Grade 10 Full Year 10th Grade Review

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1 ID : ph-10-full-year-10th-grade-review [1] Grade 10 Full Year 10th Grade Review For more such worksheets visit Answer t he quest ions (1) If cot θ = a/b and 0 > θ > 90, f ind value of cosec θ. (2) A 7 3 m high tower casts 7 m long shadow on the ground. Find the angle of Sun's elevation. (3) 12 balls and 10 bats cost 500 and 5 balls and 6 bats cost 245. Find the cost of one ball and one bat separately. (4) Simplif y sin 6 α + cos 6 α + 3sin 2 α cos 2 α (5) Find the LCM of 962 and 481. (6) A train, traveling at a unif orm speed f or 2925 km, would have taken 6 hours less to travel the same distance if its speed were 10 km/h more. Find the original speed of the train. (7) Find solution of quadratic equation 3y 2 + y - 4 = 0 Choose correct answer(s) f rom given choice (8) Which of the f ollowing can take the place of the blank in the series below C2W, F3T, I5Q,, O11K a. L8O b. M7M c. K7N d. L7N (9) Datu buys number of toys f or 36. If he had bought 3 more toys f or the same amount, each toy would have cost 1 less. How many toys did he buy? a. 12 b. 11 c. 10 d. 9 (10) (cosθ + cosecθ) 2 + (sinθ + secθ) 2 =? a. (1 + sec θ cosec θ) 2 b. (1 + sin θ cos θ) 2 c. (1 - sin θ cos θ) 2 d. (sec θ cosec θ) 2 (11) Which of the f ollowing quadratic equations have no real roots? a. 3x 2 + 6x + 4 = 0 b. 4x 2 + 7x + 3 = 0 c. 2x 2 + 5x + 3 = 0 d. 3x 2 + 7x + 3 = 0

2 ID : ph-10-full-year-10th-grade-review [2] (12) Three people go f or a morning walk together. Their steps measure 40 cm, 65 cm and 85 cm respectively. What is the minimum distance traveled when their steps will exactly match af ter starting the walk assuming that their walking speed is same? a m b m c m d m (13) Which of the f ollowing is not an irrational number.. a b c d (14) In a two digit number,its unit's digit is 5 more than ten's digit. If sum of this number and the number obtained by reversing the order of its digits is 121, f ind the number. a. 38 b. 27 c. 49 d. 83 (15) If 4 tanθ = 2, f ind the value of 4 sinθ - cosθ 4 sinθ + cosθ. a. 2/3 b. 1/4 c. 1/2 d. 1/ Edugain ( All Rights Reserved Many more such worksheets can be generated at

3 Answers ID : ph-10-full-year-10th-grade-review [3] (1) We know that, cosec θ = (1 + cot 2 θ) Now replace value of cot(θ) in above equation cosec(θ) = Simplif y RHS of above equation cosec(θ) = (2) 60 In f ollowing f igure, AC shows the tower and AB is its shadow, and angle B is the angle of Sun's elevation. tan( B) = AC/AB tan( B) = (7 3)/(7) tan( B) = 3 We know that tan(60 ) = 3, theref ore, B = 60

4 (3) 25 and 20 ID : ph-10-full-year-10th-grade-review [4] Let the cost of a ball and bat be x and y respectively. It is given that 12 x + 10 y = x + 6 y = 245 On multiplying f irst equation by 3 and second equation by 5 36 x + 30 y = x + 30 y = 1225 Subtract second equation f rom f irst equation 1 => 11 x = 275 => x = (275)/(11) = 25 Substitute this value in f irst equation => y = 500 => 10 y = = 200 => y = (200)/(10) = 20

5 (4) 1 ID : ph-10-full-year-10th-grade-review [5] S = sin 6 α + cos 6 α + 3sin 2 α cos 2 α S = (sin 2 α) 3 + (cos 2 α) 3 + 3sin 2 α + 3sin 2 α cos 2 α S = (sin 2 α + cos 2 α) [(sin 2 α) 2 - sin 2 α cos 2 α + (cos 2 α) 2 ] + 3sin 2 α cos 2 α... Using a 3 +b 3 = (a+b)(a 2 - ab + b 2 ) S = 1[(sin 2 α) 2 - sin 2 α cos 2 α + (cos 2 α) 2 ] + 3sin 2 α cos 2 α... Using sin 2 θ + cos 2 θ = 1 Step 5 S = (sin 2 α) 2 + 2sin 2 α cos 2 α + (cos 2 α) 2 Step 6 S = (sin 2 α + cos 2 α) 2 ) 2... Using a 2 + b 2 + 2ab = (a + b) 2 Step 7 S = Using sin 2 θ + cos 2 θ = 1 S = 1

6 (5) 962 ID : ph-10-full-year-10th-grade-review [6] Let us f ind the LCM of 962 and 481. All prime f actors of 962: is a factor of is a factor of is a factor of 37 1 Thus, 962 = All prime f actors of 481: is a factor of is a factor of 37 1 Thus, 481 = Thus, the LCM of 962 and 481 = = 962.

7 (6) 65 km/hour ID : ph-10-full-year-10th-grade-review [7] We know that, s = d/t, where, s = Speed of the train, d = Distance traveled by the train, t = time taken by train. Let's assume the speed of the train is 's' km/hour. It is given that, the train is traveling at a unif orm speed f or 2925 km, theref ore, s = 2925/t -----(1) or t = 2925/s (2) It is also given that, the train would have taken 6 hours less to travel the same distance if its speed were 10 km/h more. Theref ore, s + 10 = 2925 t - 6 By putting the value of 't' f rom equation (2), we get, 2925 s + 10 = 2925/s s s + 10 = s (s + 10)(2925-6s) = 2925s 2925s - 6s s = 2925s - 6s s = 0 6s s = 0 On solving the quadratic equation, 6s s = 0, we get, s = 65 or -75 s -75, since the speed of the train cannot be negative. Theref ore, s = 65 Thus, the speed of the train is 65 km/hour. (7) -4 3, 1 (8) d. L7N

8 (9) d. 9 ID : ph-10-full-year-10th-grade-review [8] Let the number of toys bought = x Price of one toy = 36/x Price of one toy, if 3 more items were bought = 36/(x + 3) Since dif f erence in price is 1 Step 5 Step = x 2 + 3x Step 7 x 2 + 3x = 0 Step 8 x x - 9x = 0 Step 9 x (x + 12) - 9(x + 12) = 0 0 (x - 9) (x + 12) = 0 1 x = 9 or -12. Since number of toys cannot be negative, x = 9 (10) a. (1 + sec θ cosec θ) 2

9 ID : ph-10-full-year-10th-grade-review [9] (11) a. 3x 2 + 6x + 4 = 0 In quadratic equation, ax 2 + bx + c = 0. D = b 2-4ac. If in a quadratic equation, D < 0, then the quadratic equation has no real roots. If in a quadratic equation, D > 0, then the quadratic equation has two distinct real roots. If in a quadratic equation, D = 0, then the quadratic equation has only one root. Let's check all of the quadratic equations f or real roots. 3x 2 + 6x + 4 = 0 Here, a = 3, b = 6 and c = 4 Now, D = b 2-4ac = (6) 2-4(3)(4) = -12 Since, D < 0, the quadratic equation 3x 2 + 6x + 4 = 0 has no real roots. 4x 2 + 7x + 3 = 0 Here, a = 4, b = 7 and c = 3 Now, D = b 2-4ac = (7) 2-4(4)(3) = 1 Since, D > 0, the quadratic equation 4x 2 + 7x + 3 = 0 has two distinct real roots. 2x 2 + 5x + 3 = 0 Here, a = 2, b = 5 and c = 3 Now, D = b 2-4ac = (5) 2-4(2)(3) = 1 Since, D > 0, the quadratic equation 2x 2 + 5x + 3 = 0 has two distinct real roots. Step 5 3x 2 + 7x + 3 = 0 Here, a = 3, b = 7 and c = 3 Now, D = b 2-4ac = (7) 2-4(3)(3) = 13 Since, D > 0, the quadratic equation 3x 2 + 7x + 3 = 0 has two distinct real roots. Step 6 Thus, the quadratic equation 3x 2 + 6x + 4 = 0 has no real roots.

10 (12) c m ID : ph-10-full-year-10th-grade-review [10] Distance af ter which their steps match should be multiple of their steps. Also since we want to f ind the miniumum distance, the distance af ter which their steps will match f or the f irst time af ter starting the walk is equal to the LCM of the steps measured f or the three persons i.e 40, 65 and 85 cm. The LCM of 40, 65 and 85 is Thus, the number of steps af ter which their steps will meet f or the f irst time af ter starting the walk are 8840 cm. On converting centimeters to meters, answer will be 88.4 meters. (13) d We know that an irrational number can not be written in the f orm p q. If we look at all the options, we notice that can be written as, = = 25 = 25 1 Hence, is not an irrational number.

11 (14) a. 38 ID : ph-10-full-year-10th-grade-review [11] Let the ten's digit be x and unit digits be y, hence number of 10x + y Now it is given that y - x = 5 (1) and (10x + y) + (10y + x) = x + 11y = 121 x + y = 11 (2) On adding two equations, y - x + (x + y) = y = 16 y = 8 x = y - 5 = 8-5 = 3 Theref ore number is 38 (15) d. 1/3 Lets S = 4 sinθ - cosθ 4 sinθ + cosθ Now divide numerator and denominator of this f raction by cosθ S = S = S = (4 sinθ - cosθ)/cosθ (4 sinθ + cosθ)/cosθ (4 sinθ/cosθ - 1) (4 sinθ/cosθ + 1) (4 tanθ - 1) (4 tabθ + 1) Now replace 4 tanθ with is value (4 tanθ = 2) (2-1) S = (2 + 1) S = 1/3