Mathematics Question for revision There will be 15 questions and timing will be 1.5 hour. 1. Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically. 2. On comparing the ratios a1/a2 , b1/b2 , c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (i) 5x – 4y + 8 = 0 7x + 6y – 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x – 3y + 10 = 0 2x – y + 9 = 0 3. Find the 31st term of an A.P. whose 11th term is 38 and the 16th term is 73. 4. If the 3rd and the 9th terms of an A.P. are 4 and − 8 respectively. Which term of this A.P. is zero. 5. Which term of the A.P. 3, 15, 27, 39,.. will be 132 more than its 54th term? 6. Determine if the points (1, 5), (2, 3) and (-2, -11) are c...

Probability and Application of Trigonometry Question There will be 15 questions and timing will be 1.5 hour. 1. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red? 2. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) a red face card (iv) the jack of hearts (v) a spade (vi) the queen of diamonds 3. 12 defective pens are accidentally mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one. 4. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divis...

Trigonometry Test There will be 25 questions and timing will be 2 hour. 1. In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C 2. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B. 3. If 3 cot A = 4, check whether (1 – tan 2 A)/(1 + tan 2 A) = cos 2 A – sin 2 A or not. 4. In triangle PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. 5. Show that : (i) tan 48° tan 23° tan 42° tan 67° = 1 (ii) cos 38° cos 52° – sin 38° sin 52° = 0 6. Prove the identities: (i) √[1 + sinA/1 – sinA] = sec A + tan A (ii) (1 + tan 2 A/1 + cot 2 A) = (1 – tan A/1 – cot A) 2 = tan 2 A 7. If sin θ + cos θ = √3, then prove that tan θ + cot θ = 1. 8. Prove that (sin A – 2 sin 3 A)/(2 cos 3 A – cos A) = tan A. 9. Prove that (1 – cos 2 A) cosec 2 A = 1 10. Prove that (sec 2 θ − 1)(cosec 2 θ − 1) = 1 11. Prove that (1 – sin θ) / (1 + sin θ) = (sec θ...