Core Mathematics — 1994

If the 2nd and 5th terms of a G.P are 6 and 48 respectively, find the sum of the first four for term

If sin\( \theta \) = K find tan\(\theta\), 0° \(\leq\) \(\theta\) \(\leq\) 90°.

Simplify: \(2\frac{1}{3} \div 2\frac{2}{3} \times 1\frac{1}{7}\)

Which of the following is equal to \(\frac{72}{125}\)

Express in \( \frac{8.75}{0.025} \)standard form

Evaluate \( \frac{27^{\frac{1}{3}}}{16^{-\frac{1}{4}}} \)

Simplify: 16\(^{\frac{5}{4}}\) x 2\(^{-3}\) x 3\(^0\)

simplify; 2log\(_{3}\) 6 + log\(_{3}\) 12 - log\(_{3}\) 16

What is the number whose logarithm to base 10 is \(\bar{3}.4771\)?

A house bought for N100,000 was later auctioned for N80,000. Find the loss percent.

A string is 4.8m. A boy measured it to be 4.95m. Find the percentage error.

The sum of the 1st and 2nd terms of an A.P. is 4 and the 10th term is 19. Find the sum of the 5th and 6th terms.

E = (integers \(\leq\) 20), P = (multiples of 3), Q = (multiples of 4), what are the elements of P'∩Q?

Given that 2p - m = 6 and 2p + 4m = 1, find the value of (4p + 3m).

Which of the following is a point on the curve y = x\(^2\) - 4x + 7?

If 8x- 4 = 6x- 10, find the value of 5x,

For what value of x is the expression \(\frac{x^2 + 15x + 50}{x - 5}\) not defined ?

If x is positive, for what range of values of x is 4 + 3x < 10?

In the graph above, the gradient of the curve at the point P is

What is the equation of the line PQ?

Which of the following equations can be solved by the points of intersection P and Q of the curve and the line PQ?

Which of the following is not a factors of 2p\(^2\) - 2?

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

Which of the following is a root of the equation x\(^2\) +6x = 0?

Factorise: 6x\(^2\) + 7xy - 5y\(^2\)

Solve the equation log8x - 4log8x = 2

The angle subtended at the centre by a chord of a circle radius 6cm is 120°. Find the length of the chord.

A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)

Two ships on the equator are on longitudes 45oW and 45oE respectively. How far are they apart along the equator, correct to 2 significant figures? (Take the radius of earth = 6400km and π = 22/7)

Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75° at the centre of the circle. [Take π = 22/7].

A circle has radius x cm. What is the area of a sector of the circle with angle 135°, leaving the answer in terms of x and π?

In the diagram, PQRS is a trapezium with PQ||SR. STR is a straight line, PSHQT, PTHQR. If |PQ| = 12cm and the height of the trapezium is 9cm, find its area.

Two solid spheres have volumes 250cm o and 128cm o respectively. Find the ratio of their radii.

In the diagram ST and QR are parallel. |PS| = 6cm, |SQ| = 8cm and |PR] = 18 2/3. Find |PT|

In the diagram, PQ||RS and angles are as shown. Find x

IF the exterior angles of a quadilateral are y o , (2y + 5) o , (y + 15) o and (3y - 10) o , find y o

The sum of the angles of regular polygon is 2520 o . How many sides does the polygon have?

Which of the following is not a property of all parallelogram?

In the diagram above, PQ is the tangent to the circle RST at T.|ST| = ST and ∠RTQ = 68 o . Find ∠PTS

The diagram above shows a circle PQRS in which ∠PRQ = 54 o and ∠SPQ = 97 o . Find ∠PQS

In the diagram, |PS| is a diameter of circle PQRS. |PQ| = |QR| and ∠RSP = 74º. Find ∠QPS

A ladder 6m long leans against a vertical wall so that it makes an angle of 60 o with the wall. Calculate the distance of the foot of the ladder from the wall

The bearing of Q from P is 122 o , what is the bearing of P from Q?

cos 57 o has the same value as

The median of the distribution is

The percentage of the students with mass less than 69kg is

The mean heights of the three groups of students consisting of 20, 16 and 14 students are 1.67m, 1.50m and 1.40m respectively. Find the mean height of the students

Two cards are drawn one after the other with replacement from a well-shuffled ordinary deck of 52 cards containing four Aces. Find the probability that they are both Aces

Find the probability that a number selected from the number 30 to 50 inclusive is a prime

The length of an exercise book is given as 20cm correct to the nearest centimeter. In which of the following ranges of possible measurement does the actual length lie?