MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS)

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MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS) SECTION A 1x4=4 1. Find the number of zeros in the following fig. 2. 3. If 4c

4=8 1. Explain why 7 11 13 + 13 is composite number. 2. On comparing the ratios, find out whether the following pair of linear equation is consistent, or inconsistent.

1 MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS) SECTION A 1x4=4 1. Find the number of zeros in the following fig If 4cotA = 3, find tan A. 4. If the less than type ogive and the more than type ogive intersect at (20, 35),find median. SECTION B 2x4=8 1. Explain why is composite number. 2. On comparing the ratios, find out whether the following pair of linear equation is consistent, or inconsistent. 3x + 2y = 5 ; 2x 3y = Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. 4. The marks obtained by 30 students of Class X of a certain school in a Mathematics paper consisting of 100 marks are presented in table below. Find the mean of the marks obtained by the students.

SECTION C 1. Find a quadratic polynomial, the sum and product of whose zeroes are 3 and 2, respectively. 2. Solve the following pairs of equations by reducing them to a pair of linear equations: 2x+3y=6, 3x+2y=5 3.

The following table shows the ages of the patients admitted in a hospital during a year: 3x6=18 Find the mode of the data given above. SECTION D 1. Prove that 5 is an irrational number. 2.

2 SECTION C 1. Find a quadratic polynomial, the sum and product of whose zeroes are 3 and 2, respectively. 2. Solve the following pairs of equations by reducing them to a pair of linear equations: 2x+3y=6, 3x+2y=5 3. Find geometrically Sin30 0. cos Evaluate: sec 30 + cosec If tan (A + B) = 3 and tan (A B) = 1 ; 0 < A + B 90 ; A > B, find A and B The following table shows the ages of the patients admitted in a hospital during a year: 3x6=18 Find the mode of the data given above. SECTION D 1. Prove that 5 is an irrational number. 2. Draw the graphs of the equations x y + 1 = 0 and 3x + 2y 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region. 3. Prove Basic Proportionality theorem. tan α cot α 4. Prove that, + = 1 + sec α.cosecα. 1 cotα 1 tan α 5. 4x5=20

3 ANSWERS: Section A Not similar 3. 4/ Section B 1. 7 x Consistent cm Section C 1. x 2 + 3x x= 3/5, y=8/5 3. to find. 4. (3 2-6)/8 5. A=45 0, B= Mode=36.8 yrs Section D 1. To prove. 2. Vertices of triangle (-1,0),(4,0),(2,3) 3. To prove. 4. To prove. 5. Write less than type CF, & draw the ogive

BRAHMAGUPTA GROUP COMMON QUESTIONS FOR SA1 SECTION A (1X4=4) Q.1 Evaluate cos 48 0 sin 42 0 (Ans. 0 ) Q.2 Find the relation among mean, median and mode. (Ans. Mode = 3median - 2mean ) Q3.

4 BRAHMAGUPTA GROUP COMMON QUESTIONS FOR SA1 SECTION A (1X4=4) Q.1 Evaluate cos 48 0 sin 42 0 (Ans. 0 ) Q.2 Find the relation among mean, median and mode. (Ans. Mode = 3median - 2mean ) Q3. Find the number of zeros. (Ans. 4) Q.4 Whether the given triangles are similar or not. If yes, mention the criteria of similarity. (Ans. Yes, SAS) SECTION B (2 X 4=8) Q.5 Find a quadratic polynomial if sum of zeros is 4 and product of zeros is 1. Q6. In the given figure DE II BC. Find EC

5 (Ans. 2) Q.7 The H.C.F of 306 and 657 is 9. Find their L.C.M. (Ans ) Q8. Check whether 4 n can end with the digit 0 for any natural number n. SECTION C (3 X 5=15) Q.9 If Tan (A+B) = 3 and Tan (A-B) = 1 3, 0 < A+B 90; A>B, find A and B (Ans. A=45 0, B=15 0 ) Q.10 If sinθ = 3 5, find cosθ x tanθ (Ans. 3 5) Evaluate (Ans ) Q.11 Prove that sin 45 = 1 2 geometrically. Q.12 Solve the following pair of linear equations Q.13 Find the zeros of the quadratic polynomial OR sin30 + tan 45 cosec 60 sec 30 + cos 60 + cot 45 3x + 4y = 10 2x 3y = 2 (Ans. x=2, y=1) X 2 + 7x +10 and verify the relationship between the zeros and coefficients. (Ans. 5 and 2) Q.14 Prove that 5 is an irrational number. SECTION D (4 X 6 =24) Q.15 Solve the pair of linear equations by graphical method.

6 x + 3y = 6 and 2x 3 y = 12 (Ans. x=6 and y=0) Q.16 Prove that in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. Q.17 Thirty women were examined in a hospital by a doctor and the number of heart beats per minute where recorded and summarised as follows. Find the mean heart beats per minute for these women choosing a suitable method. Number of heart beats per minute Number of women (Ans. 75.9) Q.18 The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Expenditure (in rupees) Number of families (Ans. Rupees ) Q.19 The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution Classes No. of shops Draw a less than type ogive for the given data.

7 COMMON QUESTIONS FOR FA-1 GROUP- C SUB: MATHS CLASS - X SECTION- A (1 X 4=4 MARKS) POLYNOMIAL 1. Find the number of zeroes from the graph. [ans:4] TRIANGLE 2. Whether the given triangles are similar or not. If yes, mention the criteria of similarity. (Ans. Yes, SAS) TRIGONOMETRY

8 3. Evaluate tan 26 0 /cot 64 0 [ans:1] STATISTICS 4. Write the relation between mean, median, mode. [3median= mode+2 mean] SECTION- B (2 X 4=8 MARKS) REAL NUMBERS 5. Given that HCF(306,657)=9. Find LCM of (306,657). [ans:22338] POLYNOMIAL 6. Find a quadratic polynomial where sum and product are given as (1/4,-1). [ans: 4x 2 -x-4] TRIANGLE 7. in the given figure, DEIIBC. Find EC. [ans:2cm] TRIGONOMETRY 8. If A,B,C are interior angles of a triangle ABC, then show that sin (B+C/2)=cos A/2 POLYNOMIAL SECTION-C (3 X 6=18 MARKS) 9. On comparing the ratios a1/a2, b1/b2 and c1/c2. find out whether the given equations are consistent or inconsistent. If consistent, find the nature of the solution. 3x +2y=5 2x -3y =7 [ans: consistent and unique soln.] 10. Solve the pair of linear equations (by any method)

9 x+ y=5 2x-3y=4 [ans: x= 19/5, y= 6/5] POLYNOMIAL 11. If tan (A+ B)= 3 and tan (A-B) = 1/ 3, 0< A+B 90 0, A >B, find A and B. [ans: A= 45 and B = 15] 12. Evaluate: cos 45 0 /( sec cosec 30 0 ). [ans: 3 2-6/ 8] STATISTICS 13. Consider the following distribution of daily wages of 50 worker of a factory Daily wages(rs) No. of workers Find the mean daily wages of the workers of the factory by any appropriate method. [ans: ] 14. A survey conducted on 20 households in a locality resulted in the following frequency table for the number of family members in a household Family size No. of family Find mode of the data. [ans: 3.286] REAL NUMBERS 15. Prove that 3 is an irrational number. POLYNOMIAL 16. Solve the equation graphically x-y = -1 3x + 2y = 12 [ans : x=2, y=3] TRIANGLE 17. Write Pythagoras theorem. TRIGONOMETRY 18. Prove that [(1 + sin A)/ (1-sin A)]= seca + tan A. STATISTICS SECTION D (4 X 5=20) 19. During the medical checkup of 35 students of a class, their weights were recorded as follows

10 Weight in kg No. of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than Less than Less than Less than Draw the less than type ogive of given data.

11 Common Questions for SA I GROUP---D ( BHASKARACHARYA GROUP) Section A ( 1 X 4 = 4 ) 1. Find the number of zeroes of p(x) from the graph. y x x Ans 3 zeroes. y 2. Compare the ratios a1, b1 c1, and.state the nature of the following lines a2 b2 c2 5x 4y + 8 = 0 7x + 6y 9 = 0 Ans Intersecting Lines 3. For a given data with 70 observations the less than ogive and more than ogive intersect at (20.5,35). Find the median of the data. 4. If ABC~ PQR, ar ABC ar PQR =9, PQ = 8cm, then find AB. 4 Ans 12cm Section B ( 2 X 6 = 12 ) 5. Find out whether 6 n can end with the digit zero for any natural number n. 6. Form a quadratic polynomial which sum and product of the zeroes are 4 and -3 respectively. Ans x 2-4x Find out whether the pair of linear equations 2x +3y +5 =0, 4x +6y -3 =0 is consistent or not. 8. If sin (A+B) = 3 and sin(a- B)= 1, Find the values of A and B. Ans A= 45, B = If cos A = 5, Find sina, tana. Ans sin A= In ABC, DE II BC. If DB = 4cm, AE = 3cm, EC = 6cm, Find AD. Ans AD = 2cm Section C (3 X 6 = 18 ) tan A= Prove that is irrational. 12. Find the zeroes of 3x 2 x 4 and verify the relationship between the zeroes and the coefficients. 13. Solve: 3x 5y 4 = 0 9x = 2y +7 x = 9 y = Find geometrically the value of sin cos²60 +4 sec² 30 tan² Evaluate: sin²30 +cos²30 Ans: 67 12

12 16. Find the mean of the given data. Class interval frequency Ans Mean =62 Section D (4 X 4 = 16 ) 17.Solve the following pair of equations graphically x + 3y = 6, 2x-3y = 12. Ans x= 6,y= 0 18.Prove that if a line intersects two sides of a triangle at distinct points and parallel to the third side, then it divides the first two sides in same ratio. 1+sin A 19.Prove that 1 sin A = sec A + tan A. 20. Convert the following distribution into a less than type distribution and draw its ogive. Class Interval Frequency

CBSE QUESTION PAPER CLASS-X MATHS

CBSE QUESTION PAPER CLASS-X MATHS SECTION - A Question 1:If sin α = 1 2, then the value of 4 cos3 α 3 cos α is (a)0 (b)1 (c) 1 (d)2 Question 2: If cos 2θ = sin(θ 12 ), where2θ and (θ 12 ) are both acute