Download Sample Question Papers for Class X SA-1 Maths

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:
3.
2x+3y=6 , 3x+2y=5
Find geometrically Sin300.
4.
Evaluate:
5.
If tan (A + B) = √3 and tan (A – B) =
6.
The following table shows the ages of the patients admitted in a hospital during a year:
cos 45°
𝑠𝑒𝑐 30° + 𝑐𝑜𝑠𝑒𝑐 30°
1
√3
; 0° < A + B ≤ 90°; A > B, find A and B.
Find the mode of the data given above.
SECTION D
4x5=20
1. Prove that √5 is an irrational number.
2.
3.
4.
5.
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.
Prove Basic Proportionality theorem.
tan 𝛼
cot 𝛼
Prove that,
+
= 1 + sec α.cosecα.
1−𝑐𝑜𝑡𝛼 1−𝑡𝑎𝑛 𝛼
ANSWERS:
Section A
1. 2
2. Not similar
3. 4/3
4. 20
Section B
1. 7 x 144
2. Consistent
11.2 cm
4. 59.3
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.
----------------
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)
Check whether 4n can end with the digit 0 for any natural number n.
Q8.
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
Number of women
65-68
68-71
71-74
74-77
77-80
80-83
83-86
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)
1000-1500
1500-2000
2000-2500
2500-3000
3000-3500
3500-4000
4000-4500
4500-5000
Number of families
24
40
33
28
30
22
16
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
No. of shops
5-10
2
10-15
12
15-20
2
Draw a less than type ogive for the given data.
20-25
4
25-30
3
30-35
4
35-40
3
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
No. of family
7
Find mode of the data.
3-5
8
[ans: 3.286]
5-7
2
7-9
2
9-11
1
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
Less than 38
Less than 40
Less than 42
Less than 44
Less than 46
Less than 48
Less than 50
Less than 52
Draw the less than type ogive of given data.
No. of students
0
3
5
9
14
28
32
35
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
,
𝑎2 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.
𝑎𝑟∆𝐴𝐵𝐶
9
4. If ∆ABC~∆PQR, 𝑎𝑟∆𝑃𝑄𝑅 =4 , PQ = 8cm, then find AB.
Ans 12cm
Section B ( 2 X 6 = 12 )
n
5. Find out whether 6 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.
√3
1
8. If sin (A+B) = 2 and sin(A- B)= 2 , Find the values of A and B.
9. If cos A =
5
13
Ans A= 45°, B = 15°
12
13
, Find sinA, tanA.
Ans sin A=
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=
14. Find geometrically the value of sin 45°.
15. Evaluate:
5 𝑐𝑜𝑠²60°+4 𝑠𝑒𝑐² 30°−𝑡𝑎𝑛² 45°
𝑠𝑖𝑛²30°+𝑐𝑜𝑠²30°
Ans:
67
12
−5
13
tan A=
12
5
16. Find the mean of the given data.
Class
interval
frequency
10-25
25-40
40-55
55-70
70-85
85-100
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
1−sin 𝐴
19.Prove that √
= sec A + tan A .
20. Convert the following distribution into a less than type distribution and draw its ogive.
Class Interval
Frequency
100-120
12
120-140
14
140-160
8
160-180
6
180-200
10