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ICSE Class X Prelims 2026 : Mathematics

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Gitanjali Pacharne
Seventh Day Adventist English High School (SDA), Sanpada, Navi Mumbai
Isce 10th Sci6

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GRADE : X - ICSE MARKS : 80 PRELIM - 1 MOCK TEST TIME : 2hrs. SET A SUBJECT : MATHEMATICS Instruction: 1.Answer to this paper must be written on the paper provided separately. 2. You will not be allowed to write during first 15 minutes. 3. This time is to be spent in reading the question paper. 4. 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 (40 Marks) (Attempt all questions from this Section) Question 1 Choose the correct answers to the questions from the given options. [15] i) A shopkeeper bought a washing machine for Rs.20,000 from a dealer. He sold it to a consumer at a profit of Rs.5,000. If the rate of GST is 28%, then the tax liability of the shopkeeper is: a) Rs.1,400 b) Rs.700 c) Rs.650 d) Nil ii) A man deposited Rs.x per month for y years in a recurring deposit account. If at the time of maturity he got Rs.z as interest, then the total maturity amount is: a) Rs.(12xy + z) b) Rs.12xyz c) Rs.(xy + 12z) d) Rs. xyz 12 iii) I. Shares of company A, Paying 12%, Rs.100 shares are at Rs.80. II. Shares of company B, Paying 12%, Rs.100 shares are at Rs.100. III. Shares of company C, Paying 12%, Rs.100 shares are at Rs.120. Shares of which company are at premium? a) Company A b) Company B c) Company C d) cannot say iv) If x 2 and ax 2a, it means: a) a 0 b) a 0 2 c) either (a) or (b) d) neither (a) nor (b) 2 v) The equation x + 2x + 1 = (4 kx) + 3 will be a quadratic equation, if: a) k = 1 b) k 4 c) k 1 d) k = 1 vi) (x + 5) is a factor of the polynomial f(x) and (x 5) is the factor of g(x). If a polynomial h(x) is defined as h(x) = f(x) g(x), then the value of h(5) is: a) 5 b) 0 c) can t determined d) None of these vii) If A is a matrix of order 3 2 and B is a matrix of order 2 3, then: a) A + B is possible b) B + A is possible c) AB is possible d) Neither AB nor BA is possible. viii) If a line ax + by + c =0 is perpendicular to both the lines 4x ky +17 =0 and kx 9y +13 =0, then the value of k is, a) 6 b) 3 c) 3 d) 2 ... 2 ... ix) Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 : 1. If AB = 8 cm and BC = 6 cm then, the length of DE is a) 2 19cm b) 15 cm c) 3 17 cm d) 13 cm x) The locus of a point equidistant from two fixed points A and B in the same plane is the called _________. a) Straight line b) Angle c) Circle d) Perpendicular bisector xi) A tangent drawn from an external point P to a circle with centre O touches the circle at point Q and QOR is a diameter of the circle such that POR = 135 ,, then OPQ is a) 60 b) 45 45 c) 30 d) 90 90 2 2 xii) Assertion (A) : If x = 2 sin and y = 2 cos + 1, then the value of x + y is 3. 2 2 Reason (R) : For any value of , sin + cos = 1. a) (A) is true, (R) is false b) (A) is false, (R) is true c) Both (A) and (R) are true, and (R) is the correct explanation for (A). d) Both (A) and (R) are true, and R is incorrect explanation for (A). xiii) Assertion (A) : If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5 then the value of b is 18. Reason (R) a) b) c) d) : Mean = Sum of observations Total number of observations [1] (A) is true, (R) is false (A) is false, (R) is true Both (A) and (R) are true, and (R) is the correct explanation for (A). Both (A) and (R) are true, and R is incorrect explanation for (A). xiv) The capacity of a cylindrical vessel with a hemispherical por portion tion raised upward at the bottom as shown in the figure is a) 1 2 r [2h 3r] 3 b) 2 2 r [3h 2r] 3 c) 1 2 r [3h 2r] 3 d) None of these xv) A school has five houses A, B, C, D and E. A class has 23 students, 4 from house A, 8 from house B, 5 from house C, 2 from house D and the rest from house E. A single student is selected at random to be the class monitor. The probability that the selected student is not from houses A, B and C is: a) 4 23 b) 6 23 c) 8 23 d) 17 23 Question 2 2 i) Solve the equation 5x 3x 4 = 0 and give your answer correct ect to 3 significant figures. [4] ii) Monica had a R.D. Account in the Unio Union n Bank of India and deposited Rs.600 per month. If the maturity value of this account was Rs.24,930 and the rate of interest was 10% per annum; find the time (in years) for which the account was held. [4] ... 3 ... iii) On a map drawn to a scale of 1 : 40000, a rrectangular ectangular plot of land, ABCD has the following measurements AB = 6 cm and BC = 8 cm. Calculate [4] a) the diagonal distance of the plot (in km) 2 b) the area of the plot (in km ) Question 3 3 0 i) If A = and B = 0 4 a b 0 c , find a, b and c, when A + B = AB. [4] ii) Using ruler and compass only: [4] a) Construct a ABC ABC with BC = 6 cm, ABC = 120 and AB = 3.5 cm. b) In above figure, draw a circle with BC as diameter. Find a point P on the circumference of the circle ircle which is equidistant from AB and BC. c) Measure BCP. iii) If two points are A( 5, 5, 2) and B (1, 4), find a) mid-point of AB. c) slope of the perpendicular to AB. [5] b) slope of AB. d) equation of perpendicular bisector of AB. Section B(40 Marks) (Attempt any four questions from this Section) Question 4 i) Solve the following inequation and answer the questions given below 1 1 1 (2x 1) 2x + 5 +x 2 2 2 a) Write the maximum mum and minimum values of x for x R b) What will be the maximum and minimum value of x if x W ii) Which term of the A. P. 121, 117, 113 is the first negative term? 4 8 16 cos ec 4 sin 4 = 2 cosec sin . iii) Prove that: [3] [3] [4] Question 5 i) Given, x 3 12 x 2 6x 8 3 = y 2 27 y . Using componendo and dividendo find x : y. 9y 27 3 2 3 [3] 2 ii) When the polynomials x px + x + 6 and 2x x (p + 3) x 6 divided by (x 3), leave the same remainder. Find the value of p. [3] iii) A solid metallic cylinder has rradius adius 3 cm and height 5 cm. It is made of metal A. To reduce its weight, a conical hole is drilled in the cylinder, as shown and it is completely filled with a lighter metal B. The conical hole has a radius of 3/2 cm and its depth is 8/9 cm. Calculate the ratio of the volume of the metal A to the volume of the metal B in the solid. [4] ... 4 ... Question 6 i) Use the graph paper for this question. The points A(2, 3), B(4, 5) and C(7, 2) are the vertices of ABC. [5] a) Write down the co-ordinates of A , B , C . If A B C is the image of ABC, when reflected in the origin. b) Write down the co-ordinates of A , B , C . If A B C is the image of ABC, when reflected in the x-axis. c) Mention the special name of the quadrilateral BCC B and find its area. ii) From the top of light house 100m high the angles of depression of two ships are 48 and 36 respectively. Find the distance between the two ships to the nearest meter if. [5] a) The ships are on the opposite sides of the light house. b) The ships are on the same side of the light house. Question 7 i) Find the fourth vertex of a parallelogram ABCD, if the three consecutive vertices are A(10, 6), B(2, 6) and C( 4, 2). [3] ii) A mathematics aptitude test of 60 students was recorded as follows Marks Number of students 0-5 6 5-10 10 10-15 20 15-20 12 20-25 8 25-30 4 Using the above data, draw a histogram using a graph paper and locate the mode. iii) Mrs. Gupta bought following articles from a departmental store. Item [4] Quantity Rate per Item (Rs.) Discount GST rate Cosmetics 2 690 5% 18% Tea set 1 1500 10% 12% Shirts 4 1200 10% 12% Packed Dry fruits 4 800 25% 18% Food Grains 1 Find (a) Total amount of GST, 560 10% (b) Total bill amount. [3] NIL Question 8 i) Vivek invest Rs.4,500 in 8%, Rs.10 shares at Rs.15. He sells the shares when the price rises to Rs.30 and invests the proceeds in 12% Rs.100 shares at Rs.125. Calculate: [3] a) the sale proceeds. b) the number of Rs.125 shares, he buys. c) the change in his annual income from dividend. ii) If the mean of the following distribution is 24, find the value of a . Marks No. of students 0 10 10 20 20 30 30 40 40 50 7 a 8 10 5 [3] iii) Rs.7,500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs.100 more. Find the original number of children. [4] ... 5 ... Question 9 i) A vessel is in the form of an inverted cone. Its height is 11 cm and the radius of its top, which is open, is 2.5 .5 cm. It is filled with water up to the rim. When lead shots, each of 2 which is a sphere of radius 0.25 cm, are dropped into the vessel, of the water flows 5 out. Find the number of lead shots dropped into the vessel. [3] ii) A box contains cards bearin bearing g numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears [3] a) a number divisible by 5 b) an odd number less than 30 c) a composite number between 50 and 70. iii) In the figure, given alongside, PQ = QR, RQP = 68 ,, PC and QC are tangents to the circle with centre O. Calculate the values of (a) QOP (b) QCP. [4] Question 10 i) The product of first three terms of G.P. is 1000. If 6 added to its second term and 7 is added to its third term, erm, the terms become in A.P. Find G.P. [3] ii) Given a triangle ABC and D is a point on BC such that BD = 4 cm and DC = x cm. If BAD = C C and AB = 8 cm, then, [3] a) prove that triangle ABD is similar to triangle CBA. b) find the value of x . iii) Use graph paper for this question. The marks obtained by 120 students in an English test are given below: Marks Number of students 0-10 5 10-20 9 20-30 16 30-40 22 40-50 26 50-60 18 60-70 11 70-80 6 80-90 4 90-100 3 Draw the Ogive and hence, estimate: a) the median marks. b) the number of students who did not pass test if the pass percentage was 50. c) the upper quartile marks. Best of Luck [4]

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