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Question 1 Report
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Calculate the variance of 2, 4, 7, 8 and 9
Question 2 Report
In XYZ, |YZ| = 32cm, < YXZ 53\(^o\) and XZY = 90\(^o\). Find, correct to the nearest centimetre, |XZ|
Question 3 Report
Simplify, correct to three significant figures, (27.63)\(^2\) - (12.37)\(^2\)
Answer Details
We can start by squaring each of the numbers in the expression: (27.63)\(^2\) = 762.9869 (12.37)\(^2\) = 153.4369 Now we can subtract the two squares: 762.9869 - 153.4369 = 609.55 Rounding the result to three significant figures, we get: 609.55 = 610 So (27.63)\(^2\) - (12.37)\(^2\) = 610.
Question 4 Report
In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70\(^o\), calculate the length of arc ZY. [Take \(\pi = \frac{22}{7}\)]
Question 5 Report
An arc subtends an angle of 72\(^o\) at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take \(\pi = \frac{22}{7}\)]
Answer Details
To find the length of the arc, we need to use the formula: Length of arc = \(\frac{\text{angle subtended by the arc}}{360^\circ} \times 2\pi r\) Here, the angle subtended by the arc is 72\(^o\) and the radius of the circle is 3.5 cm. We can substitute these values in the formula to get: Length of arc = \(\frac{72^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 3.5\) cm Simplifying this expression, we get: Length of arc = \(\frac{1}{5} \times \frac{44}{7} \times 3.5\) cm Length of arc = \(\frac{22}{5}\) cm Length of arc = 4.4 cm (approx.) Therefore, the length of the arc is 4.4 cm (option C).
Question 6 Report
Solve: \(\frac{y + 1}{2} - \frac{2y - 1}{3}\) = 4
Answer Details
To solve this equation, we can start by simplifying both sides by finding a common denominator. \(\frac{y + 1}{2} - \frac{2y - 1}{3} = 4\) Multiplying the first term by 3 and the second term by 2 (the least common multiple of 2 and 3), we get: \(\frac{3(y+1)}{6} - \frac{2(2y-1)}{6} = 4\) Simplifying this gives: \(\frac{3y + 3 - 4y + 2}{6} = 4\) Combining like terms: \(\frac{-y + 5}{6} = 4\) Multiplying both sides by 6: \(-y + 5 = 24\) Subtracting 5 from both sides: \(-y = 19\) Finally, multiplying both sides by -1 to solve for y: \(y = -19\) Therefore, the solution is y = -19.
Question 7 Report
The total surface area of a solid cylinder 165cm\(^2\). Of the base diameter is 7cm, calculate its height. [Take \(\pi = \frac{22}{7}\)]
Question 8 Report
In the diagram, PQ is parallel to RS, < QFG = 105\(^o\) and < FEG = 50\(^o\). Find the value of n
Question 10 Report
Make b the subject of the relation lb = \(\frac{1}{2}\) (a + b)h
Question 11 Report
H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.
Question 12 Report
The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?
Answer Details
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the distance from the foot of the ladder to the pole and the height of the pole where the ladder is resting form the other two sides of the right triangle. So we have: Length of ladder^2 = (distance from foot of ladder to pole)^2 + (height of pole where ladder is resting)^2 Length of ladder^2 = 6^2 + 8^2 Length of ladder^2 = 36 + 64 Length of ladder^2 = 100 Length of ladder = √100 = 10 Therefore, the length of the ladder is 10 meters. Answer option C (10m) is correct.
Question 13 Report
Express, correct to three significant figures, 0.003597.
Answer Details
To express 0.003597 correct to three significant figures, we need to round off the number to the third digit after the decimal point. The third digit after the decimal point is 7. Since 7 is greater than or equal to 5, we need to round up the second digit after the decimal point. Therefore, the third digit becomes zero. Hence, the rounded value of 0.003597 correct to three significant figures is 0.00360. Therefore, the answer is: 0.00360.
Question 14 Report
8, 18, 10,14, 18, 11, 13, 14, 13, 17, 15, 8, 16, and 13
Question 15 Report
The following are scores obtained by some students in a test. Find the median score
8 | 18 | 10 | 14 | 18 | 11 | 13 |
14 | 13 | 17 | 15 | 8 | 16 | 13 |
Question 16 Report
Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.
Answer Details
If Bala sold an article for #6,900.00 and made a profit of 15%, this means that his cost price for the article was lower than the selling price by 15%. We can calculate his cost price as follows: Cost Price = Selling Price / (1 + Profit%) Cost Price = 6,900 / (1 + 0.15) Cost Price = 6,000 Therefore, Bala's cost price was #6,000.00, and he sold the article for #6,900.00, making a profit of #900.00. Now, we need to calculate the percentage profit he would have made if he sold the article for #6,600.00 instead of #6,900.00. To do this, we can use the following formula: Percentage Profit = (Profit / Cost Price) x 100% Percentage Profit = (6,600 - 6,000) / 6,000 x 100% Percentage Profit = 10% Therefore, if Bala had sold the article for #6,600.00 instead of #6,900.00, he would have made a profit of 10%. The correct option is 10%.
Question 17 Report
Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?
Answer Details
The commission charged by the agent is 8% of the selling price. This means that the remaining amount that Eric received after the sale is 92% of the selling price (100% - 8% = 92%). We can set up an equation to solve for the selling price: 92% of selling price = $117,760.00 To solve for the selling price, we can divide both sides by 92% (or multiply by the reciprocal of 92%, which is 100/92): selling price = $117,760.00 ÷ 0.92 Using a calculator, we get: selling price = $128,000.00 Therefore, the selling price of the house was $128,000.00.
Question 18 Report
If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\)
Question 19 Report
A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.
Answer Details
Let's first find the area of the original rectangular board, which is simply the product of its length and width: original area = 15 cm x x cm = 15x cm\(^2\) When the sides are doubled, the length becomes 15 cm x 2 = 30 cm, and the width becomes x cm x 2 = 2x cm. So, the new area is: new area = 30 cm x 2x cm = 60x cm\(^2\) So, the new area of the rectangular board is 60x cm\(^2\).
Question 20 Report
In the diagram, PQ is parallel to RS, < QFG = 105\(^o\) and < FEG = 50\(^o\). Find the value of m.
Question 21 Report
If T = {prime numbers} and M = {odd numbers} are subsets of \(\mu\) = {x : 0 < x ≤ 10} and x is an integer, find (T\(^{\prime}\) n M\(^{\prime}\)).
Answer Details
The set T is the set of prime numbers less than or equal to 10, which are {2, 3, 5, 7}. The prime complement (T\(\prime\)) is the set of non-prime numbers less than or equal to 10, which are {1, 4, 6, 8, 10}. The set M is the set of odd numbers less than or equal to 10, which are {1, 3, 5, 7, 9}. The odd complement (M\(\prime\)) is the set of even numbers less than or equal to 10, which are {2, 4, 6, 8, 10}. Finally, the intersection of T\(\prime\) and M\(\prime\) is the set of numbers that are both non-prime and even, which is {4, 6, 8, 10}. So (T\(\prime\) n M\(\prime\)) = {4, 6, 8, 10}.
Question 22 Report
Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)
Answer Details
To evaluate the expression 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\), we need to simplify the square roots first. \(\sqrt{28} = 2\sqrt{7}\) \(\sqrt{50} = 5\sqrt{2}\) \(\sqrt{72} = 2\sqrt{18} = 2\sqrt{9}\sqrt{2} = 6\sqrt{2}\) Now that we have simplified the square roots, we can substitute the values back into the expression: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\) = 2 * 2\(\sqrt{7}\) - 3 * 5\(\sqrt{2}\) + 6\(\sqrt{2}\) = 4\(\sqrt{7}\) - 3 * 5\(\sqrt{2}\) + 6\(\sqrt{2}\) = 4\(\sqrt{7}\) - 15\(\sqrt{2}\) + 6\(\sqrt{2}\) = 4\(\sqrt{7}\) - 9\(\sqrt{2}\) So the expression evaluates to 4\(\sqrt{7}\) - 9\(\sqrt{2}\).
Question 23 Report
If log\(_x\) 2 = 0.3, evaluate log\(_x\) 8.
Answer Details
We can use the property of logarithms that states: $$\log_{a}(b^c) = c \log_{a}(b)$$ Using this property, we can rewrite the expression for log\(_x\) 8 as: $$\log_{x}(8) = \log_{x}(2^3) = 3\log_{x}(2)$$ We are given that log\(_x\) 2 = 0.3, so we can substitute this value: $$3\log_{x}(2) = 3(0.3) = 0.9$$ Therefore, the value of log\(_x\) 8 is 0.9. Therefore, option (C) is the correct answer: 0.9.
Question 24 Report
If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)
Answer Details
First, let's solve for a using the given equation 2\(^{a}\) = \(\sqrt{64}\). We know that \(\sqrt{64}\) is equal to 8, so we can substitute this value in the equation: 2\(^{a}\) = 8 To solve for a, we need to find the exponent that 2 is raised to in order to get 8. This exponent is 3, so a = 3. Next, we need to find the value of b. We are given that \(\frac{b}{a}\) = 3, so we can rearrange this equation to solve for b: b = 3a Substituting the value we found for a, we get: b = 3 x 3 = 9 Finally, we can evaluate a\(^2\) + b\(^2\) using the values we found for a and b: a\(^2\) + b\(^2\) = 3\(^2\) + 9\(^2\) = 9 + 81 = 90 Therefore, the answer is 90.
Question 25 Report
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Calculate the value of x.
Question 26 Report
The interior angles of a polygon are 3x\(^o\), 2x\(^o\), 4x\(^o\), 3x\(^o\) and 6\(^o\). Find the size of the smallest angle of the polygon.
Question 27 Report
If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\)
Question 28 Report
Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y)
Answer Details
To factorize the given expression, we can use the distributive property of multiplication over addition. This means that we need to multiply each term in the first set of parentheses by each term in the second set of parentheses, and then simplify: (2x + 2y)(x - y) + (2x - 2y)(x + y) = 2x(x - y) + 2y(x - y) + 2x(x + y) - 2y(x + y) (using distributive property) = 2x^2 - 2xy + 2xy + 2y^2 + 2x^2 + 2xy - 2xy - 2y^2 (combining like terms) = 4x^2 - 4y^2 Therefore, the answer is 4(x - y)(x + y). Explanation: We can factorize the given expression by grouping the terms into two sets, each set containing two terms with a common factor. We can then factor out that common factor from each set, and simplify. In this case, we can factor out 2 from the first set of parentheses, and -2 from the second set of parentheses, giving us: 2(x + y)(x - y) - 2(x + y)(x - y) We can then combine the two sets of parentheses, giving us: (2(x + y) - 2(x - y))(x - y) Simplifying the expression inside the parentheses gives us: (2x + 2y - 2x + 2y)(x - y) Which further simplifies to: 4y(x - y) However, this is not the fully factored form, since we can factor out 4 from the expression to get: 4(x - y)(y) So the answer is 4(x - y)(y), which is equivalent to option A.
Question 29 Report
A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?
Answer Details
There are 5 + 6 + 7 = 18 pencils in the box. Since there are 6 green pencils, the probability of picking a green pencil at random is 6/18, which simplifies to 1/3. Therefore, the answer is \(\frac{1}{3}\).
Question 30 Report
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
Answer Details
In an arithmetic progression (AP), the difference between any two consecutive terms is constant. So, we can find the common difference (d) between any two consecutive terms in the given AP by subtracting one term from the preceding term. Let's use the second term (P) and the first term (6) to find the common difference: d = P - 6 Now, to check whether 14 is the third term of the AP, we can use the formula for the nth term of an AP: an = a1 + (n-1)d where an = nth term a1 = first term d = common difference If 14 is the third term, then n = 3, so we have: 14 = 6 + (3-1)d 14 = 6 + 2d 2d = 8 d = 4 Now, we can substitute the value of d in the expression we got earlier: d = P - 6 4 = P - 6 P = 10 Therefore, the value of P is 10.
Question 31 Report
The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.
Answer Details
In an arithmetic progression (AP), the terms are equally spaced. Let's call the common difference "d". If we have the first term "a" and the nth term "an", we can find the common difference using the formula: d = (an - a) / (n - 1) In this case, the fourth term is 37 and the first term is -20, so we can plug in the values into the formula: d = (37 - (-20)) / (4 - 1) = 57 / 3 = 19 So the common difference is 19.
Question 32 Report
A box contains 3 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?
Question 33 Report
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Find the value of y.
Question 34 Report
Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\)
Question 35 Report
The following are scores obtained by some students in a test, Find the mode of the distribution
8 | 18 | 10 | 14 | 18 | 11 | 13 |
14 | 13 | 17 | 15 | 8 | 16 | 13 |
Answer Details
To find the mode of the distribution, we need to determine the value that appears most frequently in the dataset. Looking at the table, we can see that the value "13" appears three times, which is more than any other value. Therefore, the mode of this distribution is 13. Alternatively, we could create a frequency table or a histogram to visualize the distribution and identify the mode more easily.
Question 36 Report
Evaluate: (0.064) - \(\frac{1}{3}\)
Question 37 Report
Find the equation of a straight line passing through the point (1, -5) and having gradient of \(\frac{3}{4}\)
Question 38 Report
If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
Answer Details
We are given that \(\tan x = \frac{3}{4}\) and \(0 < x < 90^o\). Since \(\tan x = \frac{\sin x}{\cos x}\), we can rewrite the given equation as: \[\frac{\sin x}{\cos x} = \frac{3}{4}\] Multiplying both sides by \(\cos x\) gives us: \[\sin x = \frac{3}{4}\cos x\] Dividing both sides by \(2\sin x\) gives us: \[\frac{\cos x}{2\sin x} = \frac{\frac{4}{3}\sin x}{2\sin x} = \frac{4}{3} \cdot \frac{1}{2} = \frac{2}{3}\] Therefore, the value of \(\frac{\cos x}{2\sin x}\) is \(\frac{2}{3}\). Hence, the answer is: \(\frac{2}{3}\).
Question 39 Report
There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
Answer Details
The probability of an event happening is the number of ways it can happen divided by the total number of outcomes. In this case, there are 8 boys and 4 girls in the lift. If the first person who steps out of the lift is a boy, it means that any one of the 8 boys can be the first person to step out of the lift. Therefore, the number of ways the event can happen is 8. The total number of outcomes is the total number of people who can step out of the lift first. Since there are 12 people in the lift, any one of the 12 people can be the first person to step out of the lift. Therefore, the total number of outcomes is 12. Therefore, the probability that the first person who steps out of the lift will be a boy is: probability = number of ways the event can happen / total number of outcomes probability = 8 / 12 probability = 2 / 3 Hence, the answer is: \(\frac{2}{3}\).
Question 40 Report
Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm. [Take \(\pi = \frac{22}{7}\)]
Question 41 Report
Which of these values would make \(\frac{3p^-}{p^{2-}}\) undefined?
Question 42 Report
In the diagram, POS and ROT re straight lines. OPOR is a parallelogram, |OS| = |OT| and
Question 43 Report
If (0.25)\(^y\) = 32, find the value of y.
Answer Details
We can solve the given equation by taking the logarithm of both sides. Any base of the logarithm can be used, but we will use the common logarithm (base 10). log\((0.25)^y\) = log 32 Using the logarithmic identity log\((a^b)\) = b log\((a)\), we get: y log\((0.25)\) = log 32 Now, we can evaluate log\((0.25)\) using the logarithmic identity log\((a^n)\) = n log\((a)\), as follows: log\((0.25)\) = log\((\frac{1}{4})\) = log\((4^{-1})\) = -log\((4)\) We know that log\((10^x)\) = x, so log\((4)\) = log\((10^{0.602})\) \(\approx\) 0.602 Therefore, y log\((0.25)\) = log 32 y (-log\((4)\)) = log 32 y (-0.602) = log 32 y = \(\frac{\text{log } 32}{-0.602}\) Using a calculator, we get: y \(\approx\) -2.5 Therefore, the value of y is approximately -2.5. Hence, the answer is: y = -\(\frac{5}{2}\).
Question 44 Report
Simplify: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\)
Answer Details
To simplify the fraction, we need to find a common denominator for the numerator and denominator. The denominator, \(x^2 - 9x + 14\), can be factored into the product of two binomials: \((x - 7)(x - 2)\). Now, to simplify the numerator, we can factor it as well: \(x^2 - 5x - 14 = (x - 7)(x + 2)\). With this factoring, we can cancel out the common factor of \(x - 7\) in the numerator and denominator, leaving us with the simplified fraction: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14} = \frac{(x - 7)(x + 2)}{(x - 7)(x - 2)} = \frac{x + 2}{x - 2}\). So the simplified fraction is.
Question 46 Report
If 3p = 4q and 9p = 8q - 12, find the value of pq.
Question 47 Report
The pie chart represents fruits on display in a grocery shop. If there are 60 oranges on display, how many apples are there?
Question 48 Report
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
Answer Details
We can use the laws of logarithms to simplify the expression: \(\frac{\log_3 9 - \log_2 8}{\log_3 9} = \frac{\log_3 (3^2) - \log_2 (2^3)}{\log_3 (3^2)}\) Using the laws of logarithms, we can simplify the numerator: \(\frac{\log_3 (3^2) - \log_2 (2^3)}{\log_3 (3^2)} = \frac{2\log_3 3 - 3\log_2 2}{2\log_3 3}\) We know that \(\log_3 3 = 1\) and \(\log_2 2 = 1\), so we can substitute these values: \(\frac{2\log_3 3 - 3\log_2 2}{2\log_3 3} = \frac{2 - 3}{2} = -\frac{1}{2}\) Therefore, the value of the expression is -\(\frac{1}{2}\).
Question 49 Report
Evaluate: \(\frac{0.42 + 2.5}{0.5 \times 2.95}\), leaving the answer in the standard form.
Answer Details
To solve this expression, we need to follow the order of operations which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). We do not have any parentheses or exponents, so we can proceed to the multiplication and division step. We have: \[\frac{0.42 + 2.5}{0.5 \times 2.95} = \frac{2.92}{1.475}\] Next, we can simplify the fraction by dividing both the numerator and denominator by the greatest common factor which is 0.05. \[\frac{2.92}{1.475} = \frac{292}{147.5}\] Finally, we can express this fraction in standard form by moving the decimal point in the numerator to the left by two places and simultaneously moving the decimal point in the denominator to the left by two places. \[\frac{292}{147.5} = 1.98\] Therefore, the answer is 1.639 x 10\(^1\) in standard form.
Question 50 Report
From the top of a vehicle cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
Answer Details
The situation can be represented by the following diagram: ``` A /| / | 20m / | B---C 75m ``` Where A is the top of the cliff, B is the boat, and C is the point on the cliff directly above the boat. We want to find the angle of depression, which is the angle ACB. We can use trigonometry to find this angle. First, we need to find the length of AC. This is simply the height of the cliff, which is given as 20m. Next, we need to find the length of BC. This is the horizontal distance from the base of the cliff to the boat, which is given as 75m. Now we can use the tangent function to find the angle of depression: tan(ACB) = opposite / adjacent = 20 / 75 Taking the inverse tangent (or arctan) of both sides gives: ACB = arctan(20 / 75) = 15.02 degrees (to two decimal places) Therefore, the angle of depression of the boat from the top of the cliff is approximately 15 degrees (to the nearest degree). So the answer is option D: 15\(^o\).
Question 51 Report
The ages of a group of athletes are as follows: 18, 16. 18,20, 17, 16, 19, 17, 18, 17 and 13. (a) Find the range of the distribution.
(b) Draw a frequency distribution table for the data.
(c) What is the median age?
(d) Calculate, correct to two decimal places, the;
(i) mean age:
(ii) standard deviation.
Answer Details
None
Question 52 Report
The force of attraction F, between two bodies, varies directly as the product of their masses, \(m_1\) and m\(_2\) and inversely as the square of the distance, d, between them. Given that F = 20N, when m\(_1\) = 25kg, m\(_2\) = 10kg and d = 5m, find:
(I) an expression for F in terms of m\(_1\), m\(_2\) and d;
(ii) the distance, d for F = 30N, m\(_1\) = 7.5kg and m\(_2\) = 4kg
(b) Find the value of x in the diagram
Answer Details
None
Question 53 Report
(a) The curved surface areas of two cones are equal. The base radius of one is 5 cm and its slant height is 12cm. calculate the height of the second cone if its base radius is 6 cm.
(b) Given the matrices A = \(\begin{pmatrix} 2 & 5 \\ -1 & -3 \end{pmatrix}\) and B = \(\begin{pmatrix} 3 & -2 \\ 4 & 1 \end{pmatrix}\), find:
(i) BA;
(ii) the determinant of BA.
Answer Details
None
Question 54 Report
(a) Fred bought a car for $5,600.00 and later sold it at 90% of the cost price. He spent $1,310.00 out of the amount received and invested the rest at 6% per annum simple interest. Calculate the interest earned in 3 years.
(b) Solve the equations 2\(^x\)(4\(^{-7}\)) = 2 and 3\(^{-x}\)(9\(^{2y}\)) = 3 simultaneously.
Answer Details
None
Question 55 Report
(a) Given that 110\(_x\) - 40\(_{five}\). find the value of x
(b) Simplify \(\frac{15}{\sqrt{75}} + \(\sqrt{108}\) + \(\sqrt{432}\), leaving the answer in the form a\(\sqrt{b}\), where a and b are positive integers.
Answer Details
None
Question 56 Report
The data shows the marks obtained by students in a biology test
52 | 56 | 25 | 56 | 68 | 73 | 66 | 64 | 56 | 48 |
20 | 39 | 9 | 50 | 46 | 54 | 54 | 40 | 50 | 96 |
36 | 44 | 18 | 97 | 65 | 21 | 60 | 44 | 54 | 32 |
92 | 49 | 37 | 94 | 72 | 88 | 89 | 35 | 59 | 34 |
15 | 88 | 53 | 16 | 84 | 52 | 72 | 46 | 60 | 42 |
(a) Construct a frequency distribution table using the class interval 0 - 9, 10 - 19, 19, 20, 29...
(b) Draw a cumulative frequency curve for the distribution
(c) Use the graph to estimate the;
(i) median
(ii) Percentage of students who scored at least 66 marks, correct to the nearest whole number.
Answer Details
None
Question 57 Report
(a) Given that sin y = \(\frac{8}{17}\) find the value of \(\frac{tan y}{1 + 2 tan y}\)
(b) An amount of N300,000.00 was shared among Otobo, Ada and Adeola. Otobo received N60,000.00, Ada received \(\frac{5}{10}\) of the remainder, while the rest went to Adeola. In what ratio was the money shared?
Answer Details
None
Question 58 Report
(a) Without using mathematical tables or calculator, simplify: \(\frac{log_28 + \log_216 - 4 \log_22}{\log_416}\)
(b) If 1342\(_{five}\) - 241\(_{five}\) = x\(_{ten}\), find the value of x.
Answer Details
None
Question 59 Report
In the diagram, \(\overline{RT}\) and \(\overline{RT}\) are tangent to the circle with centre O. < TUS = 68 °, < SRT = x, and < UTO = y. Find the value of x.
(b) Two tanks A and B am filled to capacity with diesel. Tank A holds 600 litres of diesel more than tank B. If 100 litres of diesel was pumped out of each tank, tank A would then contain 3 times as much diesel as tank B. Find the capacity of each tank.
Answer Details
None
Question 60 Report
A ladder 11m long leans against a vertical wall at an angle of 75\(^o\) to the ground. The ladder is the pushed 0.2 m up the wall.
(a) Illustrate the information in a diagram.
(b) Find correct to the nearest whole number, the:
(i) new angle which the ladder makes with the ground:
(ii) distance the foot of the ladder has moved from its original position.
Answer Details
None
Question 61 Report
(a) The third and sixth terms of a Geometric Progression (G.P) are and \(\frac{1}{4}\) and \(\frac{1}{32}\) respectively.
Find:
(i) the first term and the common ratio;
(ii) the seventh term.
(b) Given that 2 and -3 are the roots of the equation ax\(^2\) ± bx + c = 0, find the values of a, b and c.
Answer Details
None
Question 62 Report
In the diagram, PQRS is a quadrilateral, < PQR = < PRS = 90\(^o\), |PQ| =3cm, |QR| = 4cm and |PS| = 13 cm. Find the area of the quadrilateral.
Answer Details
None
Question 63 Report
(a) If logo a = 1.3010 and log\(_{10}\)b - 1.4771. find the value of ab
(b)
In the diagram. O is the centre of the circle,< ACB = 39\(^o\) and < CBE = 62\(^o\). Find: (i) the interior angle AOC;
(ii) angle BAC.
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Question 64 Report
(a) Ali and Yusif shared N420.000.00 in the ratio 3.,; 5 : 8 respectively. Find the sum of Ali and Yusuf's shares
(b) Solve: 2(\(\frac{1}{8}\))\(^x\) = 32\(^{x - 1}\).
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Question 65 Report
NOT DRAWN TO SCALE
In the diagram, is a chord of a circle with centre 0. 22.42 cm and the perimeter of triangle MON is 55.6 cm. Calculate, correct to the nearest degree. < MON.
(b) T is equidistant from P and Q. The bearing of P from T is 60\(^o\) and the bearing of Q from T is 130\(^o\).
(i) Illustrate the information on a diagram.
(ii) Find the bearing of Q from P.
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Question 66 Report
(a) Find the equation of the line which passes through the points A(-2, 7) and B(2, -3)
(b) Given that \(\frac{5b - a}{8b + 3a} = \frac{1}{5}\) = find, correct to two decimal places, the value \(\frac{a}{b}\)
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Question 67 Report
A survey of 40 students showed that 23 students study Mathematics, 5 study Mathematics and Physics, 8 study Chemistry and Mathematics, 5 study Physics and Chemistry and 3 study all the three subjects. The number of students who study Physics only is twice the number who study Chemistry only.
(a) Find the number of students who study:
(i) only Physics.
(ii) only one subject
b) What is the probability that a student selected at random studies exactly 2 subjects?
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Question 68 Report
The cost of dinner for a group of tourist is partly constant and partly varies as the number of tourists present. It costs $740.00 when 20 tourists were present and $960.00 when the number of tourists increased by 10. Find the cost of the dinner when only 15 tourists were present.
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Question 69 Report
(a) Solve the inequality: \(\frac{1 + 4x}{2}\) -\(\frac{5 + 2x}{7}\) < x -2
(b) If x: y = 3: 5, find the value of \(\frac{2x^2 - y^2}{y^2 - x^2}\)
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Question 70 Report
a) A twenty - kilogram bag of rice is consumed by m number of boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. If the rate of consumption is the same, find the value of m.
(b) If \(\frac{5}{6}\) of a number is 10 greater than \(\frac{1}{3}\) of it. find the number
(c) Find the equation of the line which passes through the points (2, \(\frac{1}{2}\)) and (-1, -\(\frac{1}{2}\)
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Question 71 Report
Three red balls, five green balls, and a number of blue balls are put together in a sack. One ball is picked at random from the sack. If the probability of picking a red ball is \(\frac{1}{6}\) find;
(a) The number of blue balls in the sack
(b) the probability of picking a green ball
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Question 72 Report
(a)
In the diagram. \(\over{Rs}\) and \(\over{RT}\) are tangent to the circle with centre O, < TUS = 68\(^o\), < SRT = x and < UTO = y. Find the value of x.
(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.
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Question 73 Report
(a) Copy and complete the table of values for the relation y = 4x\(^2\) - 8x - 21, for -2.0 \(\leq\) x \(\leq\) 4.0
x | -2.0 | -1.5 | -1.0 | 0.5 | 0.0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 | 3.5 | 4.0 |
y | 11 | -9 | -21 | -24 | -21 | -9 | 0 |
(b) Using a scale of 2cm to 1 unit on the x-axis and 2cm to 5 units on the y-axis, draw the graph for the relation y = 4x\(^2\) - 8x - 21
(ii) Use the graph to find the solution set of
(\(\alpha\)) 4x\(^2\) - 8x = 3;
(\(\beta\)) 4x\(^2\) - 7x - 21 = 0
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Question 74 Report
A woman bought 130 kg of tomatoes for 4452,000.00. She sold half of the tomatoes at a profit of 30%. The rest of the tomatoes began to go bad, she then reduced the selling price per kg by 12%. Calculate:
(a) the new selling price per kg;
(ii) the percentage profit on the entire sales if she threw away 5 kg of bad tomatoes.
Answer Details
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Question 75 Report
(a) Copy and complete the table of values for y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) x \(\geq\) 360\(^o\)
x | 0\(^o\) | 60\(^0\) | 120\(^o\) | 180\(^o\) | 240\(^o\) | 300\(^o\) | 360\(^o\) |
y | 2.0 | - 3.6 |
(b) Using a scale of 2cm to 60\(^o\) on the x-axis and 2cm to 1 unit in the y-axis, draw the graph of y = 2 cos x + 3 sin x for 0\(^o\) \(\geq\) 360\(^o\)
(c) Using the graph,
(i) Solve 2 cos x + 3 sin x = -1
(ii) Find, correct to one decimal place, the value of y when x = 342\(^o\)
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Question 76 Report
(a) Solve the inequality 13x−14(x+2)≥3x−113
(b)
In the diagram, ABC is right-angled triangle on a horizontal ground. |AD| is a vertical tower. < BAC = 90o , < ACB = 35o , < ABD = 52o and |BC| = 66cm.
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Question 77 Report
The second, fourth and sixth terms of an Arithmetic Progression (AP.) are x - 1, x + 1 and 7 respectively. Find the:
(a) common difference;
(b) first term;
(c) value of x.
Answer Details
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