Core Mathematics — 2002

In the diagram O is the center of the circle. Reflex angle XOY = 210° and the length of the minor arc is 5.5m. Find, correct to the nearest meter, the length of the major arc.

A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid

The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area

In the diagram above, ∠PQU=36°, ∠QRT = 29°, PQ||RT. Find ∠PQR

Simplify \(5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\)

Find the value of x in 0.5x + 2.6 = 5x + 0.35

Find the value of x in the diagram

If \(M5_{ten} = 1001011_{two}\) find the value of M

The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x- axis at P and R and the y- axis at Q. What is the value of y at Q?

The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x-axis at P and R and the y-axis at Q. When \(y = 3\frac{1}{3}\), what is the positive value of x?

The length, in cm, of the sides of a right angled triangle are x, (x+2) and (x+1) where x > 0. Find , in cm, the length of its hypotenuse

If log 2 = 0.3010 and log 2\(^y\) = 1.8062, find; correct to the nearest whole number, the value of y.

Points X, Y and Z are located in the same horizontal plane such that Y is 12 km north of X and Z is on a bearing of 270° from X. If |XZ| = 6km, calculate, correct to one decimal place, lYZl

The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?

If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?

From the diagram, find the bearing of Q from P.

Find the nth term of the sequence 4, 10, 16 ,...

If (-3, -4) is a point on the line y = mx + 2 find the value of m.

Which of the following is represented by the above sketch?

In the diagram, SQ is a tangent to the circle at P, XP||YQ, ∠XPY = 56 o and ∠PXY = 80 o.Find angle PQY

For what values of x is the expression \(\frac{3x-2}{4x^2+9x-9}\) undefined?

Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\)

The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. lf the area of the trapezium is 105 cm 2 , find the perpendicular distance between the parallel sides.

The base diameter of a cone is 14cm, and its volume is 462 cm 3 . Find its height. [Taken \(\pi = \frac{22}{7}\)]

A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.

The median of the distribution is

The range of the distribution is

The upper quartile of the distribution is

In the diagram O and O' are the centres of the circles radii 15cm and 8cm respectively. If PQ = 12cm, find |OO'|.

In the diagram O is the centre of the circle. Which of the following is/are not true? I. a = b II. b + c = 180o III. a + b = c

Simplify \(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\)

In the diagram, |SR| = |RQ| and ∠PRQ = 58 o ∠VQT = 19 o , PQT, SQV and PSR are straight lines. Find ∠QPS

The angle of depression of a point Q from a vertical tower PR, 30m high, is 40°. If the foot P of the tower is on the same horizontal level as Q, find, correct to 2 decimal places, |PQ|.

The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?

Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)

Factorize m(2a-b)-2n(b-2a)

If q oranges are sold for t Naira, how many oranges can be bought for p naira?

In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = \(6\sqrt{3}cm\), calculate |RT|

In the diagram, calculate the value of x

In the diagram, \(\bar{PS}\hspace{1mm} and \hspace{1mm}\bar{QT}\) are two altitudes of ∆PQR. Which of the following is equal to ∠RQT?

In the diagram, |QR| = 10cm, PR⊥QS, angle PSR = 30° and angle PQR = 45°. Calculate in meters |QS|

Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4

To arrive on schedule, a train is to cover a distance of 60km at 72km/hr. If it starts 10 minutes late, at what speed must it move to arrive on schedule?

In the diagram, \(QR||TP and W\hat{P}T = 88^{\circ} \). Find the value of x

In the diagram O is the center of the circle, ∠SOR = 64° and ∠PSO = 36°. Calculate ∠PQR

Given that \(p = x-\frac{1}{x} and\hspace{1mm}q = x^2 + \frac{1}{x^2}\) express q in terms of p.

The number of goals scored by a school team in 10 netball matches are as follows: 3, 5, 7, 7, 8, 8, 8, 11, 11, 12. Find the probability that in a match, the school team will score at most 8 goals.

Which of the following is not a rational number?

In the diagram, LMT is a straight line. lf O is the centre of circle LMN, OMN = 20°, LTN = 32° and |NM| = |MT|, find LNM.