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Maths mock test

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ICSE MATHEMATICS MOCK TEST PAPER 2 SECTION A Attempt all Questions from this Section [Marks 40] Mathematics [M.M:80] 2 Hrs Class - X Note: Attempt all the questions from Section A and any four questions from Section B. The intended marks for questions or parts of questions are given in bracket [ ]. SECTION A [40 Marks] [ Answer all questions from this Section.] 1. (a) An article is marked at Rs 500. The wholesaler sells it to a retailer at 20% discount and charges sales-tax on the remaining price at 12.5%. The retailer, in turn, sells the article to the customer at its marked price and charges sales-tax at the same rate. Calculate : (i) The price paid by the customer. (ii) The amount pf VAT paid by the retailer. (b) Aryan and Divyanshu each lent the same sum of money for 2 years at 8% simple interest And compound interest respectively. Divyanshu received Rs 64 more than Aryan. Find the money lent by each and interest received. (c) Find the value of k for which the following equation has equal roots : (k 12)x2 + 2(k 12)x + 2 = 0 [3, 4, 3] 2. (a) Solve the inequation 3 x 4 x + 2, x R and plot the graphs of their solution sets 2 3 (b) What number must be substracted from 23, 40, 57 and 108 to make them in proportion ? (c) Without using trigonometrical table, prove that cos 70 cos 55 cosec 35 + = 2. sin 20 sin 55 sec 35 [4, 3, 3] 0 1 5 3. (a) If A = 4 3 , B = 6 and 3A M = 2B, find matrix M. (b) Find the median of 92, 35, 67, 85, 72, 81, 56, 51, 42, 69. If 35 is replaced by 58. Find the new median. (c) Use a graph paper for this question (Take 1 cm = 1 unit on both the axes). Plot the points A ( 2, 4), B (2, 1), C( 6, 1). (i) Draw the line of symmetry of ABC. 2 ICSE X MATHEMATICS (ii) Mark the point D if the line in (i) and the line BC are both lines of symmetry of the quadrilateral ABCD, write down the co-ordinate of the point D. (iii) Name the figure ABCD. (iv) Write down the equations of BC and the line of symmetry named in (i) [3, 3, 4] 4. (a) Find the money Mr. Gupta should deposit 3 years at 5% p.a. in a recurring deposit account to get Rs 1551 after this period. (b) In right ABC , B = 90 , AB = 28 cm and BC = 21 cm. A semicircle is drawn with AC as diameter and a quarter circle is drawn with BC as radius. Calculate the area of the shaded portion, correct to two places of decimal. A B C (c) The areas of two similar triangles are 169 cm2 and 121 cm2 respectively. If the median of first triangle is 13 cm. Find the length of corresponding median of the other. [3, 4, 3] SECTION-B [Answer any four question from this section.] 5. (a) Mr. Rishi sold a certain number of Rs. 20 shares paying 8% dividend at par and invested the proceeds in Rs. 10 shares, paying 12% dividend at 10% premium. If the change in his annual income is Rs 128, Find the number of shares sold by Mr. Rishi. (b) ABC is an isosceles triangle with AB = AC and D is a point on AC such that BC2 = AC AD. Prove that BD = BC. (c) In given figure, A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides. Find the radius of the inscribed circle and the area of the shaded part. [4, 3, 3] A B C 6. (a) Point (3, 0) and ( 1, 0) are inveriant points under reflection in the line L1. Point (0, 3) and (0, 1) are invariant points on reflection in the line L2. (i) Recognize the lines L1 and L2. (ii) Write down the images of the points P(3, 4) and Q( 5, 2) on reflection in the line L1. Name the image as P and Q respectively. MOCK TEST PAPER 2 3 (iii) Write down the co-ordinates of the images of P and Q on reflection in L2. Name the images as P and Q respectively. (iv) Name the single reflection that maps P onto P . (v) Find the area of the triangle PP P . (b) In the given figure, QAP is the tangent at point A and C PBD is a straight line. D If ACB = 36 and APB = 42 , find : (i) BAP , (ii) ABD (iii) QAD (iv) BCD 1 B is the solution of the equation (kx + 1) (k + 5 2) x + 1] = 0, find the value of k . [4, 3, 3] P A Q 3 2 7. (a) Show that 2x + 7 is the factor of 2x + 5x 11x 14. Hence, factorise the given expression completely, using Factor Theorem. (b) A page from the saving bank passbook of Ms. Shalini shows the following entries. Complete the table and find the interest for the period January to December at the rate of 4.5% p.a. (c) If x = Date Particular Withdrawals (In Rs.) Deposit (In Rs.) Balance Jan.1 March.7 March. 10 July. 17 Oct.5 Dec. 19 B/F By Cheque By Cash By Cheque By Cheque To Cheque 3250.00 1340.00 1875.00 625.00 2160.00 7500.00 [5, 5] 8. (a) A parachutist is descending vertically and makes angles of depression of 45 and 60 at two observation points 100 m apart from each other on his left. Find the maximum height from which he fall and the distance between the point where he fall on the ground and the first observation point. (b) Prove that the points ( 2, 1), (2, 2) and (5, 2) are the vertices of right angle triangle. (c) Prove that sin A 2 sin 3 A 2 cos3 A cos A = tan A [4, 3, 3] 9. (a) Find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the line joining (6, 8) and ( 3, 2). (b) Construct an angle AOB , in which AC = 5 cm, BC = 7 cm and AB = 6 cm. (i) Mark D, the mid point of AB. (ii) Construct the circle which touches BC at C, and passes through D. a b (c) If cos + sin = a and cos sin = b, prove that tan a+b [3, 4, 3] 4 ICSE X MATHEMATICS 10. (a) A bucket is raised from a well by means of rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascents in 1 min 28 sec with a uniform speed of 1.1 m/s. Calculate the number of complete revolution the wheel makes in raising the bucket. (b) The marks obtained by 120 student in Mathematics test is given below : Marks 0-10 No. of 5 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 9 16 22 26 18 11 6 4 3 Draw an Ogive for the given distribution on a graph sheet. Use a suitable scale for your Ogive. Use your Ogive to estimate : (i) The median; (ii) The lower quartile. (iii) The number of the students who obtained more than 75% in the test. (iv) The number of the students who did not pass in the test if the pass percentage was 40. [4, 6] 11. (a) Construct a quadrilateral ABCD, having given AB = 2.6 cm, BC = 4.0 cm, CD = 3.2 cm, AD = 2 cm and diagonal BD = 3.6 cm. Mark a point P on diagonal AC, equidistant from B and C (b) Find p, q, r in the figure given if p q r = = 2 5 6 B q P C A P D r Q (c) A line 4x 3y + 12 = 0 meets x-axis at A. Write co-ordinates of A and determine the equation of the line through A and perpendicular to 4x 3y + 12 = 0

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