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GRADE X MATHEMATICS REVISION PAPER Attempt all questions All working, including rough work, must be clearly shown and must be done on the same sheet as the rest of the answer. Omission of essential working will result in loss of marks. The intended marks for questions or parts of question are given in brackets [ ] Mathematical tables are provided. Question 1 Choose the correct answers to the questions from the given options: (i) For an intrastate transaction, marked price is 15,000, discount = 30%, GST = 18%, the amount of CGST is equal to (a) (ii) 1,890 (b) 945 (c) 10,500 (d) 11,445 Hritika deposited 1500 per month for 2 years in a Recurring Deposit Account. On maturity, she received 38,000. The interest received by her is (iii) (a) 2,000 (b) 1,500 (c) 2,500 (d) 3,000 Statement 1: When each term of an inequation is multiplied or divided by the same positive number, the sign of inequality remains the same. Statement 2: If both sides of an equation are positive or both negative, sign of inequality changes when their reciprocals are taken. (iv) (a) Both statements are correct (b) Both statements are incorrect (c) Only statement 1 is correct (d) Only statement 2 is correct The value of y which satisfies the equation (y + 5) (y 5) = 24 will be (a) (v) Given matrix (a) (vi) 7 1 1 (b) 4 sin 30 [ cos 0 (b) 1 x > 11 (d) 1 cos 0 4 ] and B = [ ]. If AX = B. then the order of matrix X is 4 sin 30 5 2 2 If 7x 77, then the value of x will be (a) (c) 7 (c) 1 2 (d) 2 1 (vii) (b) x > 11 (c) x 11 (d) x 11 The arithmetic mean of 5 and 41 is (a) (viii) 13 (b) 6 (c) 12 (d) 18 A die has 6 faces marked by the given numbers as shown below: The die is thrown once. The probability of getting the square root of 4 is 1 (a) (ix) 3 (b) 2 3 (c) 1 2 (d) 1 6 The height of a circular cylinder is 20 cm and the radius of its base is 7 cm, then the volume will be 3,800 cm3 (a) (x) (b) 3,880 cm3 (c) 3,080 cm3 (d) 3,380 cm3 Two chords, AB and CD of a circle meet at a point O, outside the circle. It is given that AB = 7 cm, CD = 4 cm, and OB = 5 cm. What is the length of OD? (xi) (a) 4 cm (b) 5 cm (c) 6 cm (d) 7 cm If one dividing 2x3 + 3x2 kx + 5 by x 2, leaves a remainder 7, then the value of k is (a) (xii) 13 If A = [ (a) (xiii) (xiv) (b) 1 3 ], then A2 = 3 4 15 15 [ ] (b) 15 25 7 [ 10 15 ] 15 25 (c) 3 (c) [ 5 15 ] 15 25 (d) 17 (d) [ 0 15 ] 15 25 The image of the point A (5, 3), under reflection in the point P ( 1, 3) is (a) ( 7, 9) (b) (7, 9) (c) ( 7, 9) (d) (7, 9) For a given A.P., If S1 = 9, S2 = 29 S3 = 57, then the common difference is equal to (S = Sum of the given terms) (a) (xv) 20 cos 1 +sin (a) (b) 10 (b) cos A (c) 10 (d) Indeterminate + tan A = sin A (c) cosec A (d) sec A Page 2 of 6 Question 2 (i) A solid metallic sphere of radius 6 cm is melted and made into a solid cylinder of height 32 cm. Find the: (ii) (a) radius of the cylinder. (b) curved surface area of the cylinder. (Take = 3.1). In a mathematics test, 90 students obtained the marks (out of 100) given in the following table: Marks 1-20 20-40 40-60 60-80 80-100 8 12 38 20 12 No. of Students Find the probability that a student obtained: (a) less than 40 marks. (b) more than 59 marks. (c) between 39 and 80. (d) 100 marks, (iii) In the given figure, CE is a tangent to the circle at point C. ABCD is a cyclic quadrilateral. If ABC = 93 and DCE = 35 . Find: (a) ADC (b) CAD (c) ACD Question 3 (i) In ABC, ABC = DAC, AB = 8 cm, AC = 4 cm, AD = 5 cm. (a) Prove that ACD is similar to BCA. (b) Find BC and CD. (i) Shahrukh opened a recurring deposit account in a bank and deposited 800 every month for 18 months. If he received 15,084 at the time of maturity, find the rate of interest per annum. (ii) Use graph paper for this question. The points A (2, 3), B (4, 5), and C (7, 2) are the vertices of ABC. (a) Write down the coordinates of A , B , and C , if A B C is the image of ABC, when reflected in the origin. (b) Write down the coordinates of A , B , and C , if A B C is the image of ABC, when reflected in the x-axis. (c) Mention the geometrical name of the quadrilateral BCC B and find its area. Page 3 of 6 Question 4 (ii) Prove that 2 + 2 = tan A + cot A (iii) In a certain A.P. 32th term is twice the 12th term. Prove that 70th term is twice the 31st term. (iv) A and B are two points on the x-axis and y-axis, respectively. If P (2, -3) is the midpoint of AB, then find the: (a) The coordinates of A and B. (b) Slope of line AB. (c) Equation of line AB. Question 5 (i) A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weights, a conical hole is drilled in the cylinder. The conical hole has a radius of 1.5 cm and its depth is 8 9 cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape. (ii) Find the value of a for which the following points A (a, 3), B (2, 1), and C (5, a) are collinear. Hence, find the equation of the line. Consider only the positive value of a . (iii) From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30 and 60 , respectively. If the height of the building is 10 m, then find the distance between A and B correct to two decimal places. Question 6 3 + 12 = 3 + 27 (i) Given (ii) The following table gives the weekly wages of workers in a factory: 6 2 + 8 9 2 + 27 . Using componendo and dividendo find x : y. Weekly wages 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 No. of Workers 5 20 10 10 9 6 12 8 Use graph paper for only (c). Take scale 2 cm = 5 on one axis and 2 cm = 10 workers on the other. Calculate: (a) the mean by step-deviation method. (b) the modal class. (c) the number of workers getting 65 or more but less than 85 as weekly wages. Page 4 of 6 Question 7 (i) Find the ratio in which the line joining (2, 2) and (3, 7) is divided by the line 2x + y = 4. (ii) Solve the following inequation and represent the solution on the number line: 3 + x (iii) 8 3 +2 14 3 + 2x, x I In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and CBD = 32 . Find: (a) OBD (b) AOB (c) BED Question 8 (i) In the adjoining figure if DAB = 60 and ACB = 70 , find the measure of DBA. (ii) Find a if the two polynomials ax3 + 3x2 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3. (iii) A positive number is divided into two parts, such that the sum of the squares of the two numbers is 208. The square of the larger part is 18 times the smaller part. Taking x as the smaller part of the two parts, find the number. Question 9 2 + 2 1 (i) Prove that: (ii) The given numbers A + 3, A + 2, 3A 7 and 2A 3 are in proportion. Find A . (iii) A shopkeeper buys a printer at a discount of 30% on the marked price of 8,000. He sells 2 = tan2A the printer to a customer at marked price. GST charged at each stage is 18%. If the sales are intra-state, find: (a) The GST paid by the shopkeeper to the Central Government. (b) The price paid by the shopkeeper for the article inclusive of tax. (c) The price paid by the consumer. (d) The amount of tax received by the State Government. Page 5 of 6 Question 10 (i) For what value of K will the following quadratic equation: (K + 1) x2 4Kx + 9 = 0, have real and equal roots? Solve the equation. (ii) Using ruler and compass only, draw a circle of radius 4 cm, Mark a point P at a distance of 6 cm from the centre of the circle drawn. Draw two tangents PA and PB to the given circle and measure the length of each tangent. All traces of constructions must be visible. (iii) Use graph paper for this question. A survey regarding height (in cm) of 60 boys belonging to class X of a school was conducted. The following date was recorded. Height (cm) 135-140 140-145 145-150 150-155 155-160 160-165 165-170 No. of boys 4 8 20 14 7 6 1 Taking 2 cm = height of 10 cm along one axis and 2 cm = 10 boys along the other axis draw an ogive of the above distribution. Use the graph to estimate the following: (a) The median. (b) Lower quartile. ******************* Page 6 of 6
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