Core Mathematics — 2007

Evaluate \((111_{two})^2\) and leave your answer in base 2

Find the LCM of \(2^{3}\times 3\times 5^{2}, 2\times 3^{2}\times 5 \hspace{1mm}and \hspace{1mm}2^{2}\times 3^{2}\times 5\)

Simplify \((0.3\times 10^{5})\div (0.4\times 10^{7})\)leaving your answer in standard form

If \(p\propto \frac{1}{q}\), which of the following is true?

Simplify \(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\)leaving your answer in surd form

Which of the following is true for the set \(P = \{-3.2\leq x< 5\}\) where x is an integer

Simplify\(\frac{3x^{3}}{(3x)^{3}}\)

N140,000 is shared between ABU, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode's share?

I am x years old and my brother is 3 years older. How old was my brother last year

For what value of x is the expression \(\frac{2x-1}{x+3}\)not defined?

If x =3, y = 2 and z = 4 what is the value of \(3x^{2}-2y+z\)

Solve the simultaneous equation: x+y=2 and 3x-2y=1

If \(8^{x+1}=\frac{1}{4}\), find x

The area of a square field is 110.25m 2 . Find the cost of fencing it round at N75.00 per meter square

A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the center of the circle

A sector of a circle of radius 14cm containing an angle 60 o is folded to form a cone. Calculate the radius of the base of the cone.

IN the diagram, |LN| = 4cm, LNM = 90 o and tan y = 2/3. What is the area of the ∆LMN?

Evaluate(111two)\(^2\) and leave your answer in base 2.

Find the LCM of 2\(^3\) x 3 x 5\(^2\), 2 x 3\(^2\) x 5 and 2\(^3\) x 3\(^3\) x 5

Simplify(0.3 x 10 5 ) \(\div\) (0.4 \(\times\) 10 7 ), leaving you answer in the standard form.

If p \(\alpha \frac{I}{Q}\) which of the following is true?

Simplify 3\(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\), leaving your answer in surd form.

Which of the following statement is true for the ste P = {-3.2 \(\leq\) x < 5} where x is an integer?

Simplify \(\frac{3x^3}{(3x)^3}\)

N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode'sshare?

I am x years old and my brother is 3 years older. How old was my brother last year?

For what value of x is the expression \(\frac{2x - 1}{x + 3}\) not defined?

If x = 3, Y = 2 and z = 4, what is the value of 3x 2 - 2y + z?

Solve the simultaneous equations x + y = 2 and 3x - 2y = 1

If 8 x-1 = \(\frac{1}{4}\), find x

A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle.

The area of a square field is 110.25m 2 . Find the cost of fencing it round at N75.00 per metre

A sector of a circle of radius 14cm containing an angle 60 o is folded to form a cone. Calculate the radius of the base of the cone

Find the volume of a solid cylinder with base radius 10cm and height 14cm.

Each of the interior angle of a regular polygon is 162 o . How many sides has the polygon?

In a , < PQR = < PRQ = 45o. which of the following statements is/are correct? i. \(\bigtriangleup\)PQR is an equalateral triangle ii. \(\bigtriangleup\)PQR is an isosceles triangle iii. \(\bigtriangleup\)PQR is a right-angled triangle

The table above gives the distribution of the marks of a number of students in a test. \(\begin{array}{c|c} Mark &1 & 2 & 3 & 4 & 5 & 6 \\ \hline Frequency & 5 & 3 & 6 & 4 & 2 & 5\end{array}\), find the mode of the distribution.

If the probability of an event occurring is x, what is the probability of the event not occurring?

The table shows the ages(in years) of twenty children chosen at random from a community. What is the mean age? \(\begin{array}{c|c} Age(years) & 1 & 2 & 3 & 4 & 5 \\ \hline {\text {Number of children}} & 2 & 3 & 5 & 6 & 4 \end{array}\)

The table shows the ages(in years) of twenty children chosen at random from a community. What is the median of the distribution? \(\begin{array}{c|c} Age(years) & 1 & 2 & 3 & 4 & 5 \\ \hline {\text {Number of children}} & 2 & 3 & 5 & 6 & 4 \end{array}\)

Divide the sum of 8, 6, 7, 2, 0, 4, 7, 2, 3, by their mean

Q is 32 km away from P on a bearing 042o and R is 25km from P on a bearing of 132o. Calculate the bearing of R from Q.

The bearing of a point P from another point Q is 310 o . If |PQ| = 200m, how far west of Q is P?

Find the value of a if log\(_{10}\) a + log\(_{10}\)a\(^2\) = 0.9030

A messenger was paid N2.50 an hour during the normal working hours and 4.00 n hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?

At what rate per cent per annum will N520.00 yield a simple interest of N39.00 in three years?

PQR is an equilateral triangle with sides 2\(\sqrt{3cm}\). calculate its height

Which of the following is a factor of 2 - x - x 2 ?

make w the subject of the relation \(\frac{a + bc}{wd + f}\) = g

For what range of values of x is 4x - 3(2x - 1) > 1?

Find the smallest value of k such that 2\(^2\) x 3\(^3\) x 5 x k is a perfect square.

Expand the expression(3a - xy)(3a + xy)

Simplify \(\frac{4}{2x} - \frac{2x + x}{x}\)

Two circles have radii 16cm and 23cm. What is the difference between their circumference? take \(\pi = \frac{22}{7}\)

The volume of a cylinder is 1200cm3 and the area of its base is 150cm2. Find the height of the cylinder.

In the diagram |LN| = 4cm, LNM = 90 o and tan y = \(\frac{2}{3}\). What is the area of the \(\bigtriangleup\)LMN?

From the diagram, find the value of x in the diagram.

In the diagram, |SP| = |SR| and < PRS = 50 o . Calculate < PQR

Find the value of x in the diagram

The venn diagram shows the choice of food of a number of visitors to a canteen. If there were 35 visitors in all, find the value of x

The venn diagram shows the choice of food of a number of visitors to a canteen. How many people took at least two kinds of food?  If there were 35 visitors in all

If the ratio x:y = 3:5 and y:z = 4:7, find the ratio x:y:z

In the diagram, O is the centre of the circle and < PQR = 106º, find the value of y

In the diagram, |XR| = 4cm |RZ| = 12cm, |SR| = n, |XZ| = m and SR||YZ. Find m in terms of n

In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4cm. Find the area of the shaded region

Find the product of 0.0409 and 0.0021 leaving your answer in the standard form

Convert 42\(_5\) to base three numeral