NECO SSCE - General Mathematics - 2005

Calculate without using tables Tan 45° + Cos 60°

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

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?

Simplify (6 - x - x2) ÷ (x2 - 4)

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

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

Simplify P^-6 × P³ × P² ÷ P⁴ × P⁰

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?

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.

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?

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

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.

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

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

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?

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

Evaluate 0.0025 × 2.5 × 102 to 2 significant figures.

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.

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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)

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

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.

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