The points of intersection of the graphs of y = x² + 2 and y = 2x + 5 when drawn on the same set of axes are

The gradient of a curve which passes through the point (1, 2) is 3+2x.
Find its equation.

Find
∫ (2+x)/x dx,   x > 0.

For what value of x the matrix 
is a skew symmetric matrix

Evaluate the integrals:

The distance s metres after time t second covered by a particle moving along a straight line is given by

s = t³ - t² - t - 2

Find the average acceleration between t = 2 and t = 4

Evaluate the definite integral:

A force of 10N, drags a mass of 10kg on a horizontal table with an acceleration of 0.2m/s². If the acceleration due to gravity is 10m/s²,  the co-efficient of friction between the moving mass and the table is

Which of the following have the same value as sin 15°?
I. sin 165°
II. sin 285°
III. sin (-15°)
IV. sin (-195°)

In the diagram below, the hanging mass M₂ is adjusted until M₁ is on the verge of sliding. The co-efficient of static friction between the mass M₁ and the table is

The gradient of a curve is given by
x² - 4x + 3
If the curve passes through the point (3, 1).
Find the area of the finite region enclosed by the curve,
the lines x = 1, x = 3 and y = 0

The prices of computers in a catalogue are: N125,000,  N99,000,  N125,000,  N120,000,   N110,000,  N115,000,   N130,000,  N120,000,   N100,000.
Calculate the mean deviation

Find the angles between 0° and 360° whose sine is -0.9781

Find the derivative of y = sin(2x³ + 3x - 4) wrt x

Find the value of

cos 200° sin 160° + sin (- 340°) cos (- 380°)

One of the roots of the equation:
6y² = 5 - 7y is

Evaluate:

  (3⁰ - 9^-1/2)^-3

Differentiate w.r.t x 

sin³x

An object of mass 80kg is pulled on a horizontal rough ground by a force of 500N. Find the coefficient of static friction. (g = 10m/s²)

Differentiate wrt x

Solve for x the equation ln (x - 1) + ln (2x - 1) = 2 ln (x + 1)

A bag containing 5 red balls and 3 green balls.
Two balls are picked, one after the other, with replacement.
The probability that both are the same colour is

A letter is chosen at random from the alphabet.
Find the probability that it is not one of the letters of the word DIAMOND

In a game involving two dice, Kamsi will win if she throws at least one six, or the sum of the numbers is 10.

The probability of Kamsi winning at the next throw is

Write the value of the angle in surd form sin 300°

Use the binomial theorem to expand (1 + 4x)⁴.
Hence, find the value of (1.04)⁴ correct to 4 decimal places

Find the remainder when
x³- 2x²-5x+6 is divided by x-1

The roots of the equation
ay² + by + c = 0 are 1/2 and -3.
The values of a, b and c are, respectively

If x= 2 is a root of the equation 2x³-2x²-5x+2 find the other roots

A binary operation * is defined over the set of real numbers such that

a * b = a (b + 2). Find 3 * (4 * 2).

Simplify

Simplify:

log₅25^x - log₅(0.04)

Subtract the polynomials: (xy + 3x + 2) - (3x² + y)

Calculate the area under the line
y = x + 2 between the limits x = 0 and x = 10

Divide
(2x³  -  xy²  +  y³)      by      (x + y)

Find the mean and  mean deviation, respectively of the following 
16, 18, 12, 14, 20, 25, 13, 15, 11

Find the value of tan (-84)°

If 
(2/3)^{x - 1}  =  27/8,
determine the value of 'x'

If 
(3/4)^x(2/3)^y = 32/27,
the values of x and y respectively are

Evaluate:

Given that

sin(θ+α) = sinθcosα + cosθsinα,
find the value of sin 75°

Simplify:

(3^{2y + 1} × 9^y × 4^2y) ÷ (18^y × 2^y × 6^2y)

Without using trigonometric tables, evaluate sin 35° sin 55° - cos 35° cos 55°

Solve the following equations:
                3x   +  4y  +  2z     =    4
                  x   -   5y   +  3z     =   -1
                 2x   + 3y   +   z      =    3

The integral values of z which satisfy the inequalitiy
-1 < 2z - 5 ≤ 5 are

Use binomial theorem to expand (1 - 4x)³ in ascending powers of x

The gradient of a curve is given by dy/dx = 10x - 3x². If the curve passes through the point (-1, 10), find the equation of the curve

The integral values of y which satisfy the inequality
-1 < 5 - 2y ≤ 7 are

A curve has equation y = x³ -4x² - 3x + 18, the point P(-2, 0) lies on the curve. Find the gradient of the tangent to the curve at P.

Divide 6x² - 13x + 5 by 2x -1

Tireni throws a coin twice.
The coin is biased so the probability of landing a head is 2/5.
Find the probability that she throws two tails

Find the value of sin 405°

Three balls are drawn one after the other, without replacement from a bag containing 4 blue, 6 white and 5 red identical balls.
The probability that all three balls are the same colour is

A bag contains only gala and royal apples.
The probability of picking a gala at random is 0.3.
Find the probability of picking a royal apple

Differentiate the function wrt x:
y = √x

If
(2/3)^a-1 = 27/8,

what is a?

Solve the equation
4 cosx - 3 = 0 
for 0° ≤x≤ 360°

 Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. 

Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?

Given that cos θ = -0.3420,
where 180° ≤θ≤ 360° , find θ

Solve the equation
4sinθ - 1 = -3
for 0° < θ < 2π