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 cm2 and 121 cm2. 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

3x6=18

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 Sin300.

4. Evaluate: cos 45°

𝑠𝑒𝑐 30° + 𝑐𝑜𝑠𝑒𝑐 30°

5. If tan (A + B) = √3 and tan (A – B) = 1

√3 ; 0° < A + B ≤ 90°; A > B, find A and B.

6. The following table shows the ages of the patients admitted in a hospital during a year:

Find the mode of the data given above.

SECTION D

4x5=20

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.

4. Prove that, tan 𝛼

1−𝑐𝑜𝑡𝛼+

cot 𝛼

1−𝑡𝑎𝑛 𝛼 = 1 + sec α.cosecα.

5.

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. x2 + 3x +2

2. x= 3/5, y=8/5

3. to find.

4. (3√2-√6)/8

5. A=450, B= 150

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.

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BRAHMAGUPTA GROUP

COMMON QUESTIONS FOR SA1

SECTION A (1X4=4)

Q.1 Evaluate cos 480 – sin 420 (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 4n 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=450, B=150 )

Q.10 If sinθ = 3∕5, find cosθ x tanθ (Ans. 3∕5)

OR

Evaluate

𝑠𝑖𝑛30 + tan 45 − 𝑐𝑜𝑠𝑒𝑐 60

sec 30 + cos 60 + cot 45

(Ans. 43-24√3 ∕ 11 )

Q.11 Prove that sin 45 = 1∕√2 geometrically.

Q.12 Solve the following pair of linear equations

3x + 4y = 10

2x – 3y = 2

(Ans. x=2, y=1)

Q.13 Find the zeros of the quadratic polynomial

X2 + 7x +10 and verify the relationship between the zeros and coefficients. (Ans. 5 and 2)

SECTION D (4 X 6 =24)

Q.14 Prove that √5 is an irrational number.

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 beats per minute

65-68 68-71 71-74 74-77 77-80 80-83 83-86

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 260/cot 640 [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: 4x2 -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

SECTION-C (3 X 6=18 MARKS)

POLYNOMIAL

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 ≤ 900, A >B, find A and B. [ans: A= 45 and B = 15]

12. Evaluate: cos 450/( sec 300 + cosec 300). [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]

SECTION – D (4 X 5=20)

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

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

𝑎2,

𝑏1

𝑏2 , 𝑎𝑛𝑑

𝑐1

𝑐2 .State the nature of the following lines

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

4 , PQ = 8cm, then find AB.

Ans 12cm

Section B ( 2 X 6 = 12 )

5. Find out whether 6n 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 x2 -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

2 and sin(A- B)=

1

2 , Find the values of A and B. Ans A= 45°, B = 15°

9. If cos A = 5

13 , Find sinA, tanA. Ans sin A=

12

13 tan A=

12

5

10. In ∆ABC, DE II BC. If DB = 4cm, AE = 3cm, EC = 6cm , Find AD. Ans AD = 2cm

Section C (3 X 6 = 18 )

11. Prove that 3 +2√5 is irrational.

12. Find the zeroes of 3x2 – x – 4 and verify the relationship between the zeroes and the

coefficients.

13. Solve: 3x – 5y – 4 = 0

9x = 2y +7 x = 9

13 y =

−5

13

14. Find geometrically the value of sin 45°.

15. Evaluate: 5 𝑐𝑜𝑠²60°+4 𝑠𝑒𝑐² 30°−𝑡𝑎𝑛² 45°

𝑠𝑖𝑛²30°+𝑐𝑜𝑠²30° Ans:

67

12

16. Find the mean of the given data.

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.

19.Prove that √1+sin 𝐴

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

Class interval

10-25 25-40 40-55 55-70 70-85 85-100

frequency 2 3 7 6 6 6