Core Mathematics — 1997

Express (0.0425 / 2.5) as a fraction

If P = {3, 5, 6} and Q = {4, 5, 6} then P∩Q equals

A and B are two sets. The number of elements in A∪B is 49, the number in A is 22 and number in B is 34. How many elements are in A ∩ E?

A student found the approximate value of 0.02548 correct to two places of decimal instead of two significant figures. Find the percentage error.

Simplify log 3 9 + log 3 15 - log 3 5

Solve me equation: 2/3 (x + 5) = 1/4(5x - 3)

Which of the following equations has its roots as 4 and -5?

Solve the equations: 4x -y = 11; 5x + 2y = 4.

Make q the subject of the relation t = √(pq/r  - r\(^2\)q)

P varies inversely as the square of W. When W = 4, P = 9. Find the value of P when W = 9

If x varies over the set of real numbers, which of the following is illustrated in the diagram above?

In the triangle XYZ , XM is the altitude from X to YZ.XY = 13cm, XZ = 15cm and YM = 5cm. Find the length of YZ

Two points P and Q are on longitude 67°W. Their latitudes differ by 90°. Calculate their distance apart in terms of π. (Take radius of the earth = 6400km).

The length of the two parallel sides of trapezium are 6cm and 10cm and the perpendicular distance between them is 5cm. Find the area of the trapezium

Calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π

The cross-section of a prism is a right-angled triangle 3cm by 4cm by 5cm. The height of the prism is 8cm. Calculate its volume

Find the radius of a circle in which an arc of length 44cm subtends angle 200° at the centre of the circle. [Take π = 22/7]

The diagram above is a triangle XYZ whose area is 23.5cm 2 . XY =1Ocm and YZ = 8cm, calculate θ correct to the nearest degree.

Which of the following is not necessarily sufficient for the construction of a triangle?

In the diagram, EF//QR, PE = 2cm, EQ = 4cm and FR = 6cm. Find x

Which of the following statements is/are true when two straight lines intersect? I. Adjacent angles are equal II. Vertically opposite angles are equal III. Adjacent angles are supplementary

PQRS and GHRS are parallelograms on the same base SR and between the same parallel straight line PH and SR. Which of the following is true?

From the diagram above, which of the following is true?

The interior angles of a pentagon are 126 o , 114 o , y, 92 o and 83 o . Find the value of y.

Solve the inequality 3x - 8 ≥ 5x

Divide 3.6721 by 4

The eleventh term of an AP, is 25 and its first term is -3. Find its common difference.

Find the common ratio in the GP: log 3, log 9, log 81 ..........

Find the value of t for which \(\frac{64}{27} = (\frac{3}{4})^{t - 1}\)

O is the centre of the circle PQRS. PR and QS intersect at T POR is a diameter, ∠PQT = 42 o and ∠QTR = 64 o ; Find ∠QRT

TR is the tangent to the circle PQR with centre O. Find the size of ∠PRT

Given that \(\frac{1}{2} \log_{10} P = 1\), find the value of P.

If two triangles are similar, which of the following is true? Their

Which of the following is not necessarily true of a rectangle?

A chord is 5cm from the centre of a circle of diameter 26cm. Find the length of the chord

The angle of elevation of a point T on a tower from a point U on the horizontal ground is 30 o . If TU = 54m, how high is T above the horizontal ground?

Express the true bearing of 250° as a compass bearing

lf sin θ= \(\frac{-1}{2}\), find all the values of θ between 0° and 360°.

Cos 65 o has the same value as

Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the nearest degree, the smallest angle of the triangle.

The graph is the cumulative frequency curve for the weight distribution of 100 workers in a factory. Which of the points P,Q,R,S and T indicates the median weight?

A bag contains red, black and green identical balls. A ball is picked and replaced. The table shows the result of 100 trials. Find the experimental probability of picking a green ball.

The table shows the scores of a group of students in a test. If the average score is 3.5, find the value of x

What is the probability of having an odd number in a single throw of a fair die with the faces numbered 1,2,3,4,5,6?

A bag contains 3 white, 6 red, 5 blue identical balls. A ball is picked at random from bag. What is the probability that is either white or blue?