Core Mathematics — 2006

Evaluate (0.13)\(^3\)correct to three significant figures

Simplify: 11011\(_2\) - 1101\(_2\)

Simplify \(\frac{25 ^\frac{2}{3} \div 25 ^\frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\)

Simplify \(\frac{x - 4}{4} - \frac{x - 3}{6}\)

Given that y = 1 - \(\frac{2x}{4x - 3}\), find the value of x for which y is undefined

P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is

A fair coin is tossed three times. Find the probability of getting two heads and one tail.

If 30% of y is equal to x, what in terms of x, is 30% of 3y?

A baker used 40% of a 50kg bag of flour. If \(\frac{1}{8}\) of the amount used was for the cake, how many kilogram of flour was used for the cake?

If tan y = 0.404, where y is acute, find cos 2y

The ratio of boys to girls in a class is 5:3. Find the probability of selecting at random, a girl from the class

\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table above satisfies the relation y = k\(\sqrt{x}\), where k is a positive constant. Find the value of K.

\(\begin{array}{c|c} x & 1 & 4 & p \\ \hline y & 0.5 & 1 & 2.5\end{array}\). The table below satisfies the relation y = k\(\sqrt{x}\), where k is a positive constant. Find the value of P,

What must be added to x 2 - 3x to make it a perfect square?

Given that (2x - 1)(x + 5) = 2x 2 - mx - 5, what is the value of m

What is the place value of 9 in the number 3.0492?

If the simple interest on a sum of money invested at 3% per annum for 2\(\frac{1}{2}\) years is N123, find the principal.

A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?

If 2x + y = 10, and y \(\neq\) 0, which of the following is not a possible value of x?

If x + y = 12 and 3x - y = 20, find the value of 2x - y

Which of these equations best describes the points of intersection of the curve and the line?

If log a 270 - log a 10 + log a \(\frac{1}{3}\) = 2, what is the value of a?

a conical water-jug is 7cm in diameter and 6cm deep. find the volume of water it can hold. [Take \(\pi = \frac{22}{7}\)]

If p = [\(\frac{Q(R - T)}{15}\)]\(^ \frac{1}{3}\), make T the subject of the relation

A seller allows 20% discount for cash payment on the marked price of his goods. What is the ratio of the cash payment to the marked price

The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? [Take \(\pi = \frac{22}{7}\)]

If p = {1, 3, 5, 7, 9} and Q = {2, 4, 6, 8, 10} are subsets of a universal set. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the elements of P 1 \(\cap\) Q 1 ?

The values of three angles at a point are 3y - 45 o , y + 25 o and y o . Find the value of y.

A rectangular carpet 2.5m long and 2.4m wide covers 5% of a rectangular floor. Calculate the area of the floor

Which of the following is not a measure of centre tendency?

The temperature in a chemical plant was -5 o C at 2.00 am. The temperature fell by 6 o C and then rose again by 7 o C. What was the final temperature?

Simplify \(\frac{20}{5\sqrt{28} - 2 \sqrt{63}}\)

A ladder 16m long leans against an electric pole. If the ladder makes an angle of 65 o with the ground, how far up the electric pole does its top reach

In the diagram, PQUV, PQTU, QRTU and QRST are parallelograms. |UV| = 4.8cm and the perpendicular distance between PR and VS is 5cm. Calculate the area of quadrilateral PRSV

In the diagram, |QR| = 5cm, PQR = 60 o and PSR = 45 o . Find |PS|, leaving your answe in surd form.

In the diagram, \(\frac{PQ}{RS}\), find x o + y o

In the diagram, PR is a diameter of the circle centre O. RS is a tangent at R and QPR = 58 o . Find < QRS

In the diagram P, Q, R, S are points on the circle RQS = 30 o . PRS = 50 o and PSQ = 20 o . What is the value of x o + y o ?

In the diagram, P, Q and R are three points in a plane such that the bearing of R from Q is 110 o and the bearing of Q from P is 050 o . Find angle PQR.

In the diagram, the two circles have a common centre O. If the area of the larger circle is 100\(\pi\) and that of the smaller circle is 49\(\pi\), find x

In the diagram, PQR is a straight line, QRST is a parallelogram, < TPQ = 72o and < RST = 126o. What type of triangle is \(\bigtriangleup\) PQT?

How many pupils took the test?

If the pass mark was 4. What percentage of the pupils failed the test?

The diagram shows an arc MN of a circle, centre O, with 10cm. If < MON = 72 o . calculate the length of the arc, correct to three significant figures. [Take \(\pi = \frac{22}{7}\)]

In the diagram what is x + y in terms of z?

In the diagram |XY| = 12cm, |XZ| = 9cm, |ZN| = 3cm and ZY||NM, calculate |MY|