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**Question 1**
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In the diagram above PS||RQ, |RQ| = 6.4cm and perpendicular PH = 3.2cm. Find the area of SQR

**Question 2**
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In a class of 80 students, every students had to study economics or geography, or both economics and geography, if 65 students studied economics and 50 studied geography, how many studied both subjects?

**Answer Details**

To find out how many students studied both economics and geography, we need to use the principle of inclusion-exclusion. First, we add the number of students who studied economics and geography, as some students could have studied both subjects. Let's call this number "x." Then, we subtract x from the total number of students (80), which gives us the number of students who studied only economics or only geography. We know that 65 students studied economics, so the number of students who studied only economics is 65 - x. Similarly, the number of students who studied only geography is 50 - x. Since every student had to study at least one subject, the total number of students who studied only economics or only geography is equal to the sum of the students who studied only economics and the students who studied only geography: (65 - x) + (50 - x) Simplifying this expression, we get: 115 - 2x But we know that this number is equal to the total number of students who studied only economics or only geography, which is 80 minus the number of students who studied both subjects: 80 - x Therefore, we can set up an equation: 115 - 2x = 80 - x Solving for x, we get: x = 35 So 35 students studied both economics and geography.

**Question 3**
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An arc of length 22cm subtends an angle of θ at the center of the circle. What is the value of θ if the radius of the circle is 15cm?[Take π = 22/7]

**Answer Details**

To find the value of θ, we can use the formula: θ = (arc length / radius) In this case, the arc length is given as 22cm, and the radius is given as 15cm. So we have: θ = (22 / 15) θ = 1.47 (approx) However, the answer options are in degrees, so we need to convert radians to degrees. We can use the formula: degrees = (radians × 180) / π Substituting θ = 1.47 and π = 22/7, we get: degrees = (1.47 × 180) / (22/7) degrees = 89.14 (approx) Therefore, the answer is closest to option (B) 84^{o}.

**Question 4**
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In the diagram above, O is the center of the circle with radius 10cm, and ?ABC = 30°. Calculate, correct to 1 decimal place, the length of arc AC [Take ? = 22/7]

**Question 5**
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If the radius of the parallel of latitude 30°N is equal to the radius of the parallel of latitude θ°S, what is the value of θ?

**Question 6**
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From the top of a building 10m high, the angle of depression of a stone lying on the horizontal ground is 69^{o}. Calculate ,correct to one decimal place, the distance of the stone from the foot of the building

**Question 7**
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The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school. What is the mode?

**Question 8**
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Solve the equation 2a\(^2\) - 3a - 27 = 0

**Answer Details**

To solve the equation 2a\(^2\) - 3a - 27 = 0, we can use the quadratic formula which is: a = (-b ± sqrt(b\(^2\) - 4ac)) / 2a In this case, we have a = 2, b = -3, and c = -27. Substituting these values into the formula, we get: a = (-(-3) ± sqrt((-3)\(^2\) - 4(2)(-27))) / 2(2) Simplifying the expression under the square root, we get: a = (-(-3) ± sqrt(225)) / 4 which gives us: a = (3 ± 15) / 4 Therefore, we have two solutions: a = 3 and a = -6/2 = -3/2 Hence, the correct option is -3, 9/2.

**Question 9**
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In the diagram below, O is the center of the circle if ?QOR = 290^{o}, find the size ?QPR

**Question 10**
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Simplify 125\(^{\frac{-1}{3}}\) x 49\(^{\frac{-1}{2}}\) x 10\(^0\)

**Question 11**
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Two groups of male students cast their votes on a particular proposal. The result are as follows:

In favor | Against | |

Group A | 128 | 32 |

Group B | 96 | 48 |

If a student in favor of the proposal is selected for a post, what is the probability that he is from group A?

**Question 12**
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In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ?BTO. Find x.

**Question 13**
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Find the 4th term of an A.P, whose first term is 2 and the common difference is 0.5

**Answer Details**

In an arithmetic progression (A.P.), the terms increase or decrease by a constant difference called the common difference. In this problem, the first term is 2, and the common difference is 0.5. Therefore, the second term would be 2 + 0.5 = 2.5, the third term would be 2.5 + 0.5 = 3, and the fourth term would be 3 + 0.5 = 3.5. Therefore, the answer is option (C) 3.5.

**Question 14**
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The table shows that the amount of money (in naira)collected through voluntary donations in a secondary school.

What is the median of distribution**Answer Details**

To find the median of a distribution, we first need to arrange the values in order from smallest to largest. In this case, the data is already presented in order, so we can simply identify the middle value of the data set. Since there are 5 values, the middle value will be the 3rd value. So, the median of the distribution is N12.00, which is the value in the middle of the data set. Therefore, the answer is (c) N12.00.

**Question 15**
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If log x = \(\bar{2}.3675\) and log y = 0.9750, what is the value of x + y? Correct to three significant figures

**Question 16**
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Factorize 2e\(^2\) - 3e + 1

**Answer Details**

To factorize 2e\(^2\) - 3e + 1, we can use the quadratic formula: e = (-b ± √(b² - 4ac)) / 2a where a = 2, b = -3, and c = 1. Plugging in the values, we get: e = (3 ± √(9 - 8)) / 4 e = (3 ± 1) / 4 So the roots are e = 1 and e = 1/2. Therefore, we can factorize 2e\(^2\) - 3e + 1 as: 2e\(^2\) - 3e + 1 = 2(e - 1)(e - 1/2) Simplifying this expression, we get: 2(e - 1)(2e - 1) Therefore, the factorization of 2e\(^2\) - 3e + 1 is (2e-1) (e-1), which corresponds to option (A).

**Question 17**
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If 3\(^{2x}\) = 27, what is x?

**Answer Details**

We can solve for x by using the laws of exponents and taking the logarithm of both sides. First, we can rewrite 3²x as (3²)ⁿ, where n = 2x. So, we have: (3²)ⁿ = 27 3ⁿ² = 27 Now, we can take the logarithm of both sides of the equation. Let's use the natural logarithm, denoted as ln, which is the logarithm to the base e: ln(3ⁿ²) = ln(27) Using the power rule of logarithms, we can simplify the left-hand side: n² ln(3) = ln(27) Now, we can solve for n: n² = ln(27) / ln(3) n² = 3 Taking the square root of both sides, we get: n = ± √3 But we know that n = 2x, so we can substitute back: 2x = ± √3 Solving for x, we get: x = ± (1/2) √3 Since the question is asking for a real value of x, we can take the positive square root: x = (1/2) √3 ≈ 0.866 Therefore, x is approximately 0.866, which is option (B) 1.5 rounded to one decimal place.

**Question 18**
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Use mathematical table to evaluate (cos40° - sin30°)

**Answer Details**

To evaluate (cos40° - sin30°), we first need to find the values of cos40° and sin30°. Using a mathematical table (such as a trigonometric table), we can look up the values of cos40° and sin30°: - cos40° = 0.7660 - sin30° = 0.5000 Now we can substitute these values into the expression: (cos40° - sin30°) = (0.7660 - 0.5000) = 0.2660 Therefore, the answer is option (D) 0.2660.

**Question 19**
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Solve the equation 7y\(^2\) = 3y

**Answer Details**

To solve the equation 7y\(^2\) = 3y, we can start by rearranging it to get 7y\(^2\) - 3y = 0. We can then factor out y to get y(7y - 3) = 0. From here, we have two solutions: y = 0 or 7y - 3 = 0, which gives us y = 3/7. Therefore, the solutions to the equation 7y\(^2\) = 3y are y = 0 or y = 3/7. Therefore, the answer is: y = 0 or 3/7.

**Question 20**
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Simplify \(\frac{\log \sqrt{8}}{\log 8}\)

**Answer Details**

We can simplify the expression using the laws of logarithms. First, we can simplify the numerator by using the fact that the square root of 8 is equal to 8 raised to the power of 1/2: log√8 = log(8^{1/2}) = 1/2 log 8 Now, we can substitute this into the original expression: \(\frac{\log \sqrt{8}}{\log 8} = \frac{1/2 \log 8}{\log 8}\) We can simplify this by canceling out the factor of log 8 in the numerator and denominator: \(\frac{1/2 \log 8}{\log 8} = \frac{1}{2}\) Therefore, the simplified expression is 1/2, which corresponds to option (B).

**Question 21**
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In the diagram above, PQRS s a cyclic quadrilateral, ?PSR = 86^{o} and ?QPR = 38^{o}. Calculate PRQ

**Answer Details**

In a cyclic quadrilateral, the opposite angles add up to 180 degrees. Therefore, we can find the value of angle PQR as follows: angle PSR + angle PQR = 180 (since PQRS is a cyclic quadrilateral) 86 + angle PQR = 180 angle PQR = 180 - 86 = 94 degrees We are given angle QPR as 38 degrees, and since angles in a triangle add up to 180 degrees, we can find angle PRQ as: angle PRQ = 180 - angle PQR - angle QPR angle PRQ = 180 - 94 - 38 angle PRQ = 48 degrees Therefore, the answer is option (C) 48^{o}.

**Question 22**
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Which triangle is equal in area to ?VWZ

**Question 23**
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Find the value of m which makes x\(^2\) + 8 + m a perfect square

**Question 24**
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The annual salary of Mr. Johnson Mohammed for 1989 was N12,000.00. He spent this on agriculture projects, education of his children, food items, saving , maintenance and miscellaneous items as shown in the pie chart

How much did he spend on food items?