Further Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

Given that \(sin x = \frac{4}{5}\) and \(cos y = \frac{12}{13}\), where x is an obtuse angle and y is an acute angle, find the value of sin (x – y).

Evaluate \(\int^1_0 x(x^2-2)^2 dx\)

The distance S metres moved by a body in t seconds is given by \(S = 5t^3 – \frac{19}{2} t^2 + 6t – 4\). Calculate the acceleration of the body after 2 seconds

Find the equation of the normal to the curve y = \(3x^2 + 2\) at point (1, 5).

Calculate, correct to one decimal place, the angle between 5 i + 12 j and -2 i + 3 j

The vectors 6i + 8j and 8i – 6j are parallel to →OP and →OQ respectively. If the magnitude of →OP and →OQ are 80 units and 120 units respectively, express: →OP and →OQ in terms of i and j;

ii. |→PQ|, in the form c√k, where c and k are constants.

A particle initially at rest moves in a straight line with an acceleration of (10t – 4t\(^2\))m/s\(^2\)
Find the:
a. velocity of the particle after t seconds;

ii. average acceleration of the particle during the 4th second.

b. A load of mass 120kg is placed on a lift. Calculate the reaction between the floor of the lift and the load when the lift moves upwards at a constant velocity. [Take g = 10m/s\(^2\)]

ii. with an acceleration of 3m/s\(^2\). [Take g = 10m/s\(^2\)]

The table shows the corresponding values of two variables X and Y.

a. plot a scatter diagram to represent the data

b i. Calculate:x̄, the mean of X and ȳ, the mean of Y;

ii. Caculate:
x̄1, the mean of X values below x̄ and ȳ1, the mean of the corresponding Y values below x̄

c.  Draw the line of best fit through (x̄,ȳ) and (x̄1,ȳ1).

d. From the graph, determine the relationship between X and Y;

ii. From the graph, determine the value of Y when X is 20.

A basket contains 12 fruits: orange, apple and avocado pear, all of the same size. The number of oranges, apples and avocado pear forms three consecutive integers.

Two fruits are drawn one after the other without replacement. Calculate the probability that:

i. the first is an orange and the second is an avocado pear.

ii.both are of same fruit;

iii. at least one is an apple

A solid rectangular block has a base that measures 3x cm by 2x cm. The height of the block is ycm and its volume is 72cm\(^3\).

i. Express y in terms of x.

ii. An expression for the total surface area of the block in terms of x only;

iii. the value of x for which the total surface area has a stationary value.

Given that nC\(_4\), nC\(_5\) and nC\(_6\) are the terms of a linear sequence (A.P), find the :

i. value of n

ii. common differences of the sequence.

Given that p = (8N,030º) and q = (9N, 150º), find, in component from, the unit vector along(p – q).

A body of mass of 18kg is suspended by an inextensible string from a rigid support and is pulled by a horizontal force F until the angle of inclination of the string to the vertical is 35º. If the system is in equilibrium, calculate the:

i. value of F

ii. tension in the string

The table shows the scores obtained by a group of artistes in Vocal (X) and the instrument (Y) musical competition.

Calculate the spearman’s rank correlation coefficient between the scores.

The probability that  Abiola will be late to the office on a given day is 2/5. In a given working week of six days, find, correct to four significant figures, the probability that he will:

(a) only be late for 3 days.

(b) not be late in the week:

(c) be late throughout the six days.

Solve 3cos2x – sinx = 0 for 0º≤x≤360º

Two functions f and g are defined on the set of real numbers, R, by

f:x → x\(^2\) + 2 and g:x → \(\frac{1}{x+2}\).Find the domain of (g∘f)\(^{-1}\)

Solve \(2^{(2y+1)} – 5(2^y) + 2\) = 0
 

A binary operation * is defined on the set T = {-2,-1,1,2} by p*q = p\(^2\) + 2pq – q\(^2\), where p,q ∊ T.
Copy and complete the table.

The length of the line joining points (x,4) and (-x,3) is 7 units. Find the value of x.

If f(x-1) = x\(^3\) + 3x\(^2\) + 4x – 5, find f(2)