?

**Answer Details**

The statement "F x varies inversely as y" can be mathematically written as x = k/y, where k is the constant of proportionality. Similarly, "y varies directly as Z" can be written as y = kz, where k is again the constant of proportionality. Substituting y in the first equation, we get x = k/(kz), which simplifies to x = 1/z. Therefore, we can conclude that x varies inversely with z, which is mathematically represented as x \(\alpha\) 1/z. So, the correct answer is: x \(\alpha \frac{1}{z}\).

**Question 22**
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Find the gradient of the line joining the points (2, -3) and 2, 5)

**Answer Details**

To find the gradient of the line joining two points, we use the formula: Gradient = (change in y) / (change in x) We can calculate the change in y by subtracting the y-coordinate of one point from the y-coordinate of the other point, and similarly, we can calculate the change in x by subtracting the x-coordinate of one point from the x-coordinate of the other point. In this case, the two points are (2, -3) and (2, 5). The change in y is: 5 - (-3) = 8 The change in x is: 2 - 2 = 0 Since the change in x is 0, we cannot divide by it, and the gradient is undefined. This means that the line joining these two points is vertical and has no slope. Therefore, the correct answer is: undefined.

**Question 23**
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Given that x > y and 3 < y, which of the following is/are true? i. y > 3 ii. x < 3 iii. x > y > 3

**Question 24**
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Find the number of term in the Arithmetic Progression(A.P) 2, -9, -20,...-141.

**Question 25**
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In the diagram, PQR is a straight line, (m + n) = 120^{o} and (n + r) = 100^{o}. Find (m + r)

**Answer Details**

Let's start by using the fact that PQR is a straight line, which means that m + n + r = 180°. We can then use the given information to form two equations and solve for m + r. From (m + n) = 120°, we can substitute n = 120° - m to get: (m + 120° - m + r) = 180° r + 120° = 180° r = 60° From (n + r) = 100°, we can substitute n = 120° - m and r = 60° to get: (120° - m + 60°) = 100° m = 80° Finally, we can find m + r by adding m and r: m + r = 80° + 60° = 140° Therefore, the answer is 140°.

**Question 26**
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A chord, 7cm long, is drawn in a circle with radius 3.7cm. Calculate the distance of the chord from the centre of the circle

**Answer Details**

To find the distance of the chord from the center of the circle, we can use the formula: distance from center = √(r^2 - (c/2)^2) where r is the radius of the circle and c is the length of the chord. In this case, r = 3.7 cm and c = 7 cm. Therefore: distance from center = √(3.7^2 - (7/2)^2) = √(13.69 - 12.25) = √1.44 = 1.2 cm Therefore, the distance of the chord from the center of the circle is **1.2 cm**. The logic behind the formula is that the distance from the center of the circle to the chord is the perpendicular distance from the center to the line that contains the chord. If we draw radii from the center of the circle to the endpoints of the chord, we can form a right triangle with the chord as the hypotenuse. The distance from the center to the chord is the height of this triangle, which can be found using the Pythagorean theorem.

**Question 27**
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A chord subtends an angle of 120^{o} at the centre of a circle of radius 3.5cm. Find the perimeter of the minor sector containing the chord, [Take \(\pi = \frac{22}{7}\)]

**Question 28**
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A box contains 13 currency notes, all of which are either N50 or N20 notes. The total value of the currency notes is N530. How many N50 notes are in the box?

**Answer Details**

Let's assume that there are x N50 notes and y N20 notes in the box. From the problem, we know that the total number of currency notes is 13, so we have: x + y = 13 ----(1) We also know that the total value of the currency notes is N530. If we express this in terms of the number of N50 and N20 notes, we get: 50x + 20y = 530 ----(2) We now have two equations (1) and (2) with two variables (x and y), which we can solve simultaneously. Multiplying equation (1) by 20, we get: 20x + 20y = 260 Subtracting this equation from equation (2), we get: 30x = 270 Dividing both sides by 30, we get: x = 9 Therefore, there are 9 N50 notes in the box. Answer: 9

**Question 29**
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Simplify \(\frac{\sqrt{8^2 \times 4^{n + 1}}}{2^{2n} \times 16}\)

**Question 30**
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In the diagram, ST is parallel to UW, < WVT = x^{o}, < VUT = y^{o}, < RSV = 45^{o} and < VTU = 20^{o}. Calculate the value of y

**Question 31**
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In parallelogram PQRS, QR is produced to M such that |QR| = |RM|. What fraction of the area of PQMS is the area of PRMS?

**Question 32**
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The graph given is for the relation y = 2x^{2} + x - 1.What are the coordinates of the point S?

**Answer Details**

To find the coordinates of point S on the graph, we need to use the equation of the graph, which is given as y = 2x^2 + x - 1. From the graph, we can see that the point S has x-coordinate of 1. To find the y-coordinate, we can substitute x=1 into the equation and solve for y: y = 2(1)^2 + (1) - 1 y = 2 + 1 - 1 y = 2 Therefore, the coordinates of point S are (1, 2). So, the answer is (c) (1, 2.0).

**Question 33**
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The bar chart shows the scores of some students in a test. If one students is selected at random, find the probability that he/she scored at most 2 marks

**Question 34**
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Three quarters of a number added to two and a half of the number gives 13. Find the number

**Answer Details**

Let's assume the number we are looking for to be 'x'. According to the problem statement, three quarters of the number can be written as \(\frac{3}{4}x\) and two and a half of the number can be written as \(2.5x\). It is given that the sum of these two quantities gives 13. So we can write it as: \(\frac{3}{4}x + 2.5x = 13\) Now, we can simplify this equation by combining the two terms on the left-hand side: \(\frac{3}{4}x + 2.5x = 13\) \(\Rightarrow \frac{3}{4}x + \frac{10}{4}x = 13\) \(\Rightarrow \frac{13}{4}x = 13\) \(\Rightarrow x = \frac{13 \times 4}{13}\) \(\Rightarrow x = 4\) Therefore, the number we are looking for is 4. Hence, the answer is 4.

**Question 35**
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A man's eye level is 1.7m above the horizontal ground and 13m from a vertical pole. If the pole is 8.3m high, calculate, correct to the nearest degree, the angle of elevation of the top of the pole from his eyes.

**Question 36**
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If x = {0, 2, 4, 6}, y = {1, 2, 3, 4} and z = {1, 3} are subsets of u = {x:0 \(\geq\) x \(\geq\) 6}, find x \(\cap\) (Y' \(\cup\) Z)

**Answer Details**

To solve this problem, we need to follow the given operations in order of precedence, i.e., first we have to find the complement of y, then union it with z and finally find the intersection of x with the resulting set. The complement of y (denoted by Y') is the set of all elements in u that are not in y. So, Y' = {0, 5, 6}. The union of Y' and Z (denoted by Y' \(\cup\) Z) is the set of all elements that are in Y' or Z or both. So, Y' \(\cup\) Z = {0, 1, 3, 5, 6}. Finally, the intersection of x with Y' \(\cup\) Z (denoted by x \(\cap\) (Y' \(\cup\) Z)) is the set of all elements that are in both x and Y' \(\cup\) Z. So, x \(\cap\) (Y' \(\cup\) Z) = {0, 6}. Therefore, the answer is {0, 6}.

**Question 37**
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In the diagram, ST is parallel to UW, < WVT = x^{o}, < VUT = y^{o}, < RSV = 45^{o} and < VTU = 20^{o}. Find the value of x

**Question 39**
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In the figures, PQ is a tangent to the circle at R and UT is parallel to PQ. if < TRQ = x^{o}, find < URT in terms of x

**Question 40**
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