Core Mathematics — 2010

Simplify 0.000215 x 0.000028 and express your answer in standard form

Factorize: x + y - ax = ay

A car uses one litre of petrol for every 14km. If one of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?

Correct 0.002473 to 3 significant figure

Simplify 1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)

The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers

A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of Copper. What is the mass of the casting?

Given that P = {x : 1 \(\leq x \leq 6\)}, and Q = {x : 2 \(\leq x \leq 10\)} where x is an integer. Find n(P \(\cap\) Q)

The sum of 6 and one-third of x is one more than twice x, find x

Given that = {x: -2 < x \(\leq\) 9}, where x is an integer what is n(T)?

Solve the inequality: 3(x + 1) \(\leq\) 5(x + 2) + 15

An empty rectangular tank is 250cm long and 120cm wide. If 180 litres of water is poured into the tank. Calculate the height of the water

Given that \(\frac{5^{n +3}}{25^{2n -3}}\) = 5º, find n

\(\begin{array}{c|c} \text{No. of pets} & 0 & 1 & 2 & 3 & 4 \\ \hline \text{No. of students} & 8 & 4 & 5 & 10 & 3\end{array}\) The table shows the number of pets kept by 30 students in a class. If a student is picked at random ftom the class. What is the probability that he/she kept more than one pet?

Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)

If sin 3y = cos 2y and 0 o \(\leq\) 90 o , find the value of y

A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x

Given that tan x = 1, where 0 o \(\geq\) x 90 o , evaluate \(\frac{1 - \sin^2 x}{\cos x}\)

What is the length of a rectangular garden whose perimeter is 32cm and area 39cm 2 ?

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

The sum of the exterior of an n-sided convex polygon is half the sum of its interior angle. find n

If y = \(\frac{(2\sqrt{x^2 + m})}{3N}\), make x the subject of the formular

The nth term of the sequence -2, 4, -8, 16.... is given by

How many times, correct to the nearest whole number, will a man run round circular track of diameter 100m to cover a distance of 1000m?

Bola sold an article for N6,900.00 and made a profit of 15%. If he sold it for N6,600.00 he would make a

The mean age of R men in a club is 50 years, Two men aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of R

\(\begin{array}{c|c} x & 0 & 2 & 4 & 6\\ \hline y & 1 & 2 & 3 & 4\end{array}\). The table is for the relation y = mx + c where m and c are constants. What is the equation of the line described in the tablet?

What is the value of x when y = 5? y = \(\frac{1}{2}\)  x + 1

The subtraction below is in base seven. Find the missing number. 5 1 6 2 seven -2 6 4 4 seven -------- 2 * 1 5 --------

If the sum of the roots of the equation (x - p)(2x + 1) = 0 is 1, find the value of x

If x2 + kx + \(\frac{16}{9}\) is a perfect square, find the value of k

If x km/h = y m/s, then y =

The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x

In an athletic composition, the probability that an athlete wins a 100m race is \(\frac{1}{8}\) and the probability that he wins in high jump is \(\frac{1}{4}\). What is the probability that he wins only one of the events?

In the diagram, < PSR = 220 o , < SPQ = 58 o and < PQR = 41 o . Calculate the obtuse angle QRS.

The bar chart shows the marks distribution in am English test. If 50% is the pass mark, how many students passed the test?

The bar chart shows the marks distribution in am English test. What percentage of the students had marks ranging from 35 to 50?

What is the value of m in the diagram?

In the diagram, QR//ST, /PQ/ = /PR/ and < PST = 75 o . Find the value of y

In the diagram, triangles HKL and HIJ are similar. Which of the following ratios is equal to \(\frac{LH}{JH}\)

In the diagram, < ROS = 66 o and < POQ = 3x. some construction lines are shown. Calculate the value of x.

In the diagram, the tangent MN makes an angle of 55 o with the chord PS. IF O is the centre of the circle, find < RPS

In the diagram, O is the centre of the circle, < SQR = 60o, < SPR = y and < SOR = 3x. Find the value of (x + y)

The shaded portion in the diagram is the solution of

In the diagram, GI is a tangent to the circle at H. If EF//GI, calculate the size of < EHF

The diagram is a net right rectangular pyramid. Calculate the total surface area

The diagram shows a rectangular cardboard from which a semi-circle is cut off. Calculate the area of the remaining part

In the diagram, 0 is the centre of the circle. Find the value x

In the diagram, < WOX = 60o, < YOE = 50o and < OXY = 30o. What is the bearing of x from y?