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ICSE Class X Mid-term 2023 : Mathematics : Term test

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ICSE 2023 HALF YEARLY EXAMINATION MATHEMATICS Maximum Marks: 80 Time allowed. Two and half hours Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during first 15 minutes. This time is to be spent in reading the question paper. The time given at the head of this Paper is the time allowed for writing the answers. Attempt all questions from Section A and any four questions from Section B. 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 questions are given in brackets [] Mathematical tables are provided. SECTION A (Attempt all questions from this Section.) Question 1 Choose the correct answers to the questions from the given options: (i) [15] The SGST paid by a customer to the shopkeeper for an article which is priced at `.1500 is `.15. The rate of GST charged is: (a) 1.5% (b) 3% (c) 5% (d) 6% 1 of 10 (ii) When the roots of a quadratic equation are real and equal then the discriminant of the quadratic equation is: (iii) (a) Infinite (b) Positive (c) Zero (d) Negative If (z 1) is a factor of 2x2 cx 1, then the value of 'a' is : (a) 1 (iv) (v) (b) 1 (c) 3 (d) 3 Given (a) 2 x2 (b) 1x2 (c) 2x1 (d) 1x1 X The order of matrix X is : 57, 54, 51, 48, .........are in Arithmetic Progression. The value of the 8th term is: (a) 36 (b) 78 (c) 36 (d) 78 (vi) The point A (p, q) is invnrinnt about x p under re flection. The coordinates o f it s image A is: (a) A p, q) (b) A ( p, q) (c) A (p, q) (d) A ( p, q) 2 of 10 In the given diagram the AB C is similar to DEF by the axiom: SSS (b) SAS (c) AAA (d) RHS E A 18 cm F 24 cm (a) 4 cm (vii) B 3 cm (viii) The volume of a right circular cone with same base radius and height as that of a right circular cylinder, is 120 cm3. The volume of the cylinder is: (ix) (a) 240 cm3 (b) 60 cm3 (c) 360 cm3 (d) 480 cm3 The solution set for the given in equation is: 8 S 2z < 8, z e W (x) (a) {-4, -3, -2, -1, 0, 1,2, 3, 4} (b) (-4, -3, -2, -1} (c) {0, 1, 2, 3} (d) {-8, -7, -6, -5, -4, -3, -2, -1, 0, 1,2, 3, 4, 5,6 7, 8} The probability of the Sun rising from the east is P(S). The value of P(S) is: (a) P(S) = 0 (b) P(S) < 0 (c) P(S) = 1 (d) P(S) > 1 3 of 10 (xi) If The value of x is: (X11) (a) 2 (b) 3 (c) 4 (d) 5 The centroid of a ABC is G (6, 7). If the coordinates of the vertices A, B and C are (a, 5), (7, 9) and (5, 7) respectively. The value of x is: (X111) (a) 9 (b) 6 (c) 3 (d) 7 In the given diagram AC is a diameter of the circle and ADB=35 3S The degree measure of x is: (a) 55 (b) 35 (c) 45 (d) 70 4 of 10 (xiv) If the nth term of an Arithmetic Progression (A.P.) is (n + 3), then the first three terms of the A.P. are: (a) 1,2,3 (b) 2,4,6 (c) 4,5,6 (d) 7,8,9 (xv) The median of a grouped frequency distribution is found graphically by drawing: (a) a linear graph (b) a histogram (c) a frequency polygon (d) a cumulative frequency curve Question: 2 (i) Salman deposits `.1200 every month in a recurring deposit account for 2 years. If [4] the rate of interest is 6% per annum, find the amount he will receive on maturity. (ii) (iii) 3, 9, m, 81 and n are in continued proportion. Find the values of m and n. Prove that: cos A 1 -1- sin A = 2 secA 1 + sin A+ cos A [4] [4] Question 3 (i) The inner circumference of the rim of a circular metal tub is 44 cm. [4] 5 of 10 Find: (a) The inner radius of the tub (b) The volume of the material of the tub if it s outer radius is 8 cm. 2Z Use u = 7 Give your answer correct to three significant figures. (ii) [4] From the given figure: 4 3 2 1 1 (iii) 2 3 4 ' (a) Write down the coordinates of A and B. (b) If P divides AB in the ratio 2:3, find the coordinates of point P (c) Find the equation of a line parallel to line AB and passing through origin. Use graph sheet for this question. Take 2 cm = 1 unit along the axes. [5] Plot the OAB, where 0 (0, 0), A (3, 2), B (2, 3). (a) Reflect the OAB through the origin and name it as OA B . (b) Reflect the Od B'on the y axis rind name it as OA B . (c) Reflect the OA'B'on the x axis and name it as OA B '. (d) Join the points AA B B A A B B and give the geometrical name of the closed figure so formed. 6 of 10 SECTION B (Attempt any four questions from this Section.) Question 4 (i) The following bill shows the GST rates and the marked price of articles: [3] BILL: COMPUTERS Articles Marked price Rate of GST Graphic Card `. 15500.00 18% `.1900.00 28% Laptop adapter Find the total amount to be paid for the above bill. (ii) Solve the following quadratic equation , [3] 7x2 + 2x 2 = 0 Give your answer correct to two places of decimal (iii) The slope of line joining P(6,k) and Q (1- 3k, 3) is Find : i) k. ii) mid-point of PQ, using the value of k found in (i). . [4] Question 5 (i) A= and C= Evaluate AB - 5C 7 of 10 (ii) In the given figure, O is the centre of circle. The tangent PT meets the diameter RQ [3] produced at P. (a) Prove PQT ~ PTR (b) I f PT 6 cm, Q R 9 cm. Find the length o f PQ R (iii) Factorise the given polynomial completely, using Remainder Theorem: [4] 6x 3 -1- 25x 2 + 31x F 10 Question 6 (i) ABCD is a square where B (1, 3), D (3, 2) are the end points of the diagonal BD. [3] Find: (a) the coordinates of point of intersection of the diagonals AC and BD (b) the equation of the diagonal AC (ii ) In the given figure, AD = AE and AD2 = BD similar. B (iii) A D E . Prove that :triangles ABD and CAE are [3] C The first, the last term and the common difference of an Arithmetic Progression are [4] 98, 1001 and 7 respectively. Find the following for the given Arithmetic Progression: (a) number of terms n . (b) Sum of the n terms. 8 of 10 Question 7 (i)Find the equation of the line passing through the point of intersection of 7x + 6y = 71 and 5x 8y = -23; and perpendicular to the line 4x 2y = 1. [3] (ii)Mrs. Geeta deposited `.350 per month in a bank for 1 year and 3 months under the Recurring Deposit Scheme. If the maturity value of her deposits is `.5, 565; Find the rate of interest per annum. [3] (iii)In the given diagram, ABCD is a cyclic quadrilateral and PQ is a tangent to the [4] smaller circle at E. Given AEP 70 , BOC 110 . Find: (a) ECB, (b) BEC, (c) BFC, A (d) DAB, 70 0 E Question 8 (i) Solve the following inequation: D [3] Represent the solution set on a number line. 9 of 10 (ii) The work done by (x 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4)Days are in the ratio 3 : 10.find the value of X. (iii) [3] In the given diagram, ABC is a triangle and BCFD is a parallelogram.AD: DB = 4: 5 and EF = 15 cm. [4] Find: (a) AE : EC (b) DE (c) BC 15 cm Question 9 (i) Amit takes 12 days less than the days taken by Bijoy to complete a certain work. If [3] both, working together, takes 8 days to complete the work, find the number of days taken by Bijoy to complete the work, working alone. (ii) The line 4x-3y +12 = 0 meets x-axis at A. Write the co-ordinates of A. Determine the equation of the line through A perpendicular to 4x 3y + 12= 0. [3] (iii) P and Q have co-ordinates (0,5) and (-2,4). i) P is invariant when reflected in an axis Name the axis. ii) Find the image of Q on reflection in the axis found in (i) iii) (0,k) on reflection in the origin is invariant. Write the value of K. iv) Write the co-ordinates of the image of Q, obtained by reflecting it in the origin followed by reflection in x- axis. [4] Question 10 (i) Solve for x, using the properties of proportion. [3] = 3 (ii) Using ruler and compasses, construct a regular hexagon of side 4.5 cm. Hence [3] construct a circle circumscribing the hexagon. Measure and write down the length of the circum-radius. (iii) Five years ago, a woman s age was the square of her son s age. Ten years hence her age will be twice that of her son s age. Find : i) The age of the son five years ago. ii) The present age of the woman. [4] 10 of 10

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