NECO SSCE - General Mathematics - 2005

Calculate without using tables Tan 45° + Cos 60°

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For what value(s) of x is the expression (x² + 15x + 50) ÷ (x - 5) not defined

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If x + \(\frac{1}{x}\) = 8, find x² + \(\frac{1}{x^2}\)

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The parallel sides of a trapezium are 13cm and 7cm. If the area of the trapezium is 50cm2, find the perpendicular distance between the parallel sides.

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A bag contains 4 blue and 8 red identical balls. If two balls are picked at random with replacement, what is the probability of picking two balls of different colours?

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Two fair dice are tossed together once. What is the probability of getting a total of at least 9 from the outcome?

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Find the Iength of a diagonal of a square whose area is 288cm².

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What is the Value of 11101\(_{two}\)+ 10011\(_{two}\) - 10001\(_{two}\)?

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Find the value of 2a - b if a + b = 8 and 4a - b = 22

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Mohammed is 8 years older than Joy now. In five years’ time he will be twice as old as Joy. How old is Joy now?

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3 - 7, 8 - 12, 13 - 17, 18 - 22. Which of the following is/are true?
I. The class Interval is 4
II. The class boundaries are 2.5, 7.5, 12.5, 18.5, 22.5
III. The mid-marks are 5, 10, 15, and 20

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A flagpole is placed at the top of a tower. The angles of elevation of the bottom and top of the flagpole from a point on the ground 10m away are 40° and 50° respectively. Find the length of the flagpole.

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Evaluate log 18 + log⁶ - log16\(^{\frac{1}{2}}\)

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Evaluate 0.0025 × 2.5 × 102 to 2 significant figures.

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Simplify (6 - x - x2) ÷ (x2 - 4)

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A is at 50°N and B is at 10°N, If A and B are on the same longitude, find the distance AS. Correct your answer to Four significant figures. (Earth radius = 6400km)

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If 2x : ( x + 1) = 3 : 2, what is the value of x?

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Find the absolute mean deviation of the sample 10, 12, 14, 11, 13.

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If y²+ 14y + k is a perfect square, then k =

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Solve for x in the quadratic equation. 2x² + 12x + 10 = 0

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If 25a² = 5^-1 × 125. Find the value of a?

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Simplify P^-6 × P³ × P² ÷ P⁴ × P⁰

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If a = {x : 1 < x < 9} ; b = {x : 0 < x < 9} ; C = {x : 2 x < 9} and a, b, c U, what are the elements in U?

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A chord 20cm long subtends an angle of 60° at the circumference of a circle, what is the diameter of the circle the nearest cm?

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Find the standard deviation of the numbers 6, 9, 10, 8 and 7

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If 7 is subtracted from twice a certain number x, the result is at most 5. What is the range of the number?

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What is the positive difference between the squares of 2.5 and 2.1 to 1 significant figures?

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A car dealer sells a car and makes a profit of 15%. If the car costs N320,000.00, how much did he sell the car?

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If (x - a) is a factor of bx - ax + x² - ab, what is the other factor?

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T varies directly as D and inversely as A. Given that T = 6, D = 3, and A = 2, find A when T = 3 and D = 6.

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If log 3 = 0.4771 and log 2 = 0.3010, what is the value of log 12?

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A surveyor measured the length of a obtained 42.55 metres. If his measurement was more than the actual length and the percentage error of his measurement was 8%, calculate the actual length of the land

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In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.

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A ship sails 6km from a port on a bearing 070° and then 8km on a bearing of 040°. Find the distance from the port.

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The diagonals of a rhombus are 6cm and 8cm. Find the area of the rhombus.

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If A(I,2,3,...,10) ; B = (-5,-4,.....,-1) ; C = (-1, 0, 1, 2,....5) List all the elements in (B ∪ C) ∩ A

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