Find the gradients and the intercepts on the y- axis for 5x = 6y

A bearing of 310°, expressed as a compass bearing is

Solve for q:

5 [2^{(q - 3)}]  =  160

Which of the following specified sets of data is not necessarily sufficient for the construction of a triangle?

ABC is a right triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB.

A bucket in the form of a truncated cone of end radii 14cm and 21cm, and height of 30cm.
What is the capacity of the bucket?

Sean opened a savings account with £1,000.00. One year later he deposited £500.00 in the account and deposited a further £500.00 two years after opening the account.

If the interest rate is 8% p.a computed annually, calculate the total amount, to the nearest pounds, in his account three years after opening the account.

A bowl contains two white, one blue and two red balls. A ball is drawn randomly from the bowl, replaced and another ball is drawn.

What is the probability that exactly one of the balls is white?

Which of the following angles cannot be constructed with a ruler and a pair of compasses only?

Find the equations of the straight lines joining (0, 3), (2, 0)

A girl walks 30 m from a point P on a bearing of 040º to a point Q.
She then walks 30 m on a bearing of 140º to a point R.
How far is R from P

If z ∝ 1/y² and z = 4 when y = 3,
find the value of z when y = 2

Factorise 2d³+ d² (3d – 1)

If m and n are the lengths of the diagonals of a rhombus of side x, and
m² + n² = kx², the value of k is

Find the area of the shaded region.

Points X and Y are respectively 48m North and 20m East of point Z, The bearing of X and Y is approximately

Which of the following statements about a cylinder is false?

The area of the trapezium PQRS in the figure is

Find the area of the quadrilateral shown in the figure.

If 2x - y = 6 and
2x + 4y = 1,
the value of 4x + 3y is

In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96⁰ , how much is the value of ∠DBC?

Two years ago, a woman was six times as old as  her son. Four years from now, she will be three times as old as the son. Find their present ages

If cos θ = 4/5,
then for 0° < θ < 90°,
tanθ is equal to

If 4x - 2 = 3x -5,
the value of 7x is

The difference between 0.003286 correct to three significant figures and 0.003286 correct to four decimal places is

If the lengths of the sides of a right-angled triangle are given as (x-1), x and (x+1), then the hypotenuse is

A sum of £50,000 was invested by two partners in a project which yielded £90,000. If the profit was shared in the ratio 3 : 5, the difference between the amounts received by the partners is

The marks scored by students in a test are recorded in the table below

Calculate the mean

The two perpendicular sides of a right-angled triangle are 9 cm and 12 cm in length.

The smallest angle of the triangle is

Find the lower and upper quartiles for the set of numbers

4, 7, 8, 10, 12, 15, 17, 20, 26, 32, 40

Factorise a²c – 2ac²

Four of five interior angles of a pentagon are equal.
If the size of the fifth angle is 80°,
then the size of each of the four equal angles is

The greatest value of an integer x which satisfies the inequality 

2 - 4x > 15 is

In the figure, the point on segment JK that is four times as far from K as it is from J is:

When the price of eggs was raised by £2 an egg, the number of eggs which can be bought by Tara for £120 is reduced by 5.
What is the present price that Tara would buy an egg?

Simplify

Find the equations of the straight lines passing through the point (2, -1) and the gradient 2

Find the gradients and the intercepts on the y- axis for 3y-2x+5 = 0

Given that a+b = 3/2
and a-b = 5/2,
the value of 2b + a is

Factorise 16b²– 1

Factorise 27 – 3p² completely

Four books whose authors' surnames start with the letters A, J, P, and W are placed randomly on a shelf.

The probability that the books will be arranged in the alphabetical order of the authors' last names is

A sector of a circle is bounded by two radii each of length 14cm and an arc of length  12 cm.
The area of the sector is

In the diagram below , WXYZ is a cyclic quadrilateral in which WZ = 6cm, ZY = 8.5cm and the diagonal WY = 10 cm. If XW = XY, calculate <XYW

Which of the following fractions is less than one quarter?

If xy + 1 = y² and
z= (1/x) - (1/xy),
express z in terms of y

If tanx = 12/5,

find the value of sinx, 0° ≤ x ≤ 90°

A sum of $50,000 was invested by two partners in a project which yielded $90,000. If the profit was shared in the 3 : 5, what is the difference between the amounts received by the partners?

The angle of a sector of a circle of radius 4.2 cm is 150°.
If π = 22/7,
the perimeter of the sector is

P is directly proportional to M and inversely proportional to N.
If P = 9 when M = 24 and N = 8,
find the value of P when M = 5 and N = 6