Question 1
Given that log₁₀5 = x and log₁₀11 = y, express log₁₀275 in terms of x and y.
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Question 2
The sets P = {x:x = 3, 5, 6} and Q = {x: 2 ≤ x ≤ 5} are subsets of μ = {x: 1 ≤ x ≤ 10, where x is an integer}. Find P' ∩ Q.
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Question 3
A pyramid has a rectangular base of length 6.5 cm and width 4.2 cm. If the height of the pyramid is 12 cm, find the volume.
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Question 4
Given that \((1 \tfrac{2}{3})^{\tfrac{x}{2}} = (4 \tfrac{17}{27})\), find the value of \(x\).
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Question 5
The first 4 terms of an Arithmetic Progression (A.P) are 8, x , y and 17. Find the value of \((x + y)\).
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Question 6
In a test, the mean mark of 25 students in a class, P, is 72.2 and the mean mark of 20 students in another class, Q, is 65. Find the mean mark of all the students in P and Q.
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Question 7
Mr. Gyan bought a car for USD 16,800.00 and later sold it at 85 % of the original cost. He spent USD 3,930.75 from the money he received from the sale of the car and invested the remaining at 18 % per annum simple interest. How much interest did he earn in 9 years?
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Question 8
The mean and range of 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10 are m and r respectively. Find the value of \((m + r)\)
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Question 9
Given that \(\dfrac{3}{x+y} - \dfrac{4}{x-y} = 0\), find the value of \(\dfrac{x}{y}\), where \(y \ne 0\).
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Question 10
The last term of the sequence: 7, 11, 15, ... is 115. Find the number of terms in the sequence.
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Question 11
Find the mean deviation of 2, 5, 7, 9 and 15.
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Question 12
The locus, L is such that \(|PM| = |PN|\). Which of the following best describes L?
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Question 13
A train is moving at 60 miles per hour. If it passes a sign post in 15 seconds, find, in yards, the length of the train. [Take 1 mile = 1760 yards]
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Question 14
Kwaku is 2 years older than Atanga and 6 years younger than Esi. The sum of their ages is 70. If they decide to share USD 153.00 in the ratio of their ages, how much will the eldest person receive?
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Question 15
Solve: \(\dfrac{\log_{3}(2x - 1)}{\log_{3}243} = \dfrac{2}{5}\).
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Question 16
The sum of the ages of Esi and Amina is 24 years and the difference in their ages is 6 years. If Amina is older than Esi, find Esi's age.
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Question 17
Solve: \(4x + 1 \equiv 3(\text{mod }11)\).
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Question 18
Diagram will be provided In the diagram, \(|PQ| = 6.7\) cm, \(|QR| = 5.5\) cm and \(|RT| = 3.3\) cm. Find the area.
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Question 19
Diagram will be provided In the diagram, \(\triangle OMN\) is similar to \(\triangle OPQ\). Find \(|MQ|\).
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Question 20
A scientific sensor records air pollution levels in base 3. If the highest recorded pollution level for a week was \(2120_3\), what is the decimal equivalent?
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Question 21
Factorize: \(5p^2 + 4pq - 15pr - 12qr\).
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Question 22
A school has a total population of 1,800 students. Out of this number \(\frac{4}{9}\) are in SHS 1, \(\frac{13}{36}\) are in SHS 2 and the rest are in SHS 3. Calculate the number of students in SHS 3.
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Question 23
The straight line \(3y + bx - 6 = 0\) passes through (3, 4). Find the value of \(b\).
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Question 24
A function is defined by \(g:x \rightarrow \dfrac{2x - 1}{3x - 2}\). For what value of x is g not defined?
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Question 25
Diagram will be provided In the diagram \(\angle QPR = 90^\circ\). If \(q^2 = 25 - r^2\), find the value of \(p\).
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Question 26
Diagram will be provided In the diagram \(PQRST\) is a trapezium. \(|ST| = 3\) cm, \(|RS| = y\) cm and \(|PS| = 4\) cm. For what values of \(y\) will the area of the trapezium \(PQRST\) be less than or equal to \(10\text{ cm}^2\)?
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Question 27
A town \(P\) is due south of town \(Q\) and town \(R\) is on a bearing of \(125^\circ\) from \(Q\). If town \(R\) is 20 km due east of \(P\), find \(|PQ|\).
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Question 28
Diagram will be provided The diagram shows a sector of a circle of radius 42 cm. If the sector is folded to form a right circular cone, find the surface area of the cone. [Take \(\pi = \frac{22}{7}\) ]
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Question 29
Diagram will be provided In the diagram, P, Q, R and S are points on the circle centre O and \(\angle PQR = 104^\circ\). Find the angle marked y.
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Question 30
Diagram will be provided In the diagram \(\overline{TX}\) and \(\overline{TY}\) are tangents to the circle \(XYZ\) at \(X\) and \(Y\) respectively, \(\overline{TX} \parallel \overline{YZ}\) and \(\angle XTY = 100^\circ\). Find \(\angle ZXY\).
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Question 31
The radius of a circle is 4 times the radius of another circle. What is the relationship between their areas?
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Question 32
Diagram will be provided In the diagram, \(\angle QMP = 40^\circ\) and \(\angle RPM = 30^\circ\). Find the value of x.
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Question 33
Some of the interior angles of a pentagon are 111°, 131° and 79°. The remaining angles are x and y in the ratio 2 : 3 respectively. Find, correct to the nearest whole number, the value of x.
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Question 34
Diagram will be provided In the diagram, P, Q, R and S are points on the circle centre O. \(\overline{QS}\) is a diameter and \(\angle ORQ = 41^\circ\). Find \(\angle QSR\).
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Question 35
Diagram will be provided In the diagram, O is the centre of the circle and \(\angle OXZ = 19^\circ\). Find \(\angle XYZ\).
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Question 36
A car consumes 36 gallons of fuel over a distance of 2,268 km. Find, in km per litre, the fuel consumption. [Take 1 gallon = 4.5 litres]
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Question 37
Make \(w\) the subject of the relation \(\dfrac{1}{w} = (h - 1)\left(\dfrac{1}{m} - \dfrac{1}{n}\right)\).
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Question 38
The inverse of the sum of −3 and twice a certain number is \(\dfrac{1}{5}\). Find the number.
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Question 39
Diagram will be provided In the diagram, \(O\) is the centre of the circle, \(\angle KLM = x\) and \(|OM| = |ML| = |LK| = |KO|\). Find \(\angle OKL\).
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Question 40
Diagram will be provided The diagram shows a field \(MNPQRST\), where \(MTS\) is a semicircle. Find the area of the field. [Take \(\pi = \dfrac{22}{7}\) ]
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Question 41
A box contains 12 red, 8 yellow and 10 green pebbles, all of the same size. If two pebbles are selected at random one after the other, with replacement, find the probability that the first is green and the second is not a red pebble.
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Question 42
Find the coefficient of \(x^2\) in the expansion of \((4x + 5)(3 - 2x)\).
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Question 43
Gifty is 19 years younger than her mother. In three years time the sum of their ages will be 67 years. Find the sum of their ages now.
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Question 44
A fair dice is thrown once. What is the probability of obtaining a 3 or 5?
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Question 45
The mean of \(a, b, c, d\) and \(e\) is 15. Calculate the mean of \((a + 1)\), \((b + 3)\), \((c + 5)\), \((d + 7)\) and \((e + 9)\).
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Question 46
If \(V = \pi r^2h\) and \(S = 2\pi rh\), express \(V\) in terms of \(r\) and \(S\).
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Question 47
A man cycles a distance of (3a) km at \(V\) km/h and then walks a distance of \(a\) km at \((V - 7)\) km/h. Find the total number of hours he spent travelling.
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Question 48
Peter is in the East of Tom and Tom is in the North of John. If Mike is in the South of John, in which direction of Peter is Mike?
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Question 49
Simplify: \(\dfrac{25p^{2}-q^{2}}{5p^{2}+6pq+q^{2}}\).
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Question 50
Correct. 5.40514 to three significant figures.
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