Question 1
A point on the ground is 5 m away from the foot of a vertical wall 12 m high. Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall.
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Question 2
The gradient of the line passing through the points (3, 6) and (x, 4) is (-\frac{2}{5}). Find the value of x.
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Question 3
A woman pours 85 litres of kerosene into a cylindrical container with radius 7 cm. Calculate, correct to the nearest cm, the depth of the kerosene in the container. [\text{Take } \pi = \frac{22}{7}]
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Question 4
Given that (x^2 - 11x + m) is a perfect square, find the value of m.
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Question 5
The sides of a scalene triangle are 4 cm, 9 cm and 11 cm. Calculate, correct to the nearest whole number, the area of the triangle.
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Question 6
In a hall, there are 175 persons. 12% are children, 56 are men and the rest are women. If one person is selected at random from the hall, find the probability that a woman is selected.
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Question 7
A student measured the length of a classroom and obtained 3.99 m which is less than the actual length. If the percentage error was 5%, what was the actual length?
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Question 8
A car covers the first 80 km of a journey in 2 hours and completes the journey by travelling further 2.5 hours at 50 km/h. What is the average speed of the entire journey?
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Question 9
If (\log x = 2 - 3\log 2), find the value of x.
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Question 10
The graph of (y = x^2 - 5x + k) passes through the point (3, 1). Find the value of k.
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Question 11
Diagram will be provided Find the value of x in the diagram.
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Question 12
Diagram will be provided In the diagram, (p + q = 250^\circ). Find the angle marked s.
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Question 13
If (x : y : z = 2 : 3 : 4), evaluate (\dfrac{9x + 3y}{6z - 2y}).
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Question 14
Find the mean of ((x + y)), ((2x + 3y)), ((2x - 2y)) and ((3x - 2y)).
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Question 15
A box contains 2 red, 6 white and 5 black balls, all of the same size. If a ball is selected at random, what is the probability that it is black?
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Question 16
Diagram will be provided In the diagram, MNPQ is a circle, centre O. (\angle MQN = 43^\circ) and (\angle QNP = 57^\circ). Find the value of y.
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Question 17
Diagram will be provided Describe the locus, l in the diagram.
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Question 18
The base radius and slant height of a solid cone are 8 cm and 14 cm respectively. Calculate, correct to two decimal places, its volume. [\text{Take } \pi = \frac{22}{7}]
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Question 19
Abudu can do a piece of work in 6 days and Efah can do the same work in 3 days. What fraction of the work can both do together in a day?
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Question 20
If (P = {x: 1 \le x \le 6}) and (Q = {x: 2 < x < 9}) where (x \in R), find (P \cap Q).
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Question 21
Given that (p^2 + q^2 + r^2 = 50), (p = 5) and (\sqrt{q} = 2), find the positive value of r.
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Question 22
If (\frac{1}{2}) and -3 are the roots of (px^2 + qx + r = 0), find the values of p, q and r.
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Question 23
A cylindrical container closed at both ends has radius 5 cm and height 10 cm. Calculate to two decimal places, the total surface area. [\text{Take } \pi = \frac{22}{7}]
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Question 24
Badu is four times as old as Juliet. In 10 years Badu will be twice as old as Juliet. Find Juliet's age.
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Question 25
When the point (4, 5) is rotated through an angle in the anticlockwise direction about the origin, its image is (-5, 4). What is the angle of rotation?
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Question 26
Diagram will be provided Find the value of x in the diagram.
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Question 27
A woman bought a washing machine for USD 18,000.00. If the exchange rate is USD 0.045 to ₦1.00, find in ₦, the cost of the machine.
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Question 28
Determine the least value of x such that (7 + x \equiv 3 \pmod{8}).
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Question 29
If (\dfrac{4m + 3n}{4m - 3n} = \frac{5}{2}), find the ratio of m : n.
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Question 30
Yakubu received (12\frac{1}{2}%) of the sales made in a certain mouth. If the amount he received was USD 35,000.00, what was the total sales made?
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Question 31
The angle of elevation of the top of a vertical pole from a point, P on a level ground is 60°. The distance from P to the foot of the pole is 55 m. Find the height of the pole.
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Question 32
The ratio of girls to boys in a certain committee is 5 : 2. If there are 35 members in the committee, how many more boys must be added to the committee to have the ratio of girls to boys as 5 : 4?
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Question 33
Find the values of x for which (\dfrac{x + 1}{3x^2 - 12}) is not defined.
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Question 34
Given that (\tan x = \frac{12}{5}), find the value of ((\sin x \cos x))
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Question 35
Consider these two statements: P: N is an odd number Q: N is a prime number greater than 2. Express "If N is not an odd number then N is not a prime number greater than 2" in symbolic form.
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Question 36
A sector which subtends an angle 150° is cut from a circular plate of radius 14 cm. Find, correct to one decimal place, the perimeter of the remaining plate. [\text{Take } \pi = \frac{22}{7}]
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Question 37
One side of a gutter is 15 cm lower than the other side. A plank of wood, which is laid across the gutter to form a bridge, slopes at an angle of 35° to the horizontal. How wide is the gutter?
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Question 38
Diagram will be provided In the diagram, MOP is the diameter of the circle MNP centre O. (\angle NMP = (2x)^\circ) and (\angle EPM = (5x + 18)^\circ). Find the value of x.
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Question 39
The height of a square base pyramid is thrice the length of a side of its base. If the base area is 324 cm², find the volume of the pyramid.
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Question 40
If (4^x = \frac{1}{1024}), find the value of x
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Question 41
"Diagram will be provided" In the diagram, O is the centre of the circle WXY. (|WX| = |XZ|) and (\angle ZXY = 26^\circ). Find (\angle XYZ).
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Question 42
Evaluate (141_6 + 233_6 - 102_6)
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Question 43
In the first year, Mr. Kwakye's annual salary was USD 1,560.00. His salary was increased each year by a constant value, y until it was USD 13,980.00 in the 13th year. Calculate the value of y.
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Question 44
Given that (\frac{16}{9}, x, 1, y) is a Geometric Progression (G.P), find the value of xy.
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Question 45
A chord of a circle, 12 cm long subtends an angle of 150° at the centre of the circle. Find the radius of the circle.
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Question 46
The lines (3x + 2y = 4) and (y = 2x - 5) intersect at a point P(x, y). Find the coordinates of P.
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Question 47
Make u the subject of the relation (\dfrac{t}{s+u} = \dfrac{s}{t-u}).
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Question 48
"Table will be provided"The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Calculate the mean of the distribution.
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Question 49
"Table will be provided" The table shows the number of subjects registered by a class of students for an examination. Use the information to answer the question below Find the median.
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Question 50
A rectangular tank of sides 4 m by 8 m by 11 m has the same volume as a cylindrical tank of height 7 m. Calculate the base radius of the cylindrical tank. [\text{Take } \pi = \frac{22}{7}]
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