MODEL QUESTION FOR SA1 (FOR LATE BLOOMERS) SECTION A 1x4=4 1. Find the number of zeros in the following fig. 2. 3. 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 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. 3x + 2y = 5 ; 2x 3y = 7. 3. 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. Find geometrically Sin30 0. cos 45 4. Evaluate: sec 30 + cosec 30 5. If tan (A + B) = 3 and tan (A B) = 1 ; 0 < A + B 90 ; A > B, find A and B. 3 6. 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
ANSWERS: Section A 1. 2 2. Not similar 3. 4/3 4. 20 Section B 1. 7 x 144 2. Consistent 3. 11.2 cm 4. 59.3 Section C 1. x 2 + 3x +2 2. x= 3/5, y=8/5 3. to find. 4. (3 2-6)/8 5. A=45 0, B= 15 0 6. 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. 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
(Ans. 2) Q.7 The H.C.F of 306 and 657 is 9. Find their L.C.M. (Ans. 22338) 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. 43-24 3 11 ) 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.
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 65-68 68-71 71-74 74-77 77-80 80-83 83-86 beats per minute Number of women 2 4 3 8 7 4 2 (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 1000-1500 24 1500-2000 40 2000-2500 33 2500-3000 28 3000-3500 30 3500-4000 22 4000-4500 16 4500-5000 7 (Ans. Rupees 1847.83) Q.19 The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution Classes 5-10 10-15 15-20 20-25 25-30 30-35 35-40 No. of shops 2 12 2 4 3 4 3 Draw a less than type ogive for the given data.
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
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)
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 30 0 + 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) 100-120 120-140 140-160 160-180 180-200 No. of workers 12 14 8 6 10 Find the mean daily wages of the workers of the factory by any appropriate method. [ans: 145.20] 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 1-3 3-5 5-7 7-9 9-11 No. of family 7 8 2 2 1 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
Weight in kg No. of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35 Draw the less than type ogive of given data.
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 -3 7. 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 = 15 2 2 9. If cos A = 5, Find sina, tana. Ans sin A=12 13 13 10. 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= 12 5 11. Prove that 3 +2 5 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 = 5 13 13 14. Find geometrically the value of sin 45. 5 cos²60 +4 sec² 30 tan² 45 15. Evaluate: sin²30 +cos²30 Ans: 67 12
16. Find the mean of the given data. Class 10-25 25-40 40-55 55-70 70-85 85-100 interval frequency 2 3 7 6 6 6 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 100-120 120-140 140-160 160-180 180-200 Frequency 12 14 8 6 10