Sample Question Paper Mathematics First Term (SA  I) Class X. Time: 3 to 3 ½ hours


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1 Sample Question Paper Mathematics First Term (SA  I) Class X Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided into four sections A, B, C and D. Section A comprises of 8 questions of 1 mark each, section B comprises of 6 questions of 2 marks each, section C comprises of 10 questions of 3 marks each and section D comprises of 10 questions of 4 marks each. (iii) Question numbers 1 to 8 in section A are multiple choice questions where you have to select one correct option out of the given four. (iv) There is no overall choice. However, internal choice has been provided in 1 question of two marks, 3 questions of three marks each and 2 questions of four marks each. You have to attempt only one of the alternatives in all such questions.
2 SECTION A Question numbers 1 to 8 carry 1 mark each. For each question four alternative choices have been provided of which only one is correct. You have to select the correct choice Q. 1 Ans : (B) Q. 2 (A) a = 2, b = 5 (B) a = 5, b = 2 : (C) (D) a = 2, b = Solution :
3 Q. 3 In the given figure, if (A) 3 cm (C) 4 cm (B) 6 cm (D) 6.7 cm Solution : In the given figure, Q. 4
4 Q. 5
5 Q. 6 (A) an even prime number (C) an odd prime number (B) an even composite number (D) an odd composite number Q. 7 The number of solutions of the pair of linear equations x 2y 8 0 and 2x 4y 16 is : (A) 0 (B) 1 (C) infinitely many (D) 2
6 Q. 8 If the mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is : (A) 4 (B) 7 (C) 11 (D) 6 SECTION B Question numbers 9 to 14 carry 2 marks each : Q. 9 Find the zeroes of the quadratic polynomial
7 Q. 10 Without using trigonometric table, evaluate Q. 11 In the figure
8 Q. 12 Given that the HCF(306, 657) = 9, find HCF (306, 657) = 9 Q. 13 In triangles PQR and MST
9 Q. 14 Write the following distribution as less than type cumulative frequency distribution: C.I Frequency OR In a frequency distribution, the mode and mean are 26.6 and 28.1 respectively. Find out the median. Class interval Cumulative frequency less than 10 5 = 5 less than = 8 less than = 12 less than = 15 less than = 18 less than = 22 less than = 29 less than = 38 OR Mode = 26.6, Mean = 28.1 SECTION C Question numbers 15 to 24 carry 3 marks each.
10 Q. 15 Use Euclid s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m OR Consider the number, where n is a natural number. Check whether there is any value of for which ends with the digit 0 Let n be a positive integer. Taking a = n and b = 3 in Euclid s division lemma OR If the number, for any n, were to end with the digit zero, then it would be divisible by 5. That is, the prime factorisation of would contain the prime 5 This is not possible because
11 Q. 16 Solve for x and y: OR For what value of k, will the following system of equations have infinitely many solutions? OR
12 The given system of linear equations is Q. 17 On dividing by a polynomial g(x ), the quotient and remainder were respectively. Find g(x)
13 Q. 18 Prove that
14 Q. 19. Find the length of PQ and PR
15 Q. 20 Use Euclid s algorithm to find the HCF of 96 and 60. Q. 21 In an isosceles triangle ABC with AB = AC, E is a point on side CB produced. If, prove that
16 Q. 22 is right angled at B. AD and CE are the two medians drawn from A and C, respectively. If AC = 5 cm, find the length of CE In right triangle ABD, right angled at B
17 Q. 23 The mean of the following frequency distribution is 52. Find the missing frequency. C.I Frequency F C.I Frequency Class Mark f 45 45f = 33 + f
18 Q. 24 Find the mean of the following frequency distribution using assumed mean method: Classes Frequency OR 200 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows No. of letters No. of surnames Find the median. Classes Frequency Class Mark OR No. of letters No. of surnames Cumulative frequency n = 200
19 SECTION D Question numbers 25 to 34 carry 4 marks each. Q. 25 Find all the zeroes of the polynomial if its two zeroes are
20 Q. 26 In the given figure, in and XY divides the into two regions such that. OR Two poles of height p and q metres are standing vertically on a levelled ground, a metres apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by.
21 In the given figure
22 OR Let the height of two poles AB and CD be p and q respectively. The height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is EF i.e. x
23 Q. 27 OR Prove the identity OR
24
25 Q. 28 In an acute angled
26 Q. 29 Draw the graphs of the following equations: x + y = 5, x y = 5 (i) Find the solution of the equations from the graph. (ii) Shade the triangular region formed by the lines and the yaxis
27 (i) The two straight lines intersect each other at the point A(5, 0) (ii) The region bounded by the two lines and the y axis is shaded in the graph
28 Q. 30 If the median of the following data is 525, find the values of x and y if the sum of the frequencies is 100 Class interval Frequency x y C.I Frequency Cumulative frequency x y n = 100
29 The sum of the frequencies = 100
30 Q. 31 Prove that is irrational Solutin: Let us assume to the contrary, that Q. 32 State and prove Pythagoras theorem Pythagoras Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Given:
31
32 Q. 33 The following table shows the marks obtained by 100 students of class X in a school during a particular academic session. Find the mode of this distribution. Marks Number of students less than less than less than less than less than less than less than less than less than Class Cumulative Frequency Interval Frequency Total 100
33 Q. 34 Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other they meet in 1 hour. What are the speeds of the two cars? Let X and Y be two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of y be y km/hr Case I : When two cars move in the same direction: Let these cars meet at point C. Distance travelled by car X = AC and distance travelled by car Y = BC Two cars meet in 5 hours.
34 Case II : When two cars move in opposite direction: Let these cars meet at point D. Distance travelled by car X = AD Distance travelled by car Y = BD Two cars meet in 1 hour. Hence, speed of car X is 60 km/hr and speed of car Y is 40 km/hr
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