CBSE Mathematics sample paper Class 10 Notes | EduRev

Class 10 : CBSE Mathematics sample paper Class 10 Notes | EduRev

 Page 1


56 X – Maths
DESIGN OF SAMPLE QUESTION PAPER
MATHEMATICS, SA - 1
Type of Question Marks per Total No. of Total Marks
Question Questions
MCQ 1 10 10
SA - I 2 8 16
SA - II 3 10 30
LA 4 6 24
Total 34 80
BLUE PRINT
SAMPLE QUESTION PAPER
Topic/Unit MCQ SA (I) SA (II) LA Total
Number System 2 (2) 1 (2) 2 (6) – 5 (10)
Algebra 2 (2) 2 (4) 2 (6) 2 (8)
8 (20)
Geometry 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Trigonometry 4 (4) 1 (2) 2 (6) 2 (8) 9 (20)
Statistics 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Total 10 (10) 8 (16) 10 (30) 6 (24) 34 (80)
Note : Marks are within brackets.
Page 2


56 X – Maths
DESIGN OF SAMPLE QUESTION PAPER
MATHEMATICS, SA - 1
Type of Question Marks per Total No. of Total Marks
Question Questions
MCQ 1 10 10
SA - I 2 8 16
SA - II 3 10 30
LA 4 6 24
Total 34 80
BLUE PRINT
SAMPLE QUESTION PAPER
Topic/Unit MCQ SA (I) SA (II) LA Total
Number System 2 (2) 1 (2) 2 (6) – 5 (10)
Algebra 2 (2) 2 (4) 2 (6) 2 (8)
8 (20)
Geometry 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Trigonometry 4 (4) 1 (2) 2 (6) 2 (8) 9 (20)
Statistics 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Total 10 (10) 8 (16) 10 (30) 6 (24) 34 (80)
Note : Marks are within brackets.
X – Maths 57
SAMPLE QUESTION PAPER - I
MATHEMATICS, SA - 1
Time allowed : 3½ hours Maximum Marks : 80
General Instructions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A,
B, C and D. Section A comprises of 10 questions of 1 mark each. Section
B comprises of 8 questions of 2 marks each. Section C comprises of 10
questions of 3 marks each and Section D comprises of 6 questions of 4
marks each.
3. Question numbers 1 to 10 in Section A are multiple choice questions
where you are to select one correct option out of the given four.
4. There is no overall choice. How ever, internal choice has been provided
in 1 question of 2 marks 3 questions of three marks each and 2 questions
of 4 marks each. You have to attempt only one of the alternatives in all
such questions.
5. Use of calculators is not permitted.
SECTION A
Question number 1 to 10 are of 1 mark each
1. ?ABC is right angled at A. The value of tan B . tan C is _______
(a) tan B (b) tan C
(c) 0 (d) 1
2. In Euclid Division Lemma, when x = yq + r, where x and y are positive
integers which one is correct.
(a) 0 ? r < y (b) 0 ? r < y
(c) 0 < r < y (d) 0 ? r ? y
Page 3


56 X – Maths
DESIGN OF SAMPLE QUESTION PAPER
MATHEMATICS, SA - 1
Type of Question Marks per Total No. of Total Marks
Question Questions
MCQ 1 10 10
SA - I 2 8 16
SA - II 3 10 30
LA 4 6 24
Total 34 80
BLUE PRINT
SAMPLE QUESTION PAPER
Topic/Unit MCQ SA (I) SA (II) LA Total
Number System 2 (2) 1 (2) 2 (6) – 5 (10)
Algebra 2 (2) 2 (4) 2 (6) 2 (8)
8 (20)
Geometry 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Trigonometry 4 (4) 1 (2) 2 (6) 2 (8) 9 (20)
Statistics 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Total 10 (10) 8 (16) 10 (30) 6 (24) 34 (80)
Note : Marks are within brackets.
X – Maths 57
SAMPLE QUESTION PAPER - I
MATHEMATICS, SA - 1
Time allowed : 3½ hours Maximum Marks : 80
General Instructions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A,
B, C and D. Section A comprises of 10 questions of 1 mark each. Section
B comprises of 8 questions of 2 marks each. Section C comprises of 10
questions of 3 marks each and Section D comprises of 6 questions of 4
marks each.
3. Question numbers 1 to 10 in Section A are multiple choice questions
where you are to select one correct option out of the given four.
4. There is no overall choice. How ever, internal choice has been provided
in 1 question of 2 marks 3 questions of three marks each and 2 questions
of 4 marks each. You have to attempt only one of the alternatives in all
such questions.
5. Use of calculators is not permitted.
SECTION A
Question number 1 to 10 are of 1 mark each
1. ?ABC is right angled at A. The value of tan B . tan C is _______
(a) tan B (b) tan C
(c) 0 (d) 1
2. In Euclid Division Lemma, when x = yq + r, where x and y are positive
integers which one is correct.
(a) 0 ? r < y (b) 0 ? r < y
(c) 0 < r < y (d) 0 ? r ? y
58 X – Maths
3. If the mean of 2, 4, 6, 8, 10, x, 14, 16 is 9 then the value of x is
(a) 10 (b) 11
(c) 12 (d) 13
4. Graph of y = ax
2
 + bx + c intersects x-axis at 2 distinct points if
(a) b
2
 – 4ac = 0 (b) b
2
 – 4ac > 0
(c) b
2
 – 4ac < 0 (d) b
2
 – 4ac ? 0
5. If 5 tan ? – 4 = 0 then the value of
? ? ?
? ? ?
5 sin 4 cos
5 sin 4 cos
 is
(a)
5
3
(b)
5
6
(c) 0 (d)
1
6
6. The modal class of the following distribution is
Class Interval : 10–20 20–30 30–40 40–50 50–60 60–70 70–80
Frequency : 3 5 8 10 9 4 3
(a) 70–80 (b) 40–50
(c) 50–60 (d) 30–40
7. If product of the zeroes is 5 and sum of the zeroes is –2 then the
quadratic polynomial will be–
(a) x
2
 – 5x – 2 (b) x
2
 + 5x – 2
(c) x
2
 + 2x – 5 (d) x
2
 + 2x + 5
8. The relationship in mean, median and mode is
(a) Mode = 2 median – 3 mean
(b) Mode = 2 median - mean
(c) Mode = 3 median + 2 mean
(d) Mode = 3 median – 2 mean
Page 4


56 X – Maths
DESIGN OF SAMPLE QUESTION PAPER
MATHEMATICS, SA - 1
Type of Question Marks per Total No. of Total Marks
Question Questions
MCQ 1 10 10
SA - I 2 8 16
SA - II 3 10 30
LA 4 6 24
Total 34 80
BLUE PRINT
SAMPLE QUESTION PAPER
Topic/Unit MCQ SA (I) SA (II) LA Total
Number System 2 (2) 1 (2) 2 (6) – 5 (10)
Algebra 2 (2) 2 (4) 2 (6) 2 (8)
8 (20)
Geometry 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Trigonometry 4 (4) 1 (2) 2 (6) 2 (8) 9 (20)
Statistics 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Total 10 (10) 8 (16) 10 (30) 6 (24) 34 (80)
Note : Marks are within brackets.
X – Maths 57
SAMPLE QUESTION PAPER - I
MATHEMATICS, SA - 1
Time allowed : 3½ hours Maximum Marks : 80
General Instructions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A,
B, C and D. Section A comprises of 10 questions of 1 mark each. Section
B comprises of 8 questions of 2 marks each. Section C comprises of 10
questions of 3 marks each and Section D comprises of 6 questions of 4
marks each.
3. Question numbers 1 to 10 in Section A are multiple choice questions
where you are to select one correct option out of the given four.
4. There is no overall choice. How ever, internal choice has been provided
in 1 question of 2 marks 3 questions of three marks each and 2 questions
of 4 marks each. You have to attempt only one of the alternatives in all
such questions.
5. Use of calculators is not permitted.
SECTION A
Question number 1 to 10 are of 1 mark each
1. ?ABC is right angled at A. The value of tan B . tan C is _______
(a) tan B (b) tan C
(c) 0 (d) 1
2. In Euclid Division Lemma, when x = yq + r, where x and y are positive
integers which one is correct.
(a) 0 ? r < y (b) 0 ? r < y
(c) 0 < r < y (d) 0 ? r ? y
58 X – Maths
3. If the mean of 2, 4, 6, 8, 10, x, 14, 16 is 9 then the value of x is
(a) 10 (b) 11
(c) 12 (d) 13
4. Graph of y = ax
2
 + bx + c intersects x-axis at 2 distinct points if
(a) b
2
 – 4ac = 0 (b) b
2
 – 4ac > 0
(c) b
2
 – 4ac < 0 (d) b
2
 – 4ac ? 0
5. If 5 tan ? – 4 = 0 then the value of
? ? ?
? ? ?
5 sin 4 cos
5 sin 4 cos
 is
(a)
5
3
(b)
5
6
(c) 0 (d)
1
6
6. The modal class of the following distribution is
Class Interval : 10–20 20–30 30–40 40–50 50–60 60–70 70–80
Frequency : 3 5 8 10 9 4 3
(a) 70–80 (b) 40–50
(c) 50–60 (d) 30–40
7. If product of the zeroes is 5 and sum of the zeroes is –2 then the
quadratic polynomial will be–
(a) x
2
 – 5x – 2 (b) x
2
 + 5x – 2
(c) x
2
 + 2x – 5 (d) x
2
 + 2x + 5
8. The relationship in mean, median and mode is
(a) Mode = 2 median – 3 mean
(b) Mode = 2 median - mean
(c) Mode = 3 median + 2 mean
(d) Mode = 3 median – 2 mean
X – Maths 59
9. The coordinates of the point where y-axis and the line represented by
? ? 1
2 3
x y
 intersect are :
(a) (0, 2) (b) (2, 0)
(c) (0, 3) (d) (3, 0)
10. If x = tan 2° · tan 36° · tan 54° · tan 88° then the value of x is ______
(a) 45° (b) 1
(c) 2 (d) 90°
SECTION B
Question number 11 to 18 are of 2 marks each
11. Find HCF and LCM of 90 and 144 by prime factorisation method.
12. Find the mean of the following distribution :
x : 12 16 20 24 28 32
f : 5 7 8 5 3 2
13. In ?ABC, D is the mid point of the side AB and DE || BC meets AC at
E. Prove that ?
1
.
2
AE AC
OR
If ?ABC ~ ?DEF, BC = 5 cm, EF = 4 cm and ar ( ?ABC) = 75 cm
2
. Find
the area of ?DEF.
14. If ? and ? are the zeros of the quadratic polynomial f(x) = x
2
 – px + q,
then find the value of 
?
? ?
3 3
1 1
.
Page 5


56 X – Maths
DESIGN OF SAMPLE QUESTION PAPER
MATHEMATICS, SA - 1
Type of Question Marks per Total No. of Total Marks
Question Questions
MCQ 1 10 10
SA - I 2 8 16
SA - II 3 10 30
LA 4 6 24
Total 34 80
BLUE PRINT
SAMPLE QUESTION PAPER
Topic/Unit MCQ SA (I) SA (II) LA Total
Number System 2 (2) 1 (2) 2 (6) – 5 (10)
Algebra 2 (2) 2 (4) 2 (6) 2 (8)
8 (20)
Geometry 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Trigonometry 4 (4) 1 (2) 2 (6) 2 (8) 9 (20)
Statistics 1 (1) 2 (4) 2 (6) 1 (4) 6 (15)
Total 10 (10) 8 (16) 10 (30) 6 (24) 34 (80)
Note : Marks are within brackets.
X – Maths 57
SAMPLE QUESTION PAPER - I
MATHEMATICS, SA - 1
Time allowed : 3½ hours Maximum Marks : 80
General Instructions
1. All questions are compulsory.
2. The question paper consists of 34 questions divided into four sections A,
B, C and D. Section A comprises of 10 questions of 1 mark each. Section
B comprises of 8 questions of 2 marks each. Section C comprises of 10
questions of 3 marks each and Section D comprises of 6 questions of 4
marks each.
3. Question numbers 1 to 10 in Section A are multiple choice questions
where you are to select one correct option out of the given four.
4. There is no overall choice. How ever, internal choice has been provided
in 1 question of 2 marks 3 questions of three marks each and 2 questions
of 4 marks each. You have to attempt only one of the alternatives in all
such questions.
5. Use of calculators is not permitted.
SECTION A
Question number 1 to 10 are of 1 mark each
1. ?ABC is right angled at A. The value of tan B . tan C is _______
(a) tan B (b) tan C
(c) 0 (d) 1
2. In Euclid Division Lemma, when x = yq + r, where x and y are positive
integers which one is correct.
(a) 0 ? r < y (b) 0 ? r < y
(c) 0 < r < y (d) 0 ? r ? y
58 X – Maths
3. If the mean of 2, 4, 6, 8, 10, x, 14, 16 is 9 then the value of x is
(a) 10 (b) 11
(c) 12 (d) 13
4. Graph of y = ax
2
 + bx + c intersects x-axis at 2 distinct points if
(a) b
2
 – 4ac = 0 (b) b
2
 – 4ac > 0
(c) b
2
 – 4ac < 0 (d) b
2
 – 4ac ? 0
5. If 5 tan ? – 4 = 0 then the value of
? ? ?
? ? ?
5 sin 4 cos
5 sin 4 cos
 is
(a)
5
3
(b)
5
6
(c) 0 (d)
1
6
6. The modal class of the following distribution is
Class Interval : 10–20 20–30 30–40 40–50 50–60 60–70 70–80
Frequency : 3 5 8 10 9 4 3
(a) 70–80 (b) 40–50
(c) 50–60 (d) 30–40
7. If product of the zeroes is 5 and sum of the zeroes is –2 then the
quadratic polynomial will be–
(a) x
2
 – 5x – 2 (b) x
2
 + 5x – 2
(c) x
2
 + 2x – 5 (d) x
2
 + 2x + 5
8. The relationship in mean, median and mode is
(a) Mode = 2 median – 3 mean
(b) Mode = 2 median - mean
(c) Mode = 3 median + 2 mean
(d) Mode = 3 median – 2 mean
X – Maths 59
9. The coordinates of the point where y-axis and the line represented by
? ? 1
2 3
x y
 intersect are :
(a) (0, 2) (b) (2, 0)
(c) (0, 3) (d) (3, 0)
10. If x = tan 2° · tan 36° · tan 54° · tan 88° then the value of x is ______
(a) 45° (b) 1
(c) 2 (d) 90°
SECTION B
Question number 11 to 18 are of 2 marks each
11. Find HCF and LCM of 90 and 144 by prime factorisation method.
12. Find the mean of the following distribution :
x : 12 16 20 24 28 32
f : 5 7 8 5 3 2
13. In ?ABC, D is the mid point of the side AB and DE || BC meets AC at
E. Prove that ?
1
.
2
AE AC
OR
If ?ABC ~ ?DEF, BC = 5 cm, EF = 4 cm and ar ( ?ABC) = 75 cm
2
. Find
the area of ?DEF.
14. If ? and ? are the zeros of the quadratic polynomial f(x) = x
2
 – px + q,
then find the value of 
?
? ?
3 3
1 1
.
60 X – Maths
15. Draw ‘less than ogive’ for the following distribution :
Class Interval : 0–10 10–20 20–30 30–40 40–50 50–60
Frequency : 5 8 12 10 7 4
16. Without using trigonometric tables, evaluate
2
sin 54
3 2 tan 14 tan 30 tan 76 .
cos 36
? ?
? ? ? ?
? ?
? ?
17. For what value of p, the pair of linear equations
y – 2x – 5 = 0
px = 2y has unique solution.
18. If ? ? ?
?
1
tan 2,
tan
 find the value of ? ?
?
2
2
1
tan .
tan
SECTION C
Question number 19 to 28 carry 3 marks each
19. Draw the graph of x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the
coordinates of the vertices of the triangle formed by these lines and
x-axis, shade the triangular region.
20. Prove that 
?
1
5 2 3
 is irrational.
OR
Prove ? 5 2 that is irrational.
21. In ?ABC, ?C = 90° points P and Q lies on sides CA and CB respectively
prove that
AQ
2
 + BP
2
 = AB
2
 + PQ
2
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