- Question 1
(a) If b is the mean proportion between a and c, show that .
(b) Solve the equation 4x2 – 5x – 3 = 0 and give your answer correct to two decimal places.
(c) AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm.If the radius of the circle is 13 cm, find the distance between the two chords.
VIEW SOLUTION
- Question 2
(a) Evaluate without using trigonometric tables, sin2 28° + sin2 62° + tan2 38° – cot2 52° + sec2 30°
(b) If . Find matrix C where C is a 2 by 2 matrix.
(c) Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively.She repays 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.VIEW SOLUTION
- Question 3
(a) The catalogue price of a computer set is Rs. 42,000. The shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. However, sales tax at 8% is charged on the remaining price after the two successive discounts.
(b) P(1, –2) is a point on the line segment A(3, –6) and B(x, y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.
Find:
(i) the amount of sales tax a customer has to pay
(ii) the total price to be paid by the customer for the computer set.
(c) The marks of 10 students of a class in an examination arranged in ascending order is as follows:13, 35, 43, 46, x, x + 4, 55, 61, 71, 80VIEW SOLUTION
If the median marks is 48, find the value of x. Hence find the mode of the given data.
- Question 4
(a) What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
(b) In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of which are of radius 5 cm.
Find the area of the shaded region. Give your answer correct to three significant figures.
(c) Solve the following in-equation and represent the solution set on a number line.VIEW SOLUTION