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ICSE Class X Mid-term 2023 : Mathematics

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THE HERITAGE SCHOOL FIRST TERM EXAMINATION 2023-2024 MATHEMATICS CLASS X Maximem Marks 80 Time Teo and half hours Answers lo this paper mua he writlen on the paper provided separately You will not be allowed to write dring first 15 minutes. This time is to he spent in reading the question paper Ts lime ghen at the heud of this Paper is the allowedfor writng the anwers Aitempt all questionsfrom Section Aand any fourquestions from Section B. A working, including rough work, mst be clearty shown, and must be done on the same sheet as the rest of the answer. Omission ofessential working will result in loss of marks. The intended marks for questions orparts of questionsare given in brackets I/ This question paper comsists of 4sided printed pages SECTION A (40 Marks) (Attempt all questions from this Section) Question 1 [15] Choose the correct answers to the questions from the pven options (Do not copy the questions, write the correct answers only) () If imran opened arocurring deposit acoount in a bank and depositcd Rs 800 per month for 12 years, then the total money deposited in the account is (a) Rs I I400 (C) Rs L3680 (b) Rs 14400 (d) 13860 IfxER, the solution set of 6S-3(2x - 4) <12 is (b) (xx ER, 0Sx<1) (a) (xxER,0<xS1) (d) (x: xER,0K<11 (c) [0, 1 (H) Which of the fotfowing is not a quadratic eqution ? (a) (x+2y2(x+3) (b) x+3x-1X1-3x) (d)x2x+1 (x+1) (c) (x+2)x-)--2x-3 (iv) On dividing 4x 3x + 5 by x+2, the remainder is -3 then the value ofkis (a) 4 (V) (d) -3 (c)3 The mcan proportion betwccn and 128 is (a) 64 (v) (b) -4 IfA (a) A (b) 32 (c) 16 (d) 8 (c)l (d) 2A then A' (b) O (vii) Ifthe common difference of an AP. is 5, then ay- y is (a) 5 (d) 30 (c) 25 (b) 20 (vi)) The l1 tern of theG.P-2,-1,.. is (a) 64 (N) (b) -64 (c) 128 (d) -128 Which of thefollowing point is invariat with respect to the ltne y -27 (a) (3.2) (b)(3,-2) (c) (2, 3) (d)(-2, 3) The point which divides the line segment joining the points (7, -3) and ( 3, 4) in the ratio I:2 internally lies in the (a) Ist quadrant (b) Tind quadrant (c) 1Mird quadrant This Paper Consists of 4 Printed Pages (d) IVih quadrant The slope of the line i perpenicular to the line passes through the points (0, 6) and (7. 3) is ASmBte amgle ofa right angle then the value of Sin A cos(90- A) t cos Asim (90- A)triangle, s (b)2sin Acos A ()1 () ZsinA the lengrth of the shadow ofa tower is v3 times that of its height, the sun iS then the angle of elevation of (a) 15 (bi30 (c45 60 (V) the classes of a frequency distrnbution are 1-10,(d)11-20, class is 21-30.. S1-60, then the size of cach (a)9 ( (b) 10 (XV) Tbe peobability that a (c) 11 non-lcap year sclected at random has 53 Sundays is Question2. Mr Mehra opened a deposit acoount in a bank He deposited Rs 2.500 per two years At the timerecurring of maturity, he got Rs month for 67,500. Find (a) Total interest earmed by Mr. Mehra? (b) The rate of interest per ? annum The sum of the first n terms of the progression -30, -24.-18, -12,... is 540. Find the value of n?4] na school, the weekly pocket money of [41 50 students is as follows: 40-50 ( Weekly pocket 50-60 60-70 70-80 12 14 TmOney (Rs) No of Students 2 80-90 90-100 Draw the histogram and find its mode 4] Question 3. () A card is drawn from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (a) A black card (b) Neither king nor a qucen (c) A king card (d) A card of club or an ace (0) (ii1) 41 Aman observes the angle of elevation of the top ofa to be 30. He walks towards it in a horizontal line through its base. On covering 40 m, thebuilding angle of clevation changes to 45 . Find the height of the building corect to the nearest metre (use v3 1732) [4] Plot A(2, 1), B(5. 2) and C(3, 3) on the graplh paper to fom AABC (a) Write downthe coordinate of A', B, is reflected in x-axis (b) Write down the coordinate of A, B",CifAABC C ifAABC is reflected in the origin, (C) Write the name of the figure ACCA' (d) Find the equation of the line BB". (Page 2) SECTIONB(40 Marks) (Attempt any four questions from this Section) Question 4 (0) 6 is the mean proportion between two numbers x and y, and 48 is the third proportional of x and [31 y. Find the numbers. If the line joining A(4,-5) andB(4,5) is divided by the point Psuch that AB =Find the (i1 |3) coordinates of P. In a school , students are arranged in rows. If 100 students are in the first row, 96 are in the (iii) second row, 92 are in third row and 24 in the fast row, find (a) Total nunber of rows? [41 (b) Total nunber of students ? Question 5 When divided by x-3,the polynomialsx-px +x+ 6and 2x-x-(p+ 3)x - 6leave () () the same reminder. Find the value of p. sin A 1+cos A Prove the following identity: 1+cos A sin A (ii) Given A- .8- C-5 [3) 2 coscc A [3) and BA = C .Find the values of pand q. 4] Question6 Find the equation of the line with x-intercept () (ii) 6 and passing through the point (4,-7) 31 From the top of 200 m bigh ighthouse the angle of depression of two ships on opposite sides of it are 45 and 30 respectively. Find the distance between the two ships. (use v3 = 1.732) A positive number is divided into two parts such that the sum of the squares of the two parts is (iii) (31 208. The square of the larger part is 18 times the smaller part. Taking xas the smaller part of the two parts, find the value of x and hence the larger part of that number. (41 Question 7 (6) Solve the following inequation and represent the solution set on the number line, 2x-5<5x +4<11, where xis set of integers. 31 Find the coordinates of the points Aand B where the line 5xty- 10 cuts the x-axis and y-axis (iii) respectively. Hence, find the coordinates of the midpoints of AB. Two different dice are thrown simultaneously. What is the probability that the sum of two [31 numbers appearing on the top of thedice is (a) 8? (b) at least 11? (c) 14? 14] Question 8 Solve the following cquation : x x =6. Give your answer corect to two significant figures. 3) () (ii1) Prove that (sin A-os AXtan A t cot A) - sec A-cosec A (31 The 4, 7 and the last terms of ageometric progression are 10,80 and 640 respectively. Ifthe common ratio is positive , find the first term, common ratio and the number of terms of the progression. [4] (Page 3) Question9 The cquation of a line 2x+3y-7-0. find (a) slope of the line. (D) the equation of a line perpendicular to the piven line and passing through the intersection of the lines x-y+2-0 and 3xty-10-0 (1) 51 The table bclow shows the distribution of the scores obtained by 120 shooters in a shootns competition. Usinga graph sheet, draw an ogive for the distribution. Scores 0-10 obtained 10-20 20-30 30-40 40-50 50-60 60-70 No of 10 1S 23 25 19 12 shooters 70-80 80-90 90-100 3 4 (a) Use the ogive curve to estimate the median (b) Find the number of shooter who obtained more than 75%7 Question 10 () () Ifx =Var-VaT' using properties of Given proportion, show thatx-2ax +1=0 [3) (cosec 30 o tan45 1 Ltan 60 sect601X lawrite (a) the order ofmatrix X (b) the matrix X (ii1) [31 The weights of 50 apples were recorded as given below. Calculate the mean weight by step deviation method. [41 Weight 70-75 (gm) No of apples 5 75-80 80-85 85-90 90-95 95-100 100-105 105-110 9 3 8 4 3 (Page 4)

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