Core Mathematics — 1999

The side of a rhombus is 10cm long, correct to the nearest whole number. Between what limits should the perimeter P lie?

Simplify log\(_7\) 8 - log\(_7\) 2 + log\(_7\) 4.

If \(K\sqrt{28}+\sqrt{63}-\sqrt{7}=0\), find K.

From a set \(A = [3, \sqrt{2}, 2\sqrt{3}, \sqrt{9}, \sqrt{7}]\), a number is selected at random. Find the probability that is a rational number

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below Find the value of K

The pie chart illustrate the amount of private time a student spends in a week studying various subjects. use it to answer the question below If he sends \(2\frac{1}{2}\) hours week on science, find the total number of hours he studies in a week

A group of 11 people can speak either English or French or Both. Seven can speak English and six can speak French. What is the probability that a person chosen at random can speak both English and French?

The interior angle of a regular polygon is twice the exterior angle. How many sides has the polygon?

Which of the following figures have one line of symmetry only? I. Isosceles triangle II. Rhombus III. Kite

In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

Calculate the value of Y in the diagram

In the diagram, POR is a circle with center O. ∠QPR = 50°, ∠PQO = 30° and ∠ORP = m. Find m.

Given that m = -3 and n = 2 find the value of \(\frac{3n^2 - 2m^3}{m}\)

Simplify \(\frac{2-18m^2}{1+3m}\)

If \(y = \sqrt{ax-b}\) express x in terms of y, a and b

Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)

Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)

If y varies inversely as x\(^2\), how does x vary with y?

If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)

From the top of a cliff 20m high, a boat can be sighted at sea 75m from the foot of the cliff. Calculate the angle of depression of the boat from the top of the cliff

From the diagram above. ABC is a triangle inscribed in a circle center O. ∠ACB = 40º and |AB| = x cm. Calculate the radius of the circle.

The diagram shows the position of three ships A, B and C at sea. B is due north of C such that |AB| = |BC| and the bearing of B from A = 040°. What is the bearing of A from C

A pole of length L leans against a vertical wall so that it makes an angle of 60 o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.

In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.

The height of a pyramid on square base is 15cm. If the volume is 80cm\(^3\), find the length of the side of the base

Simplify 3.72 x 0.025 and express your answer in the standard form

Two numbers 24\(_{x}\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y

A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed

The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.

Water flows from a tap into cylindrical container at the rate 5πcm\(^3\) per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.

Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.

Which of the following pairs of inequalities is represented on the number line?

If \(x^2 +15x + 50 = ax^2 + bx + c = 0\). Which of the following statement is not true?

The root of a quadratic equation in x, are -m and 2n. Find the equation

A survey shows that 28% of all the men in a village wear size 9 shoes. What is the probability that a man selected at random in the village wears size 9 shoes?

Solve the inequality 2x + 3 < 5x

In the diagram, DE||BC, |AD| = x cm and |DB| = |AE| = ycm. Find |CE| in terms of x and y

Describe the locus L shown in the diagram below

Which of the following statements is true from the diagram above?

In the diagram, O is the centre of the circle ∠PQR = 75o, ∠OPS = yo and \(\bar{OR}\) is parallel to \(\bar{PS}\). Find y

The sides of a right angle triangle in ascending order of magnitude are 8cm, (x-2)cm and x cm. Find x

In the diagram, CDE is a triangle, ABEF is cyclic quadrilateral, AB||CD, ∠BAF = 65 o and ∠AFE = 85 o calculate ∠CDE

In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.