Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35°, find ∠PQS

• A. 35
• B. 45
• C. 55
• D. 70

If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y)

• A. 1\(\frac{1}{4}\)
• B. 2\(\frac{1}{2}\)
• C. 3\(\frac{3}{4}\)
• D. 5

If the locus of the points which are equidistant from point P and Q meets line PQ at point N, then PN equals

• A. NQ
• B. 1/4NQ
• C. 2NQ
• D. 1/2NQ

Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)

• A. \(q = \frac{b^2(mn - a^2)}{a^2 p}\)
• B. \(q = \frac{m^2 n - a^2}{p^2}\)
• C. \(q = \frac{mn - 2b^2}{a^2}\)
• D. \(q = \frac{b^2 (n^2 - ma^2)}{n}\)

(a) The angle of depression of a boat from the mid-point of a vertical cliff is 35°. If the boat is 120m from the foot of the cliff, calculate the height of the cliff.

(b) Towns P and Q are x km apart. Two motorists set out at the same time from P to Q at steady speeds of 60 km/h and 80 km/h. The faster motorist got to Q 30 minutes earlier than the other. Find the value of x.

Evaluate \(\frac{xy^2 - x^2y}{x^2 - xy^1}\) When x = -2 and y = 3

• A. 3
• B. -\(\frac{3}{5}\)
• C. \(\frac{3}{5}\)
• D. -3

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

• A. I and II only
• B. II and III only
• C. II only
• D. III only

What is the solution of \(\frac{x - 5}{x + 3}< -1\)?

• A. -3< x< 1
• B. x< -3 or x > 1
• C. -3< x< 5
• D. x< -3 or x > 5

A 5 sided figure is called a

• (a)quadrilateral
• (b)septagon
• ( c)pentagon
• (d)octagon

The value x in the figure given is

• A. 110°
• B. 100°
• C. 70°
• D. 130°