Core Mathematics — 2009

Simplify: (3\(\frac{1}{2} + 4\frac{1}{3}) \div (\frac{5}{6} - \frac{2}{3}\))

In a particular year, the exchange rate of naira (N) varies directly with the Dollars{$}. If N1122 is equivalent to $8, find the Naira equivalent of $36

If log 2 = x, log 3 = y and log 7 = z, find, in terms of x, y and z, the value of log (\(\frac{28}{3}\))

Arrange the following numbers in descending orders of magnitude: 22 three , 34 five , 21 six

Find the value to which N3000.00 will amount in 5 years at 6% per annum simple interest

Express the square root of 0.000144 in the standard form

Two sets are disjoint if

If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x

If (2x + 3) 3 = 125, find the value of x

Factorize x 2 - 2x - 3xy completely

The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take \(\pi \frac{22}{7}\)

The interior angles of a pentagon are (2x + 5)o, (x + 20)o, xo, (3x - 20)o and (x + 15)o. Find the value of x

If M and N are two fixed points in a plane. Find the locus L = [P : PM = PN]

Given that sin 60 o = \(\frac{\sqrt{3}}{2}\) and cos 60 o = \(\frac{1}{2}\), evaluate \(\frac{1 - sin 60^o}{1 + cos 60^o}\)

In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x

What is the median of the following scores: 22 35 41 63 74 82

Express 2.7864 x 10 -3 to 2 significant figures

If 9 2x = \(\frac{1}{3}\)(27 x ), find x

If 85% of x is N3230, what is the value of x?

The capacity of a water tank is 1,800 litres. If the tank is in form of a cuboid with base 600cm by 150 cm. Find the height of the tank

An arc of a circle subtends an angle of 60 o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc

solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0

If a positive integer, list the values of x which satisfy the equation 3x - 4 < 6 and x - 1 > 0

If c and k are the roots of 6 - x - x 2 = 0, find c + k

Each of the interior angles of a regular polygon is 140 o . Calculate the sum of all the interior angles of the polygon

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of size 8m x 7m x 5m.(1 litre = 1000cm 3 )`

A box contains black, white and red identical balls. The probability of picking a black ball at random from the box is \(\frac{3}{10}\) and the probability of picking a white ball at random is \(\frac{2}{5}\). If there are 30 balls in the box, how many of them are red?

Simplify; \(\frac{1}{2}\sqrt{32} - \sqrt{18} + \sqrt{2}\)

The angles of triangle are (x + 10) o , (2x - 40) o and (3x - 90) o . Which of the following accurately describes the triangle?

Simplify (x - 3y) 2 - (x + 3y) 2

Find the quadratic equation whose roots are -\(\frac{1}{2}\) and 3

The following is the graph of a quadratic friction, find the co-ordinates of point P

The following is the graph of a quadratic friction, find the value of x when y = 0

PQRS is a trapezuim. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42 o . Calculate the perpendicular distance between the parallel sides

PQRS is a trapezium. QR//PS, /PQ/ = 5cm, /OR/ = 6cm, /PS/ = 10cm and angle QPS = 42 o . Calculate, correct to the nearest cm 2 , the area of the trapezium (h = 3.35cm 2 )

In the diagram, /TP/ = 12cm and it is 6cm from O, the centre of the circle, Calculate < TOP

In the diagram, IG is parallel to JE, JEF = 120 o and FHG = 130 o , fins the angle marked t

Find the value of x in the diagram

In the diagram, \SQ\ = 4cm, \PT\ = 7cm. /TR/ = 5cm and ST//OR. If /SP/ = xcm, find the value of x

Using the diagram, find the bearing of X from Y

If /XY/ = 50m, how far cast of X is Y?

in the diagram, angle 20º is subtended at the centre of the circle, find the value of x

The pie chart shows the distribution of 4320 students who graduated from four departments in a university. How many students graduated from the science department?

The pie chart shows the distribution of 4320 students who graduated from four departments in a university. If a student is picked at random from the four departments, what id the probability that he is not from the education department?

From the diagram which of the following statements are correct? i. XQ is a radius of a circle centre Q. ii. /XQ/ = /QY/. iii. /QX/ = /XY/

Find the value of x in the diagram