Karnataka 9th Model Question Paper Maths
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Karnataka 9th Model Question Paper Maths – Text
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Page 1
SAMPLE PAPER
Karnataka
Board
Model Paper
Karnataka
Board
Model Paper
Page 2
PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë 1ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - Model Paper
Subject : Mathematics Marks : 80
Class : 9 Time : 3 Hours
Medium : English
Information to be filled by the Student
Name of the Student : _____________________________________________________________
Student SATS No : Signature
of the Student :________________
Information to be filled by the Room Invigilator
School DISE Code :
School Name :____________________________________________________________________
Cluster :__________________ Block :______________________ District :__________________
School Type : Govt. Aided Un-aided
(Put “” mark for applicable information)
Signature of the Room Invigilator : ______________________
Information to be filled by the Evaluator at the time of evaluation
Question Number Obtained marks Question Number Obtained marks Question Number Obtained marks
1 14 27
2 15 28
3 16 29
4 17 30
5 18 31
6 19 32
7 20 33
8 21 34
9 22 35
10 23 36
11 24 37
12 25 38
13 26
Total marks Total marks Total marks
Grand Total
Total marks obtained (in words) :____________________________________________________
Signature of the Evaluator : _______________________
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - Model Paper
Subject : Mathematics Marks : 80
Class : 9 Time : 3 Hours
Medium : English
Information to be filled by the Student
Name of the Student : _____________________________________________________________
Student SATS No : Signature
of the Student :________________
Information to be filled by the Room Invigilator
School DISE Code :
School Name :____________________________________________________________________
Cluster :__________________ Block :______________________ District :__________________
School Type : Govt. Aided Un-aided
(Put “” mark for applicable information)
Signature of the Room Invigilator : ______________________
Information to be filled by the Evaluator at the time of evaluation
Question Number Obtained marks Question Number Obtained marks Question Number Obtained marks
1 14 27
2 15 28
3 16 29
4 17 30
5 18 31
6 19 32
7 20 33
8 21 34
9 22 35
10 23 36
11 24 37
12 25 38
13 26
Total marks Total marks Total marks
Grand Total
Total marks obtained (in words) :____________________________________________________
Signature of the Evaluator : _______________________
Page 3
2
I. For each of the following questions / incomplete statements four alternates are given.
Choose the most appropriate among them and write it along with the alphabet.
8x1=8
3
1. The value of 4 2 is
A. 8 B. 16 C. 32 D. 64
Answer: ____________________
2. The measure 'x' in the given figure is
A. 600 B. 900 C. 1200 D. 1800
n
Q 600
l
P
m
xº
Answer: ____________________
3. In a polynomial p(x)=3x2-2, the value of p(1) is
A. 2 B. 1 C. 5 D. 0
Answer: ____________________
I. For each of the following questions / incomplete statements four alternates are given.
Choose the most appropriate among them and write it along with the alphabet.
8x1=8
3
1. The value of 4 2 is
A. 8 B. 16 C. 32 D. 64
Answer: ____________________
2. The measure 'x' in the given figure is
A. 600 B. 900 C. 1200 D. 1800
n
Q 600
l
P
m
xº
Answer: ____________________
3. In a polynomial p(x)=3x2-2, the value of p(1) is
A. 2 B. 1 C. 5 D. 0
Answer: ____________________
Page 4
3
4. Among these one of the solution for the equation x + 2y = 6 is
A. (1,3) B. (3,1) C. (4,2) D. (2,2)
Answer: ____________________
5. If a point 'M' lies on x-axis then its co-ordinates are
A. (0.x) B. (0,-x) C. (x,0) D. (x,-x)
Answer: ____________________
6. If the probability of winning a game is 0.86, then probability of not
winning the game is
A. 0.14 B. 0.76 C. 0.85 D. 0.41
Answer: ____________________
7. The area of triangle ABC in the given figure is A
A. 32.5 cm2 B. 15 cm2 12
5
C. 78 cm2 D. 30 cm2
B C
13
Answer: ____________________
8. Observe the given figure.
A P Q R B
The correct relationship among these is
A. AP > PQ + QR+RB B. AP + P Q + QR <AB
C. AR > AB D. PQ > PQ + QR
Answer: ____________________
[ Turn over
4. Among these one of the solution for the equation x + 2y = 6 is
A. (1,3) B. (3,1) C. (4,2) D. (2,2)
Answer: ____________________
5. If a point 'M' lies on x-axis then its co-ordinates are
A. (0.x) B. (0,-x) C. (x,0) D. (x,-x)
Answer: ____________________
6. If the probability of winning a game is 0.86, then probability of not
winning the game is
A. 0.14 B. 0.76 C. 0.85 D. 0.41
Answer: ____________________
7. The area of triangle ABC in the given figure is A
A. 32.5 cm2 B. 15 cm2 12
5
C. 78 cm2 D. 30 cm2
B C
13
Answer: ____________________
8. Observe the given figure.
A P Q R B
The correct relationship among these is
A. AP > PQ + QR+RB B. AP + P Q + QR <AB
C. AR > AB D. PQ > PQ + QR
Answer: ____________________
[ Turn over
Page 5
4
II. Answer the following questions 8x1=8
9. Write the number that is to be multiplied to 3 + √3 to make it rational number.
10. How many straight lines can be drawn that passes through two distinct points ?
11. Write the sum of interior angles of a trapezium.
A E B F
12. In the given figure, if the area of
parallelogram ABCD is 42 cm2 then find
the area of parallelogram EFCD.
D C
13. Write the expanded form of (x + y + z)2 .
14. Write the distance of a point P (- 3, 8) from x-axis.
II. Answer the following questions 8x1=8
9. Write the number that is to be multiplied to 3 + √3 to make it rational number.
10. How many straight lines can be drawn that passes through two distinct points ?
11. Write the sum of interior angles of a trapezium.
A E B F
12. In the given figure, if the area of
parallelogram ABCD is 42 cm2 then find
the area of parallelogram EFCD.
D C
13. Write the expanded form of (x + y + z)2 .
14. Write the distance of a point P (- 3, 8) from x-axis.
Page 6
5
15. In the given figure AB= CD and ON= 3 cm. A
C
Find the length of OM.
N
M
O
D
B
16. Find the volume of a cube whose edges are 9 cm each.
III. Answer the following questions 8 x 2 = 16
p
17. Express 0.3 in the form of q (here, p and q are co-primes).
[ Turn over
15. In the given figure AB= CD and ON= 3 cm. A
C
Find the length of OM.
N
M
O
D
B
16. Find the volume of a cube whose edges are 9 cm each.
III. Answer the following questions 8 x 2 = 16
p
17. Express 0.3 in the form of q (here, p and q are co-primes).
[ Turn over
Page 7
6
18. In the given figure AB || CD. Find the value of x.
570
A B
1170
C D
x
19. In the given figure, if p is any point in the interior A B
of a parallelogram ABCD, then show that ar
P
(∆ABP) + ar (∆PCD) = ½ ar ( ABCD).
D C
18. In the given figure AB || CD. Find the value of x.
570
A B
1170
C D
x
19. In the given figure, if p is any point in the interior A B
of a parallelogram ABCD, then show that ar
P
(∆ABP) + ar (∆PCD) = ½ ar ( ABCD).
D C
Page 8
7
20. Find the cube of (2a + 3b) using suitable identity.
[ Turn over
20. Find the cube of (2a + 3b) using suitable identity.
[ Turn over
Page 9
8
21. The below table contains the marks scored by 50 students of a class in mathematics
examination. Draw a histogram for the given data.
Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 5 10 15 12 8
21. The below table contains the marks scored by 50 students of a class in mathematics
examination. Draw a histogram for the given data.
Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
Frequency 5 10 15 12 8
Page 10
9
22. One day a man observes 230 two wheeler, 160 three wheeler and 70 four wheeler
vehicles passing in front of his shop. Find the probability of the vehicle observed by
him is a two wheeler.
23. The curved surface area of a right circular cylinder of height 14 cm is 176 cm2. Find
the diameter of the base of the cylinder.
[ Turn over
22. One day a man observes 230 two wheeler, 160 three wheeler and 70 four wheeler
vehicles passing in front of his shop. Find the probability of the vehicle observed by
him is a two wheeler.
23. The curved surface area of a right circular cylinder of height 14 cm is 176 cm2. Find
the diameter of the base of the cylinder.
[ Turn over
Page 11
10
24. The length, breadth and height of a room are 5m, 4m and 3m respectively. Find the
cost of whitewashing the walls of the room and the ceiling at the rate of ` 10 per m2.
24. The length, breadth and height of a room are 5m, 4m and 3m respectively. Find the
cost of whitewashing the walls of the room and the ceiling at the rate of ` 10 per m2.
Page 12
11
IV. Answer the following questions 9 x 3 = 27
25. Represent √5.6 on number line.
[ Turn over
IV. Answer the following questions 9 x 3 = 27
25. Represent √5.6 on number line.
[ Turn over
Page 13
12
26. The following data have been arranged in ascending order. If the median of the data
is 47 then find the value of x and also find the mean of given data.
17, 28, 31, 39, x, x+2, 51, 58, 63, 71
26. The following data have been arranged in ascending order. If the median of the data
is 47 then find the value of x and also find the mean of given data.
17, 28, 31, 39, x, x+2, 51, 58, 63, 71
Page 14
13
27. Prove that "a diagonal of a parallelogram divides it into two congruent triangles".
[ Turn over
27. Prove that "a diagonal of a parallelogram divides it into two congruent triangles".
[ Turn over
Page 15
14
28. In the given figure E is the centre of a circle with ABC = 69° and ACB = 31°.
Find the measures of angle BDC , BEC and BFC .
D
A
E
690 310
B C
F
28. In the given figure E is the centre of a circle with ABC = 69° and ACB = 31°.
Find the measures of angle BDC , BEC and BFC .
D
A
E
690 310
B C
F
Page 16
15
29. If x+y+z=0, then prove that x +y +z =3xyz
3 3 3
30. In the given figure line 'l' is the bisector
of an angle A and B is any point on 'l'. BP Q
and BQ are the perpendiculars from B to l
the arms of A . Show that BP = BQ. B
A P
[ Turn over
29. If x+y+z=0, then prove that x +y +z =3xyz
3 3 3
30. In the given figure line 'l' is the bisector
of an angle A and B is any point on 'l'. BP Q
and BQ are the perpendiculars from B to l
the arms of A . Show that BP = BQ. B
A P
[ Turn over
Page 17
16
31. Draw the graph for the linear equation 2x+y=7.
31. Draw the graph for the linear equation 2x+y=7.
Page 18
17
32. In the given figure, BE the bisector of ABQ A E
is parallel to the CG the bisector of BCS .
Prove that PQ || RS.
P Q
B
G
C
R S
D
[ Turn over
32. In the given figure, BE the bisector of ABQ A E
is parallel to the CG the bisector of BCS .
Prove that PQ || RS.
P Q
B
G
C
R S
D
[ Turn over
Page 19
18
33. A triangular shaped land is to be divided equally among three persons. The length of
its two sides are 100m and 160m and perimeter is 360m. Find the area of land that
each person would get.
33. A triangular shaped land is to be divided equally among three persons. The length of
its two sides are 100m and 160m and perimeter is 360m. Find the area of land that
each person would get.
Page 20
19
V. Answer the following questions 4 x 4 = 16
34. Construct a triangle XYZ in which = Y = 30o, Z = 90o and XY+YZ+ZX = 11cm
[ Turn over
V. Answer the following questions 4 x 4 = 16
34. Construct a triangle XYZ in which = Y = 30o, Z = 90o and XY+YZ+ZX = 11cm
[ Turn over
Page 21
20
35. 30 children were asked about the number of hours they used mobile in the last
month. The results are recorded as follows
5, 10, 11, 16, 15, 8, 21, 26, 14, 6, 8, 9, 10, 14, 20, 10,
12, 11, 3, 7, 12, 19, 28, 30, 8, 12, 17, 16, 10, 12.
Construct a grouped frequency distribution table with class intervals as 0-5, 5-10...
etc (of equal size). With the help of this table answer the following questions.
1. Find the number of students who used mobile less than 10 hours ?
2. Find the number of students who used mobile more than 25 hours ?
35. 30 children were asked about the number of hours they used mobile in the last
month. The results are recorded as follows
5, 10, 11, 16, 15, 8, 21, 26, 14, 6, 8, 9, 10, 14, 20, 10,
12, 11, 3, 7, 12, 19, 28, 30, 8, 12, 17, 16, 10, 12.
Construct a grouped frequency distribution table with class intervals as 0-5, 5-10...
etc (of equal size). With the help of this table answer the following questions.
1. Find the number of students who used mobile less than 10 hours ?
2. Find the number of students who used mobile more than 25 hours ?
Page 22
21
36. Prove that "Angles opposite to equal sides of an isosceles triangle are equal."
[ Turn over
36. Prove that "Angles opposite to equal sides of an isosceles triangle are equal."
[ Turn over
Page 23
22
37. x-1 is one of the factor of p(x) = 4x -3x-k. Find the value of K. Also find another
2
factor for the given polynomial.
37. x-1 is one of the factor of p(x) = 4x -3x-k. Find the value of K. Also find another
2
factor for the given polynomial.
Page 24
23
VI. Answer the following question 1x5=5
38. The circumference and height of a right circular cylinder are 44 cm and 24 cm
respectively. Find its volume. Also find the volume and curved surface area of the
cone whose radius and height are same as given cylinder.
[ Turn over
VI. Answer the following question 1x5=5
38. The circumference and height of a right circular cylinder are 44 cm and 24 cm
respectively. Find its volume. Also find the volume and curved surface area of the
cone whose radius and height are same as given cylinder.
[ Turn over
Page 25
24
Page 26
PÀ£ÁðlPÀ ±Á¯Á ¥ÀjÃPÉë ªÀÄvÀÄÛ ªÀiË®å¤tðAiÀÄ ªÀÄAqÀ°
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - ªÀiÁZïð 2024 - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - March 2024 Model Paper
CAPÀUÀ¼ÀÄ : 80
vÀgÀUÀw : 9 «µÀAiÀÄ : UÀtÂvÀ
¸ÀªÀÄAiÀÄ : 3 UÀAmÉ
«zÁåyðUÀ¼ÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
«zÁåyðAiÀÄ ºÉ¸ÀgÀÄ : _____________________________________________________________________
«zÁåyðAiÀÄ SATS ¸ÀASÉå : «zÁåyðAiÀÄ ¸À» :_______________
PÉÆoÀr ªÉÄðéZÁgÀPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
±Á¯ÉAiÀÄ qÉʸï PÉÆÃqï :
±Á¯ÉAiÀÄ ºÉ¸ÀgÀÄ :_________________________________________________________________________
PÀè¸ÀÖgï :______________________ ¨ÁèPï :_______________________ f¯Éè :_______________________
±Á¯ÉAiÀÄ «zsÀ : ¸ÀPÁðj C£ÀÄzÁ¤vÀ C£ÀÄzÁ£À gÀ»vÀ
(C£Àé¬Ä¸ÀĪÀ ªÀiÁ»wUÉ “” UÀÄgÀÄvÀÄ ºÁQj)
PÉÆoÀr ªÉÄðéZÁgÀPÀgÀ ¸À» :______________________________
ªÀiË®åªÀiÁ¥À£À ¸ÀªÀÄAiÀÄzÀ°è ²PÀëPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁzÀ ªÀiÁ»w
¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ
1 14 27
2 15 28
3 16 29
4 17 30
5 18 31
6 19 32
7 20 33
8 21 34
9 22 35
10 23 36
11 24 37
12 25 38
13 26
MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ
MlÄÖ UÀ½¹zÀ CAPÀ
MlÄÖ UÀ½¹zÀ CAPÀUÀ¼ÀÄ (CPÀëgÀUÀ¼À°è)___________________________________________________________
ªÀiË®åªÀiÁ¥ÀPÀgÀ ¸À» : _______________________
PÉJ¸ïPÀÄåJJ¹, ªÀįÉèñÀégÀA, ¨ÉAUÀ¼ÀÆgÀÄ-560003.
KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD
KSQAAC, Malleshwaram, Bengaluru-560003.
ªÀi˯ÁåAPÀ£À - ªÀiÁZïð 2024 - ªÀiÁzÀj ¥Àæ±ÉÆßÃvÀÛgÀ ¥ÀwæPÉ
Assessment - March 2024 Model Paper
CAPÀUÀ¼ÀÄ : 80
vÀgÀUÀw : 9 «µÀAiÀÄ : UÀtÂvÀ
¸ÀªÀÄAiÀÄ : 3 UÀAmÉ
«zÁåyðUÀ¼ÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
«zÁåyðAiÀÄ ºÉ¸ÀgÀÄ : _____________________________________________________________________
«zÁåyðAiÀÄ SATS ¸ÀASÉå : «zÁåyðAiÀÄ ¸À» :_______________
PÉÆoÀr ªÉÄðéZÁgÀPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁVgÀĪÀ ªÀiÁ»w
±Á¯ÉAiÀÄ qÉʸï PÉÆÃqï :
±Á¯ÉAiÀÄ ºÉ¸ÀgÀÄ :_________________________________________________________________________
PÀè¸ÀÖgï :______________________ ¨ÁèPï :_______________________ f¯Éè :_______________________
±Á¯ÉAiÀÄ «zsÀ : ¸ÀPÁðj C£ÀÄzÁ¤vÀ C£ÀÄzÁ£À gÀ»vÀ
(C£Àé¬Ä¸ÀĪÀ ªÀiÁ»wUÉ “” UÀÄgÀÄvÀÄ ºÁQj)
PÉÆoÀr ªÉÄðéZÁgÀPÀgÀ ¸À» :______________________________
ªÀiË®åªÀiÁ¥À£À ¸ÀªÀÄAiÀÄzÀ°è ²PÀëPÀgÀÄ ¨sÀwð ªÀiÁqÀ¨ÉÃPÁzÀ ªÀiÁ»w
¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ ¥Àæ±Éß ¸ÀASÉå ¥ÀqÉzÀ CAPÀUÀ¼ÀÄ
1 14 27
2 15 28
3 16 29
4 17 30
5 18 31
6 19 32
7 20 33
8 21 34
9 22 35
10 23 36
11 24 37
12 25 38
13 26
MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ MlÄÖ CAPÀUÀ¼ÀÄ
MlÄÖ UÀ½¹zÀ CAPÀ
MlÄÖ UÀ½¹zÀ CAPÀUÀ¼ÀÄ (CPÀëgÀUÀ¼À°è)___________________________________________________________
ªÀiË®åªÀiÁ¥ÀPÀgÀ ¸À» : _______________________
Page 27
2
I. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ C¥ÀÇtð ºÉýPÉUÀ½UÉ £Á®ÄÌ ¥ÀAiÀiÁðAiÀÄUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ. CªÀÅUÀ¼À°è CvÀåAvÀ
¸ÀÆPÀÛªÁzÀzÀ£ÀÄß Dj¹ PÀæªÀiÁPÀëgÀzÉÆqÀ£É §gɬÄj. 8x1=8
3
1. 4 2 gÀ ¨É¯ÉAiÀÄÄ
A. 8 B. 16 C. 32 D. 64
GvÀÛgÀ: ____________________
2. PÉÆnÖgÀĪÀ avÀæzÀ°è 'x' £À C¼ÀvÉAiÀÄÄ
A. 600 B. 900 C. 1200 D. 1800
n
Q 600
l
P
m
xº
GvÀÛgÀ: ____________________
3. §ºÀÄ¥ÀzÉÆÃQÛ p(x)=3x2-2 gÀ°è, p (1) gÀ ¨É¯ÉAiÀÄÄ
A. 2 B. 1 C. 5 D. 0
GvÀÛgÀ: ____________________
4. F PɼÀV£ÀªÀÅUÀ¼À°è ¸À«ÄÃPÀgÀt x + 2y = 6 gÀ, MAzÀÄ ¥ÀjºÁgÀªÀÅ
A. (1,3) B. (3,1) C. (4,2) D. (2,2)
GvÀÛgÀ: ____________________
I. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ C¥ÀÇtð ºÉýPÉUÀ½UÉ £Á®ÄÌ ¥ÀAiÀiÁðAiÀÄUÀ¼À£ÀÄß ¤ÃqÀ¯ÁVzÉ. CªÀÅUÀ¼À°è CvÀåAvÀ
¸ÀÆPÀÛªÁzÀzÀ£ÀÄß Dj¹ PÀæªÀiÁPÀëgÀzÉÆqÀ£É §gɬÄj. 8x1=8
3
1. 4 2 gÀ ¨É¯ÉAiÀÄÄ
A. 8 B. 16 C. 32 D. 64
GvÀÛgÀ: ____________________
2. PÉÆnÖgÀĪÀ avÀæzÀ°è 'x' £À C¼ÀvÉAiÀÄÄ
A. 600 B. 900 C. 1200 D. 1800
n
Q 600
l
P
m
xº
GvÀÛgÀ: ____________________
3. §ºÀÄ¥ÀzÉÆÃQÛ p(x)=3x2-2 gÀ°è, p (1) gÀ ¨É¯ÉAiÀÄÄ
A. 2 B. 1 C. 5 D. 0
GvÀÛgÀ: ____________________
4. F PɼÀV£ÀªÀÅUÀ¼À°è ¸À«ÄÃPÀgÀt x + 2y = 6 gÀ, MAzÀÄ ¥ÀjºÁgÀªÀÅ
A. (1,3) B. (3,1) C. (4,2) D. (2,2)
GvÀÛgÀ: ____________________
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5. 'M' ©AzÀĪÀÅ x-CPÀëzÀ ªÉÄðzÀÝgÉ CzÀgÀ ¤zÉÃð±ÁAPÀUÀ¼ÀÄ
A. (0.x) B. (0,-x) C. (x,0) D. (x,-x)
GvÀÛgÀ: ____________________
6. MAzÀÄ DlzÀ°è UÉ®ÄèªÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 0.86 DzÀgÉ, D DlªÀ£ÀÄß UÉ®è¢gÀĪÀ
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ
A. 0.14 B. 0.76 C. 0.85 D. 0.41
GvÀÛgÀ: ____________________
7. PÉÆnÖgÀĪÀ avÀæzÀ°è ∆ABC AiÀÄ «¹ÛÃtðªÀÅ A
A. 32.5 cm2 B. 15 cm2 12
5
C. 78 cm2 D. 30 cm2
B C
13
GvÀÛgÀ: ____________________
8. PÉÆnÖgÀĪÀ avÀæªÀ£ÀÄß UÀªÀĤ¹.
A P Q R B
EªÀÅUÀ¼À°è ¸ÀjAiÀiÁzÀ ¸ÀA§AzsÀªÀÅ.
A. AP > PQ + QR+RB B. AP + P Q + QR <AB
C. AR > AB D. PQ > PQ + QR
GvÀÛgÀ: ____________________
[ Turn over
5. 'M' ©AzÀĪÀÅ x-CPÀëzÀ ªÉÄðzÀÝgÉ CzÀgÀ ¤zÉÃð±ÁAPÀUÀ¼ÀÄ
A. (0.x) B. (0,-x) C. (x,0) D. (x,-x)
GvÀÛgÀ: ____________________
6. MAzÀÄ DlzÀ°è UÉ®ÄèªÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 0.86 DzÀgÉ, D DlªÀ£ÀÄß UÉ®è¢gÀĪÀ
¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ
A. 0.14 B. 0.76 C. 0.85 D. 0.41
GvÀÛgÀ: ____________________
7. PÉÆnÖgÀĪÀ avÀæzÀ°è ∆ABC AiÀÄ «¹ÛÃtðªÀÅ A
A. 32.5 cm2 B. 15 cm2 12
5
C. 78 cm2 D. 30 cm2
B C
13
GvÀÛgÀ: ____________________
8. PÉÆnÖgÀĪÀ avÀæªÀ£ÀÄß UÀªÀĤ¹.
A P Q R B
EªÀÅUÀ¼À°è ¸ÀjAiÀiÁzÀ ¸ÀA§AzsÀªÀÅ.
A. AP > PQ + QR+RB B. AP + P Q + QR <AB
C. AR > AB D. PQ > PQ + QR
GvÀÛgÀ: ____________________
[ Turn over
Page 29
4
II. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 8x1=8
9. 3 + √3 £ÀÄß MAzÀÄ ¨sÁUÀ®§Ý ¸ÀASÉåAiÀÄ£ÁßV ªÀiÁqÀ®Ä UÀÄt¸À¨ÉÃPÁzÀ ¸ÀASÉåAiÀÄ£ÀÄß §gɬÄj.
10. JgÀqÀÄ «©ü£Àß ©AzÀÄUÀ¼À ªÀÄÆ®PÀ ºÁzÀÄ ºÉÆÃUÀĪÀAvÉ JµÀÄÖ ¸ÀgÀ¼À gÉÃSÉUÀ¼À£ÀÄß J¼ÉAiÀħºÀÄzÀÄ?
11. vÁæ¦dåzÀ M¼À PÉÆãÀUÀ¼À ªÉÆvÀÛªÀ£ÀÄß §gɬÄj.
A E B F
12. PÉÆnÖgÀĪÀ avÀæzÀ°è ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðd
ABCD AiÀÄ «¹ÛÃtðªÀÅ 42 cm2 DzÀgÉ
¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðd EFCD AiÀÄ «¹ÛÃtðªÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
D C
13. (x + y + z)2 £À «¸ÀÛöÈvÀ gÀÆ¥ÀªÀ£ÀÄß §gɬÄj.
14. P (- 3, 8) ©AzÀÄ«UÉ x -CPÀë¢AzÀ EgÀĪÀ zÀÆgÀªÀ£ÀÄß §gɬÄj.
II. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 8x1=8
9. 3 + √3 £ÀÄß MAzÀÄ ¨sÁUÀ®§Ý ¸ÀASÉåAiÀÄ£ÁßV ªÀiÁqÀ®Ä UÀÄt¸À¨ÉÃPÁzÀ ¸ÀASÉåAiÀÄ£ÀÄß §gɬÄj.
10. JgÀqÀÄ «©ü£Àß ©AzÀÄUÀ¼À ªÀÄÆ®PÀ ºÁzÀÄ ºÉÆÃUÀĪÀAvÉ JµÀÄÖ ¸ÀgÀ¼À gÉÃSÉUÀ¼À£ÀÄß J¼ÉAiÀħºÀÄzÀÄ?
11. vÁæ¦dåzÀ M¼À PÉÆãÀUÀ¼À ªÉÆvÀÛªÀ£ÀÄß §gɬÄj.
A E B F
12. PÉÆnÖgÀĪÀ avÀæzÀ°è ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðd
ABCD AiÀÄ «¹ÛÃtðªÀÅ 42 cm2 DzÀgÉ
¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðd EFCD AiÀÄ «¹ÛÃtðªÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
D C
13. (x + y + z)2 £À «¸ÀÛöÈvÀ gÀÆ¥ÀªÀ£ÀÄß §gɬÄj.
14. P (- 3, 8) ©AzÀÄ«UÉ x -CPÀë¢AzÀ EgÀĪÀ zÀÆgÀªÀ£ÀÄß §gɬÄj.
Page 30
5
15. PÉÆnÖgÀĪÀ avÀæzÀ°è AB = CD ªÀÄvÀÄÛ ON= 3 cm DVzÉ OM A
C
£À C¼ÀvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
N
M
O
D
B
16. ¥Àæw CAa£À GzÀÝ 9 cm DVgÀĪÀ ZËPÀWÀ£ÀzÀ WÀ£À¥sÀ®ªÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
III. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 8 x 2 = 16
p
17. 0.3 £ÀÄß q gÀÆ¥ÀzÀ°è ªÀåPÀÛ¥Àr¹. (E°è p ªÀÄvÀÄÛ q ¸ÀºÀ C«¨sÁdåUÀ¼ÀÄ)
[ Turn over
15. PÉÆnÖgÀĪÀ avÀæzÀ°è AB = CD ªÀÄvÀÄÛ ON= 3 cm DVzÉ OM A
C
£À C¼ÀvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
N
M
O
D
B
16. ¥Àæw CAa£À GzÀÝ 9 cm DVgÀĪÀ ZËPÀWÀ£ÀzÀ WÀ£À¥sÀ®ªÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
III. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 8 x 2 = 16
p
17. 0.3 £ÀÄß q gÀÆ¥ÀzÀ°è ªÀåPÀÛ¥Àr¹. (E°è p ªÀÄvÀÄÛ q ¸ÀºÀ C«¨sÁdåUÀ¼ÀÄ)
[ Turn over
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6
18. PÉÆnÖgÀĪÀ avÀæzÀ°è AB || CD DVzÉ x £À ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
570
A B
1170
C D
x
19. PÉÆnÖgÀĪÀ avÀæzÀ°è, P AiÀÄÄ ¸ÀªÀiÁ£ÁAvÀgÀ ZÀvÀĨsÀÄðd ABCD AiÀÄ M¼ÀV£À AiÀiÁªÀÅzÁzÀgÀÆ
A B
MAzÀÄ ©AzÀĪÁzÀgÉ
«(∆ABP) + «(∆PCD) = ½ « ( ABCD).
P
JAzÀÄ ¸Á¢ü¹.
D C
18. PÉÆnÖgÀĪÀ avÀæzÀ°è AB || CD DVzÉ x £À ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
570
A B
1170
C D
x
19. PÉÆnÖgÀĪÀ avÀæzÀ°è, P AiÀÄÄ ¸ÀªÀiÁ£ÁAvÀgÀ ZÀvÀĨsÀÄðd ABCD AiÀÄ M¼ÀV£À AiÀiÁªÀÅzÁzÀgÀÆ
A B
MAzÀÄ ©AzÀĪÁzÀgÉ
«(∆ABP) + «(∆PCD) = ½ « ( ABCD).
P
JAzÀÄ ¸Á¢ü¹.
D C
Page 32
7
20. (2a + 3b) AiÀÄ WÀ£ÀªÀ£ÀÄß ¸ÀÆPÀÛ ¤vÀå ¸À«ÄÃPÀgÀt §¼À¹ PÀAqÀÄ»r¬Äj.
[ Turn over
20. (2a + 3b) AiÀÄ WÀ£ÀªÀ£ÀÄß ¸ÀÆPÀÛ ¤vÀå ¸À«ÄÃPÀgÀt §¼À¹ PÀAqÀÄ»r¬Äj.
[ Turn over
Page 33
8
21. PɼÀV£À PÉÆõÀÖPÀzÀ°è MAzÀÄ vÀgÀUÀwAiÀÄ 50 «zÁåyðUÀ¼ÀÄ UÀtÂvÀ ¥ÀjÃPÉëAiÀÄ°è ¥ÀqÉ¢gÀĪÀ CAPÀUÀ¼À£ÀÄß
¤ÃrzÉ. F zÀvÁÛA±ÀPÉÌ »¸ÉÆÖÃUÁæªÀiï J¼É¬Äj.
CAPÀUÀ¼ÀÄ 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
DªÀÈwÛ 5 10 15 12 8
21. PɼÀV£À PÉÆõÀÖPÀzÀ°è MAzÀÄ vÀgÀUÀwAiÀÄ 50 «zÁåyðUÀ¼ÀÄ UÀtÂvÀ ¥ÀjÃPÉëAiÀÄ°è ¥ÀqÉ¢gÀĪÀ CAPÀUÀ¼À£ÀÄß
¤ÃrzÉ. F zÀvÁÛA±ÀPÉÌ »¸ÉÆÖÃUÁæªÀiï J¼É¬Äj.
CAPÀUÀ¼ÀÄ 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50
DªÀÈwÛ 5 10 15 12 8
Page 34
9
22. MAzÀÄ ¢£À M§â ªÀåQÛAiÀÄÄ vÀ£Àß CAUÀrAiÀÄ ªÀÄÄAzÉ 230 ¢éZÀPÀæ, 160 wæZÀPÀæ ºÁUÀÆ 70 £Á®ÄÌ
ZÀPÀæzÀ ªÁºÀ£ÀUÀ¼ÀÄ ºÁzÀÄ ºÉÆÃUÀĪÀÅzÀ£ÀÄß «ÃQë¹zÀ£ÀÄ. D ªÀåQÛAiÀÄÄ «ÃQë¹zÀ ªÁºÀ£ÀUÀ¼À°è MAzÀÄ
ªÁºÀ£À ¢éZÀPÀæªÁºÀ£ÀªÁVgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
23. MAzÀÄ £ÉÃgÀ ªÀÈvÀÛ ¥ÁzÀ ¹°AqÀj£À JvÀÛgÀ 14cm ªÀÄvÀÄÛ CzÀgÀ ªÀPÀæ ªÉÄïÉäöÊ «¹ÛÃtðªÀÅ 176 cm2
DzÀgÉ ¹°AqÀj£À ¥ÁzÀzÀ ªÁå¸ÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
[ Turn over
22. MAzÀÄ ¢£À M§â ªÀåQÛAiÀÄÄ vÀ£Àß CAUÀrAiÀÄ ªÀÄÄAzÉ 230 ¢éZÀPÀæ, 160 wæZÀPÀæ ºÁUÀÆ 70 £Á®ÄÌ
ZÀPÀæzÀ ªÁºÀ£ÀUÀ¼ÀÄ ºÁzÀÄ ºÉÆÃUÀĪÀÅzÀ£ÀÄß «ÃQë¹zÀ£ÀÄ. D ªÀåQÛAiÀÄÄ «ÃQë¹zÀ ªÁºÀ£ÀUÀ¼À°è MAzÀÄ
ªÁºÀ£À ¢éZÀPÀæªÁºÀ£ÀªÁVgÀĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
23. MAzÀÄ £ÉÃgÀ ªÀÈvÀÛ ¥ÁzÀ ¹°AqÀj£À JvÀÛgÀ 14cm ªÀÄvÀÄÛ CzÀgÀ ªÀPÀæ ªÉÄïÉäöÊ «¹ÛÃtðªÀÅ 176 cm2
DzÀgÉ ¹°AqÀj£À ¥ÁzÀzÀ ªÁå¸ÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
[ Turn over
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24. MAzÀÄ PÉÆoÀrAiÀÄ GzÀÝ, CUÀ® ªÀÄvÀÄÛ JvÀÛgÀUÀ¼ÀÄ PÀæªÀĪÁV 5m, 4m ªÀÄvÀÄÛ 3m DVªÉ. PÉÆoÀrAiÀÄ
UÉÆÃqÉUÀ½UÉ ªÀÄvÀÄÛ ªÉÄïÁѪÀtÂUÉ ¸ÀÄtÚ §½AiÀÄ®Ä ¥Àæw «ÄÃlgïUÉ `10 gÀAvÉ vÀUÀ®ÄªÀ ªÉZÀѪÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
24. MAzÀÄ PÉÆoÀrAiÀÄ GzÀÝ, CUÀ® ªÀÄvÀÄÛ JvÀÛgÀUÀ¼ÀÄ PÀæªÀĪÁV 5m, 4m ªÀÄvÀÄÛ 3m DVªÉ. PÉÆoÀrAiÀÄ
UÉÆÃqÉUÀ½UÉ ªÀÄvÀÄÛ ªÉÄïÁѪÀtÂUÉ ¸ÀÄtÚ §½AiÀÄ®Ä ¥Àæw «ÄÃlgïUÉ `10 gÀAvÉ vÀUÀ®ÄªÀ ªÉZÀѪÀ£ÀÄß
PÀAqÀÄ»r¬Äj.
Page 36
11
IV. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 9 x 3 = 27
25. √5.6 C£ÀÄß ¸ÀASÁågÉÃSÉAiÀÄ ªÉÄÃ¯É ¥Àæw¤¢ü¹.
[ Turn over
IV. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 9 x 3 = 27
25. √5.6 C£ÀÄß ¸ÀASÁågÉÃSÉAiÀÄ ªÉÄÃ¯É ¥Àæw¤¢ü¹.
[ Turn over
Page 37
12
26. F PɼÀV£À ¥Áæ¥ÁÛAPÀUÀ¼À£ÀÄß KjPÉ PÀæªÀÄzÀ°è eÉÆÃr¸À¯ÁVzÉ. EªÀÅUÀ¼À ªÀÄzsÁåAPÀªÀÅ 47 DzÀgÉ, x £À
¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj ªÀÄvÀÄÛ F ¥Áæ¥ÁÛAPÀUÀ¼À ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
17, 28, 31, 39, x, x+2, 51, 58, 63, 71
26. F PɼÀV£À ¥Áæ¥ÁÛAPÀUÀ¼À£ÀÄß KjPÉ PÀæªÀÄzÀ°è eÉÆÃr¸À¯ÁVzÉ. EªÀÅUÀ¼À ªÀÄzsÁåAPÀªÀÅ 47 DzÀgÉ, x £À
¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj ªÀÄvÀÄÛ F ¥Áæ¥ÁÛAPÀUÀ¼À ¸ÀgÁ¸Àj PÀAqÀÄ»r¬Äj.
17, 28, 31, 39, x, x+2, 51, 58, 63, 71
Page 38
13
27. 'MAzÀÄ ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðdzÀ PÀtðªÀÅ CzÀ£ÀÄß JgÀqÀÄ ¸ÀªÀð¸ÀªÀÄ wæ¨sÀÄdUÀ¼ÁV «¨sÁV¸ÀÄvÀÛzÉ',
JAzÀÄ ¸Á¢ü¹.
[ Turn over
27. 'MAzÀÄ ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðdzÀ PÀtðªÀÅ CzÀ£ÀÄß JgÀqÀÄ ¸ÀªÀð¸ÀªÀÄ wæ¨sÀÄdUÀ¼ÁV «¨sÁV¸ÀÄvÀÛzÉ',
JAzÀÄ ¸Á¢ü¹.
[ Turn over
Page 39
14
28. PÉÆnÖgÀĪÀ avÀæzÀ°è E AiÀÄÄ ªÀÈvÀÛ PÉÃAzÀæªÁVzÀÄÝ A
D
ABC = 69° ªÀÄvÀÄÛ ACB = 31° DVzÉ. BDC ,
BEC ªÀÄvÀÄÛ BFC UÀ¼À C¼ÀvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
E
69 0
310
B C
F
28. PÉÆnÖgÀĪÀ avÀæzÀ°è E AiÀÄÄ ªÀÈvÀÛ PÉÃAzÀæªÁVzÀÄÝ A
D
ABC = 69° ªÀÄvÀÄÛ ACB = 31° DVzÉ. BDC ,
BEC ªÀÄvÀÄÛ BFC UÀ¼À C¼ÀvÉUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.
E
69 0
310
B C
F
Page 40
15
29. x+y+z=0 DzÀgÉ x +y +z =3xyz
3 3 3
JAzÀÄ ¸Á¢ü¹.
30. PÉÆnÖgÀĪÀ avÀæzÀ°è 'l' gÉÃSÉAiÀÄÄ A £À
PÉÆãÁzsÀðPÀ gÉÃSÉAiÀiÁVzÀÄÝ, B AiÀÄÄ CzÀgÀ Q
ªÉÄð£À AiÀiÁªÀÅzÁzÀgÀÆ MAzÀÄ ©AzÀĪÁVzÉ l
BP ªÀÄvÀÄÛ BQ UÀ¼ÀÄ A £À ¨ÁºÀÄUÀ½UÉ J¼ÉzÀ B
®A§UÀ¼ÁzÀgÉ BP = BQ JAzÀÄ ¸Á¢ü¹.
A P
[ Turn over
29. x+y+z=0 DzÀgÉ x +y +z =3xyz
3 3 3
JAzÀÄ ¸Á¢ü¹.
30. PÉÆnÖgÀĪÀ avÀæzÀ°è 'l' gÉÃSÉAiÀÄÄ A £À
PÉÆãÁzsÀðPÀ gÉÃSÉAiÀiÁVzÀÄÝ, B AiÀÄÄ CzÀgÀ Q
ªÉÄð£À AiÀiÁªÀÅzÁzÀgÀÆ MAzÀÄ ©AzÀĪÁVzÉ l
BP ªÀÄvÀÄÛ BQ UÀ¼ÀÄ A £À ¨ÁºÀÄUÀ½UÉ J¼ÉzÀ B
®A§UÀ¼ÁzÀgÉ BP = BQ JAzÀÄ ¸Á¢ü¹.
A P
[ Turn over
Page 41
16
31. 2x+y=7 F gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀtPÉÌ £ÀPÉë gÀa¹.
31. 2x+y=7 F gÉÃSÁvÀäPÀ ¸À«ÄÃPÀgÀtPÉÌ £ÀPÉë gÀa¹.
Page 42
17
32. PÉÆnÖgÀĪÀ avÀæzÀ°è ABQ £À PÉÆãÁzsÀðPÀ BE AiÀÄÄ A E
BCS £À PÉÆãÁzsÀðPÀ CG UÉ ¸ÀªÀiÁAvÀgÀªÁVzÉ.
PQ || RS JAzÀÄ ¸Á¢ü¹.
P Q
B
G
C
R S
D
[ Turn over
32. PÉÆnÖgÀĪÀ avÀæzÀ°è ABQ £À PÉÆãÁzsÀðPÀ BE AiÀÄÄ A E
BCS £À PÉÆãÁzsÀðPÀ CG UÉ ¸ÀªÀiÁAvÀgÀªÁVzÉ.
PQ || RS JAzÀÄ ¸Á¢ü¹.
P Q
B
G
C
R S
D
[ Turn over
Page 43
18
33. MAzÀÄ wæ¨sÀÄeÁPÁgÀzÀ d«ÄãÀ£ÀÄß ªÀÄÆgÀÄ d£ÀjUÉ ¸ÀªÀÄ£ÁV ºÀAZÀ¨ÉÃPÁVzÉ. d«Ää£À JgÀqÀÄ
¨ÁºÀÄUÀ¼ÀÄ 100 «ÄÃlgï ªÀÄvÀÄÛ 160 «ÄÃlgï DVzÀÄÝ CzÀgÀ ¸ÀÄvÀÛ¼ÀvÉAiÀÄÄ 360 «ÄÃlgï DVzÉ.
¥ÀæwAiÉƧâjUÀÆ ¹UÀ§ºÀÄzÁzÀ d«Ää£À «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
33. MAzÀÄ wæ¨sÀÄeÁPÁgÀzÀ d«ÄãÀ£ÀÄß ªÀÄÆgÀÄ d£ÀjUÉ ¸ÀªÀÄ£ÁV ºÀAZÀ¨ÉÃPÁVzÉ. d«Ää£À JgÀqÀÄ
¨ÁºÀÄUÀ¼ÀÄ 100 «ÄÃlgï ªÀÄvÀÄÛ 160 «ÄÃlgï DVzÀÄÝ CzÀgÀ ¸ÀÄvÀÛ¼ÀvÉAiÀÄÄ 360 «ÄÃlgï DVzÉ.
¥ÀæwAiÉƧâjUÀÆ ¹UÀ§ºÀÄzÁzÀ d«Ää£À «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
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V. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 4 x 4 = 16
34. Y = 30o, Z = 90o ªÀÄvÀÄÛ XY+YZ+ZX = 11cm EgÀĪÀAvÉ ∆XYZ gÀa¹.
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V. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 4 x 4 = 16
34. Y = 30o, Z = 90o ªÀÄvÀÄÛ XY+YZ+ZX = 11cm EgÀĪÀAvÉ ∆XYZ gÀa¹.
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35. 30 «zÁåyðUÀ½UÉ PÀ¼ÉzÀ wAUÀ½£À°è CªÀgÀÄ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ ¸ÀªÀÄAiÀĪÀ£ÀÄß UÀAmÉUÀ¼À°è
w½¸ÀĪÀAvÉ PÉüÀ¯Á¬ÄvÀÄ. CzÀgÀ ¥sÀ°vÁA±ÀªÀ£ÀÄß F PɼÀV£ÀAvÉ zÁR°¸À¯ÁVzÉ.
5, 10, 11, 16, 15, 8, 21, 26, 14, 6, 8, 9, 10, 14, 20, 10,
12, 11, 3, 7, 12, 19, 28, 30, 8, 12, 17, 16, 10, 12.
F zÀvÁÛA±ÀUÀ½UÉ ªÀUÀðAvÀgÀUÀ¼À£ÀÄß ¸ÀªÀÄUÁvÀæUÀ¼ÁV 0-5, 5-10 EvÁå¢AiÀiÁV vÉUÉzÀÄPÉÆAqÀÄ MAzÀÄ
ªÀVÃðPÀÈvÀ DªÀÈwÛ «vÀgÀuÁ ¥ÀnÖAiÀÄ£ÀÄß vÀAiÀiÁj¹ CzÀgÀ ¸ÀºÁAiÀÄ¢AzÀ F PɼÀV£À ¥Àæ±ÉßUÀ¼À£ÀÄß
GvÀÛj¹.
1. 10 UÀAmÉUÀ½VAvÀ PÀrªÉÄ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ «zÁåyðUÀ¼À ¸ÀASÉå JµÀÄÖ?
2. 25 UÀAmÉUÀ½VAvÀ ºÉZÀÄÑ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ «zÁåyðUÀ¼À ¸ÀASÉå JµÀÄÖ?
35. 30 «zÁåyðUÀ½UÉ PÀ¼ÉzÀ wAUÀ½£À°è CªÀgÀÄ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ ¸ÀªÀÄAiÀĪÀ£ÀÄß UÀAmÉUÀ¼À°è
w½¸ÀĪÀAvÉ PÉüÀ¯Á¬ÄvÀÄ. CzÀgÀ ¥sÀ°vÁA±ÀªÀ£ÀÄß F PɼÀV£ÀAvÉ zÁR°¸À¯ÁVzÉ.
5, 10, 11, 16, 15, 8, 21, 26, 14, 6, 8, 9, 10, 14, 20, 10,
12, 11, 3, 7, 12, 19, 28, 30, 8, 12, 17, 16, 10, 12.
F zÀvÁÛA±ÀUÀ½UÉ ªÀUÀðAvÀgÀUÀ¼À£ÀÄß ¸ÀªÀÄUÁvÀæUÀ¼ÁV 0-5, 5-10 EvÁå¢AiÀiÁV vÉUÉzÀÄPÉÆAqÀÄ MAzÀÄ
ªÀVÃðPÀÈvÀ DªÀÈwÛ «vÀgÀuÁ ¥ÀnÖAiÀÄ£ÀÄß vÀAiÀiÁj¹ CzÀgÀ ¸ÀºÁAiÀÄ¢AzÀ F PɼÀV£À ¥Àæ±ÉßUÀ¼À£ÀÄß
GvÀÛj¹.
1. 10 UÀAmÉUÀ½VAvÀ PÀrªÉÄ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ «zÁåyðUÀ¼À ¸ÀASÉå JµÀÄÖ?
2. 25 UÀAmÉUÀ½VAvÀ ºÉZÀÄÑ ªÉƨÉÊ¯ï §¼ÀPÉ ªÀiÁrzÀ «zÁåyðUÀ¼À ¸ÀASÉå JµÀÄÖ?
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36. MAzÀÄ ¸ÀªÀÄ¢é¨ÁºÀÄ wæ¨sÀÄdzÀ°è ¸ÀªÀÄ ¨ÁºÀÄUÀ½UÉ C©üªÀÄÄRªÁVgÀĪÀ PÉÆãÀUÀ¼ÀÄ ¸ÀªÀÄ£ÁVgÀÄvÀÛªÉ
JAzÀÄ ¸Á¢ü¹.
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36. MAzÀÄ ¸ÀªÀÄ¢é¨ÁºÀÄ wæ¨sÀÄdzÀ°è ¸ÀªÀÄ ¨ÁºÀÄUÀ½UÉ C©üªÀÄÄRªÁVgÀĪÀ PÉÆãÀUÀ¼ÀÄ ¸ÀªÀÄ£ÁVgÀÄvÀÛªÉ
JAzÀÄ ¸Á¢ü¹.
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37. x-1 EzÀÄ p(x) = 4x -3x-k £À MAzÀÄ C¥ÀªÀvÀð£ÀªÁVzÉ k £À ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj ºÁUÀÆ
2
F §ºÀÄ¥ÀzÉÆÃQÛAiÀÄ ªÀÄvÉÆÛAzÀÄ C¥ÀªÀvÀð£ÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
37. x-1 EzÀÄ p(x) = 4x -3x-k £À MAzÀÄ C¥ÀªÀvÀð£ÀªÁVzÉ k £À ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj ºÁUÀÆ
2
F §ºÀÄ¥ÀzÉÆÃQÛAiÀÄ ªÀÄvÉÆÛAzÀÄ C¥ÀªÀvÀð£ÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
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VI. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 1x5=5
38. 24 cm JvÀÛgÀ«gÀĪÀ MAzÀÄ £ÉÃgÀ ªÀÈvÀÛ ¥ÁzÀ ¹°AqÀj£À ¥ÁzÀzÀ ¥Àj¢üAiÀÄÄ 44 cm EzÉ.
EzÀgÀ WÀ£À¥sÀ®ªÀ£ÀÄß PÀAqÀÄ»r¬Äj. zÀvÀÛ ¹°AqÀj£ÀµÉÖà JvÀÛgÀ ªÀÄvÀÄÛ ¥ÁzÀzÀ wædåzÀ C¼ÀvÉAiÀÄ£ÀÄß
ºÉÆA¢gÀĪÀ ±ÀAPÀÄ«£À WÀ£À¥sÀ® ªÀÄvÀÄÛ ªÀPÀæ ªÉÄïÉäöÊ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
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VI. F PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. 1x5=5
38. 24 cm JvÀÛgÀ«gÀĪÀ MAzÀÄ £ÉÃgÀ ªÀÈvÀÛ ¥ÁzÀ ¹°AqÀj£À ¥ÁzÀzÀ ¥Àj¢üAiÀÄÄ 44 cm EzÉ.
EzÀgÀ WÀ£À¥sÀ®ªÀ£ÀÄß PÀAqÀÄ»r¬Äj. zÀvÀÛ ¹°AqÀj£ÀµÉÖà JvÀÛgÀ ªÀÄvÀÄÛ ¥ÁzÀzÀ wædåzÀ C¼ÀvÉAiÀÄ£ÀÄß
ºÉÆA¢gÀĪÀ ±ÀAPÀÄ«£À WÀ£À¥sÀ® ªÀÄvÀÄÛ ªÀPÀæ ªÉÄïÉäöÊ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.
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Document Details
| Board / Org | Karnataka Board |
| Exam | Class 9 |
| Type | Sample Paper |
| Pages | 48 |
| Updated | 30 Apr 2026 |