MODEL QUESTION PAPER 10th STANDARD SUBJECT: MATHEMATICS Time: 2 Hours 45 Min.
Max. Marks: 80
I.
Four alternatives are given for each of the following questions / incomplete statements. Only one of them is correct or most approprite. Choose the correct alternative and write the complete answer along with its alphabet in the space provided against each question. (1 x 8 = 8)
1)
If the third term of a Geometic Progression is 2, then the Product of its first five terms is, (A) 52
2)
(B) 25
(B) 20
If tan x =
(D) 100
(B) 0.2
(C) 20
(D) 0.02
(B) 5
(C) 8
(D) 10
7 then cot x is, 24
(B) 24
(C)
7 24
(D)
24 7
The cordinates of the mid point of the line segments joining the points (2, 3) and (4, 7) is, (A) (3, 5)
8)
(C) 10
If f(x) = x2 + 7x - 10 then the value of f(2) is,
(A) 7 7)
(B) 1
(A) 3 6)
(D) 30
If Mean score X = 20 and the coefficient of variation is 0.1, then the Standard deviation is, (A) 2
5)
(C) 25
Probability of an impossible event is, (A) 0
4)
(D) 15
If nC8 = nC12 then the value of n is, (A) 10
3)
(C) 10
(B) (7, 3)
(C) (3, 4)
(D) (8, 3)
The slope of the line joining the points (3, - 2) and (4, 5) is, (A) 3
(B) 5
(C) 7
II.
Answer the following
9)
Express 6762 as a Product of Prime factors.
(D) 8 (1 x 6 = 6)
10) If Universal U = {1, 2, 3, 4, 5, 6, 7, 8} and subject A = {1, 2, 3} find A|. 11) Find the zero of the Polynomial x2 + 2x + 1. 12) In leABC, ABC = 900, BD AC.
A D
If BD = 8cm and AD = 4cm find CD.
B
C .......2
-- 2 -13) In the figure ‘O’ is the centre of the circle
o
PT is a tangent and if PTQ = 300, find POT. 14) Find the Surface Area of a sphere of radius 7cm.
P
(2 x 16 = 32)
III. Answer the following 15) Prove that 5 -
T
3 is an Irrational number.
16) In a college, 60 students enrolled in Chemistry, 40 in Physics, 30 in Biology and 15 in Chemistry and Physics, 10 in Physics and Biology, 5 in Biology and Chemistry. No one enrolled in all the three subjects. Find how many are enrolled in atleast one of the subjects. 17) Classify the following into Permutations and Combinations. a) Five different subject books to be arranged on a shelf. b) There are 8 chairs and 8 people to occupy them. c) In a committee of 7 persons, a chair person, a secretary and a treasurer are to be chosen. d) Five keys are to be arranged in a circular key ring. 18) A committee of 5 is to be formed out of 6 men and 4 ladies. In how may ways can this be done when at least 2 ladies are included. 19) Rationalise the denominator and simplify : 20) Simplify : 8
5 2 3 . 3 2 5
1 1 8 2 2
21) What must be added to 2x3 + 3x2 - 22x + 12 so that the result is exactly divisible by 2x2 + 5x - 14 ? OR 2 Divide P(x) = x + 4x + 4 by g(x) = x + 2 and verify division algorithm. 1 1 1 22) Three numbers are in the ratio : : . If the sum of their squares is 644, find 3 5 6 the numbers.
23) Show that,
tan . sin + cos = sec .
24) Find the value of x, such that the distance between the points (2, 5) and (x, - 7) is 13 units. 25) Draw a circle of radius 3.5cm and construct a chord of length 6cm in it. Measure the shortest distance between the centre and the chord. 26) Draw a plan for the recordings from the surveyor’s field work book given below. (Scale 20 meters = 1cm) Meters to D 14 0 120 ------------- 60 to C to E 80 ------------- 100 50 ------------- 40 to B From A
.......3
-- 3 -27) A solid cylinder has a T.S.A. of 462 square cm. Its C.S.A. is one third of the T.S.A. Find the radius of the cylinder. OR A right circular metallic cone of height 20 cm and base radius 5 cm is melted and recast into a sphere. Find the radius of the sphere. R 28) Verify Euler’s formula for the given network.
Q
P A 29) In leABC, PQ II BC. AP = 3 cm, AR = 4.5 cm, AQ = 6 cm, AB = 5 cm and AC = 10 cm.
P R
Q
Find the length of AD .
B
C
D
30) A Bag contains 27 balls, of which some are White and others are Red. A ball is 2 . Find the number 3
chosed at random. The probability of getting a Red ball is of White balls.
(3 x 6 = 18)
IV. Answer the following questions
31) The third term of an Arithmetic Progression is 8 and the ninth term of the Arithmetic Progression exceeds three times the third term by 2. Find the sum of its first 19 terms. 32) Calculate the Standard Deviation of the given data. C.I. 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 f
7
10
15
8
10
33) The ages of Kavya and Karthik are 11 years and 14 years. In how many years will the product of their ages be 304. OR A motor boat whose speed is 15km/hr in still water goes 30 km down stream and comes back in a total of a 4 hours 30 minutes. Determine the speed of the stream. 34) Through the mid point M of the sides of a
E
Parallelogram ABCD, the line BM is drawn intersecting AC at L and AD Produced at E.
D
Prove that EL = 2BL.
M
C
L A
B
OR Prove that any two medians of a triangle divide each other in the ratio 2 : 1.
.......4
-- 4 --
A
35) The angle of elevation of the top of a tower of height “h” meters from two points at a distance of “a” and “b” meters from the base, and in the same straight line
h
with it are complementary. Prove that the height of the tower is
ab meters. OR
Prove that
B
a
D
b C
sin 1 cos = 2 cosee . 1 cos sin
36) Prove that the tangents drawn from an external point to a circle. a) are equal. b) subtend equal angles at the centre. c) are equally inclined to the line joining the centre and the external point. OR If two circles touch each other externally the centres and the point of contact are collinear. Prove. V.
(4 x 4 = 16)
Answer the following questions
37) The sum of an infinite geometric progression is 15 and the sum of the squares of these terms is 45. Find the series. OR The common difference between any two consecutive interior angles of a Polygon is 50. If the smallest angle is 1200. Find the number of sides of the Polygon ? 38) Solve Graphically: x2 - x - 2 = 0. 39) “If the square on the longest side of a triangle is equal to the sum of the squares on the other two sides, then those two sides contain a right angle” Prove. 40) Draw two direct common tangents to two circles of radii 5cm and 3cm having their centre 11cm apart. Measure the length of D.C.T. and verify. *****
ªÀiÁzÀj ¥Àæ±Éß ¥ÀwæPÉ 10£Éà vÀgÀUÀw
«µÀAiÀÄ: UÀtÂvÀ ¸ÀªÀÄAiÀÄ: 2 UÀAmÉ 45 ¤«ÄµÀUÀ¼ÀÄ.
UÀjµÀ× CAPÀUÀ¼ÀÄ: 80
I.
PɼÀV£À ¥Àæ±ÉßUÀ½UÉ CxÀªÁ C¥ÀÆtð ºÉýPÉUÀ½UÉ £Á®ÄÌ ¥ÀAiÀiÁðAiÀÄ GvÀÛgÀUÀ¼À£ÀÄß PÉÆnÖzÉ. CªÀÅUÀ¼À°è ¸ÀjAiÀiÁzÀ ªÀÄvÀÄÛ ºÉZÀÄÑ ¸ÀÆPÀÛªÁzÀ GvÀÛgÀªÀ£ÀÄß Dj¹, GvÀÛgÀPÉÌ PÉÆnÖgÀĪÀ eÁUÀzÀ°èAiÉÄà PÀæªÀigÀÁPÀzë ÉÆqÀ£É ¥ÀÆtð GvÀÛgÀªÀ£ÀÄß §gɬÄj. (1 x 8 = 8)
1)
UÀÄuÉÆÃvÀÛgÀ ±ÉæÃrüAiÀÄ ªÀÄÆgÀ£Éà ¥ÀzÀªÀÅ 2 DVzÀÝgÉ ±ÉæÃrüAiÀÄ ªÉÆzÀ® LzÀÄ ¥ÀzÀUÀ¼À UÀÄt®§ÞªÀÅ, (A) 52
2)
n
(B) 25
(B) 20
(B) 1
(B) 0.2
tan x =
(B) 5
(C) 20
(D) 0.02
(C) 8
(D) 10
(B) 24
(C)
7 24
(D)
24 7
(2, 3) ªÀÄvÀÄÛ (4, 7) ©AzÀÄUÀ¼À£ÀÄß ¸ÉÃj¸ÀĪÀ gÉÃSÁRAqÀzÀ ªÀÄzsÀå©AzÀÄ«£À ¤zÉðñÁAPÀUÀ¼ÀÄ, (A) (3, 5)
8)
(D) 100
7 DzÀgÉ cot x UÉ ¸ÀªÀÄ£ÁzÀÄzÀÄ, 24
(A) 7
7)
(C) 10
f(x) = x2 + 7x - 10 DzÁUÀ f(2) £À ¨É¯ÉAiÀÄÄ, (A) 3
6)
(D) 30
¸ÀgÁ¸Àj ¥Àæ¥ÁÛAPÀ X = 20 ªÀÄvÀÄÛ ªÀiÁ¦ð£À UÀÄuÁAPÀªÀÅ 0.1 EzÀÝgÉ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄÄ, (A) 2
5)
(C) 25
C¸ÀA¨sÀªÀ WÀl£ÉAiÀÄ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ, (A) 0
4)
(D) 15
C8 = nC12 DzÁUÀ n£À ¨É¯ÉAiÀÄÄ,
(A) 10
3)
(C) 10
(B) (7, 3)
(C) (3, 4)
(D) (8, 3)
(3, -2) ªÀÄvÀÄÛ (4, 5) ©AzÀÄUÀ¼À£ÀÄß ¸ÉÃj¸ÀĪÀ gÉÃSÉAiÀÄ E½eÁgÀÄ, (A) 3
(B) 5
(C) 7
II.
PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹.
9)
6762 £ÀÄß C«¨sÁdå C¥ÀªÀvÀð£ÀUÀ¼À UÀÄt®§ÞªÁV ¤gÀƦ¹.
(D) 8 (1 x 6 = 6)
10) «±ÀéUÀt U = {1, 2, 3, 4, 5, 6, 7, 8} ªÀÄvÀÄÛ G¥ÀUÀt A = {1, 2, 3} DzÀgÉ A| PÀAqÀÄ»r¬Äj. 11) x2 + 2x + 1 §ºÀÄ¥ÀzÉÆÃQÛAiÀÄ ±ÀÆ£ÀåvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. 12) ABC wæ¨sÀÄdzÀ°è ABC = 900 ªÀÄvÀÄÛ BD AC.
A D
BD = 8¸ÉA«Äà ªÀÄvÀÄÛ AD = 4¸ÉA«Äà EzÀÝgÉ CD AiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.
B
C .......2
-- 2 --
13) F avÀæzÀ°è ‘O’ ªÀÈvÀÛPÉÃAzÀæ PT ¸Àà±ÀðPÀ ªÀÄvÀÄÛ
o
0
PTQ = 30 EzÀÝgÉ POT ªÀ£ÀÄß PÀAqÀÄ»r¬Äj. P
T
14) 7¸ÉA«Äà wædåªÀżÀî MAzÀÄ UÉÆüÀzÀ ªÉÄïÉäöÊ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj. III. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. (2 x 16 = 32) 15) 5 - 3 MAzÀÄ C¨sÁUÀ®§Þ ¸ÀASÉå JAzÀÄ ¸Á¢ü¹. 16) MAzÀÄ PÁ¯ÉÃf£À°è 60 «zÁåyðUÀ¼ÀÄ gÀ¸ÁAiÀÄ£À±Á¸ÀÛçPÀÆÌ, 40 «zÁåyðUÀ¼ÀÄ ¨sËvÀ±Á¸ÀÛçPÀÆÌ, 30 «zÁåyðUÀ¼ÀÄ fêÀ±Á¸ÀÛçPÀÆÌ, ªÀÄvÀÄÛ 15 «zÁåyðUÀ¼ÀÄ ¨sËvÀ±Á¸ÀÛç ªÀÄvÀÄÛ gÀ¸ÁAiÀÄ£À±Á¸ÀÛçPÀÆÌ, 10 «zÁåyðUÀ¼ÀÄ ¨sËvÀ±Á¸ÀÛç ªÀÄvÀÄÛ fêÀ±Á¸ÀÛçPÀÆÌ ºÁUÀÆ 5 «zÁåyðUÀ¼ÀÄ fêÀ±Á¸ÀÛç ªÀÄvÀÄÛ gÀ¸ ÁAiÀ Ä£À ±Á¸À ÛçPÀÆ Ì £ÉÆ ÃAzÁ¬Ä¹zÁÝgÉ . AiÀ iÁªÀ «zÁåyðAiÀ ÄÆ ªÀ ÄÆgÀ Ä «µÀ AiÀ ÄUÀ¼ À° è £ÉÆÃAzÁ¬Ä¹®è. PÀ¤µÀ× MAzÀÄ «µÀAiÀÄzÀ°è JµÀÄÖ «zÁåyðUÀ¼ÀÄ £ÉÆÃAzÁ¬Ä¹zÁÝgÉ JA§ÄzÀ£ÀÄß PÀAqÀÄ»r¬Äj. 17) PɼÀV£ÀªÀÅUÀ¼À£ÀÄß PÀæªÀÄAiÉÆÃd£ÉUÀ¼ÀÄ ªÀÄvÀÄÛ «PÀ®àUÀ¼ÁV «AUÀr¹. a) LzÀÄ ««zsÀ «µÀAiÀÄUÀ¼À ¥ÀĸÀÛPÀUÀ¼À£ÀÄß MAzÀÄ PÀ¥Án£À°è eÉÆÃr¸À¨ÉÃPÁVzÉ. b) 8 PÀÄaðUÀ¼À°è 8 ªÀåQÛUÀ¼ÀÄ PÀĽvÀÄPÉƼÀî ¨ÉÃPÁVzÉ. c) 7 ¸ÀzÀ¸ÀåjgÀĪÀ MAzÀÄ ¸À«Äw¬ÄAzÀ M§â CzsÀåPÀëgÀÄ, M§â PÁAiÀÄðzÀ²ð ºÁUÀÆ M§â ReÁAaAiÀÄ£ÀÄß DAiÉÄÌ ªÀiÁqÀ¨ÉÃPÁVzÉ. d) ªÀÈvÁÛPÁgÀ Qð jAUï£À°è 5 QðUÀ¼À£ÀÄß eÉÆÃr¸À¨ÉÃPÁVzÉ. 18) 6 ¥ÀÄgÀĵÀgÀÄ ªÀÄvÀÄÛ 4 ªÀÄ»¼ÉAiÀÄjAzÀ 5 d£ÀgÀ ¸À«ÄwAiÀÄ£ÀÄß gÀa¸À¨ÉÃPÁVzÉ. PÀ¤µÀ× E§âgÀÄ ªÀÄ»¼ÉAiÀÄjgÀĪÀAvÉ JµÀÄÖ jÃwAiÀÄ°è ¸À«ÄwAiÀÄ£ÀÄß gÀa¸À§ºÀÄzÀÄ PÀAqÀÄ»r¬Äj. 5 2 3
19) bÉÃzÀªÀ£ÀÄß CPÀgÀtÂÃPÀj¹, ¸ÀÄ®¨sÀ gÀÆ¥ÀPÉÌ vÀ¤ß : 3 2 5 . 1 1 8 20) ¸ÀAPÉëæ¹ : 8 2
2
21) 2x3 + 3x2 -22x + 12 PÉÌ JµÀÖ£ÀÄß PÀÆrzÁUÀ §gÀĪÀ ¥ÀzÀªÀÅ 2x2 + 5x - 14 jAzÀ ¤±ÉåõÀªÁV ¨sÁUÀªÁUÀÄvÀÛzÉ ? CxÀªÁ 2 P(x) = x + 4x + 4 £ÀÄß g(x) = x + 2 ¤AzÀ ¨sÁV¹ ¨sÁUÁPÁgÀzÀ C¯ÁÎjxÀA £ÀÄß vÁ¼É£ÉÆÃr. 1 1 1
22) ªÀÄÆgÀÄ ¸ÀASÉåUÀ¼ÀÄ : : C£ÀÄ¥ÁvÀzÀ°èªÉ. CªÀÅUÀ¼À ªÀUÀðUÀ¼À ªÉÆvÀÛªÀÅ 644 EzÀÝgÉ, ¸ÀASÉåUÀ¼À£ÀÄß 3 5 6 PÀAqÀÄ»r¬Äj. 23) tan . sin + cos = sec JAzÀÄ vÉÆÃj¹. 24) (2, 5) ªÀÄvÀÄÛ (x, - 7) ©AzÀÄUÀ¼À £ÀqÀÄ«£À zÀÆgÀªÀÅ 13 ªÀiÁ£À DVzÀÝgÉ “ x ” £À ¨É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. 25) 3.5¸ÉA«Äà wædåªÀżÀî ªÀÈvÀÛªÀ£ÀÄß J¼É¬Äj. CzÀgÀ°è 6¸ÉA«Äà GzÀÝzÀ eÁåªÀ£ÀÄß gÀa¹, PÉÃAzÀæ¢AzÀ eÁåUÉ EgÀĪÀ Cw PÀrªÉÄ zÀÆgÀªÀ£ÀÄß C¼ÀvÉ ªÀiÁr. 26) M§â ªÉÆÃf¤zÁgÀ£À zÁR¯É ¥ÀĸÀÛPÀ¢AzÀ PÉÆnÖgÀĪÀ zÀvÁÛA±ÀUÀ½UÉ MAzÀÄ AiÉÆÃd£ÉAiÀÄ£ÀÄß vÀAiÀiÁj¹. (¥ÀæªÀiÁt 20 «ÄÃlgï = 1¸ÉA«ÄÃ) «ÄÃlgïUÀ¼ÀÄ D UÉ 14 0 120 ------------- C
E
UÉ
UÉ
60
UÉ
40
80 ------------- 100 50 -------------- B A
¬ÄAzÀ
.......3
-- 3 --
27) MAzÀÄ WÀ£À ¹°AqÀgï£À ¥ÀÆtð ªÉÄïÉäöÊ «¹ÛÃtð 462 ZÀzÀgÀ ¸ÉA«ÄÃ. EzÀÄÝ, CzÀgÀ ªÀPÀæªÉÄïÉäöÊ «¹ÛÃtðªÀÅ, ¥ÀÆtðªÉÄïÉäöÊ «¹ÛÃtðzÀ ªÀÄÆgÀ£Éà MAzÀgÀµÀÄÖ EzÀÝgÉ, ¹°AqÀgï£À wædåªÀ£ÀÄß PÀAqÀÄ»r¬Äj. CxÀªÁ ¥ÁzÀzÀ wædå 5 ¸ÉA«Äà ªÀÄvÀÄÛ JvÀÛgÀ 20 ¸ÉA«Äà EgÀĪÀ MAzÀÄ ªÀÈvÀÛPÁgÀzÀ ¯ÉÆúÀzÀ ±ÀAPÀĪÀ£ÀÄß PÀgÀV¹, CzÀ£ÀÄß UÉÆüÀªÀ£ÁßV ¥ÀjªÀwð¸À¯ÁVzÉ. ºÁUÁzÀgÉ D UÉÆüÀzÀ wædåªÀ£ÀÄß PÀAqÀÄ»r¬Äj. R 28) ¥ÀPÀÌzÀ°è PÉÆnÖgÀĪÀ eÁ¯ÁPÀÈwUÉ DAiÀÄègï£À ¸ÀÆvÀæªÀ£ÀÄß vÁ¼É£ÉÆÃr. A
29) ABC wæ¨sÀÄdzÀ°è PQ II BC. AP = 3 ¸ÉA«ÄÃ, AR = 4.5 ¸ÉA«ÄÃ, AQ = 6 ¸ÉA«ÄÃ,
P R
AB = 5 ¸ÉA«Äà ªÀÄvÀÄÛ AC = 10 ¸ÉA«Äà EzÀÝgÉ, AD AiÀÄ GzÀݪÀ£ÀÄß PÀAqÀÄ»r¬Äj.
B
D
Q
P Q C
30) MAzÀÄ aîzÀ°ègÀĪÀ 27 ZÉAqÀÄUÀ¼À°è PÉ®ªÀÅ ©½ ªÀÄvÀÄÛ PÉ®ªÀÅ PÉA¥ÀÄ §tÚzÁÝVgÀÄvÀÛªÉ. AiÀiÁzÀÈaÒPÀªÁV MAzÀÄ ZÉAqÀ£ÀÄß vÉUÉAiÀĨÉÃPÁVzÉ. PÉA¥ÀÄ ZÉAqÀ£ÀÄß vÉUÉAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄÄ 2 DzÀgÉ, ©½ §tÚzÀ ZÉAqÀ£ÀÄß vÉUÉAiÀÄĪÀ ¸ÀA¨sÀªÀ¤ÃAiÀÄvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. 3 IV. PɼÀV£À ¥Àæ±ÉßUÀ½UÉ GvÀÛj¹. (3 x 6 = 18)
31) ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÉÆAzÀgÀ°è, ªÀÄÆgÀ£Éà ¥ÀzÀªÀÅ 8 DVzÀÄÝ, MA¨sÀvÀÛ£Éà ¥ÀzÀªÀÅ ªÀÄÆgÀ£Éà ¥ÀzÀzÀ ªÀÄÆgÀgÀµÀÖQÌAvÀ 2 ºÉZÀÄÑ EzÉ. CzÀgÀ ªÉÆzÀ® 19 ¥ÀzÀU¼ À À ªÉÆvÀª Û À£ÀÄß PÀAqÀÄ»r¬Äj. 32) PɼÀUÉ PÉÆnÖgÀĪÀ zÀvÁÛA±ÀUÀ½UÉ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. D ªÀUÁðAvÀgÀ 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 DªÀÈwÛ 7 10 15 8 10 33) PÁªÀå ªÀÄvÀÄÛ PÁwðÃPÀgÀ ªÀAiÀĸÀÄì 11 ªÀÄvÀÄÛ 14 ªÀµÀðUÀ¼ÀÄ. EªÀj§âgÀ ªÀAiÀĹì£À UÀÄt®§ÞªÀÅ 304 ªÀµð À UÀ¼ÁUÀ®Ä JµÀÄÖ ªÀµÀðUÀ¼ÀÄ ¨ÉÃPÁUÀÄvÀÛzÉ PÀAqÀÄ»r¬Äj. CxÀªÁ MAzÀÄ ªÉÆÃlgï zÉÆÃtÂAiÀÄ ªÉÃUÀ ¤±ÀÑ® ¤Ãj£À°è 15 Q.«ÄÃ./UÀAmÉUÀ¼ÁVªÉ. D zÉÆÃtÂAiÀÄÄ 4 UÀAmÉ 30 ¤«ÄµÀUÀ¼À°è £À¢AiÀÄ°è 30 Q.«ÄÃ. zÀÆgÀ PɼÀPÉÌ ZÀ°¹ ªÀÄvÉÛ ªÉÆzÀ°£À ¸ÁÜ£ÀPÉÌ »A¢gÀÄVzÀgÉ, £À¢AiÀÄ ªÉÃUÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj. 34) ABCD ¸ÀªÀiÁAvÀgÀ ZÀvÀĨsÀÄðdzÀ°è M JA§ÄzÀÄ CD AiÀÄ ªÀÄzsÀå©AzÀĪÁVzÉ. M ªÀÄÆ®PÀ J¼ÉzÀ BM gÉÃSÉAiÀÄÄ AC AiÀÄ£ÀÄß L JA§°èAiÀÄÆ ªÀÄvÀÄÛ AD AiÀÄ£ÀÄß ªÀÈ¢Þ¹zÁzÀ E JA§°èAiÀÄÆ bÉâ¸ÀÄvÀÛzÉ. EL = 2BL JAzÀÄ ¸Á¢ü¹. CxÀªÁ
E
D
M
C
L A
B
wæ¨sÀÄdzÀ AiÀiÁªÀÅzÉà JgÀqÀÄ ªÀÄzsÀågÉÃSÉUÀ¼ÀÄ ¥ÀgÀ¸ÀàgÀ 2 : 1 gÀ ¥ÀæªÀiÁtzÀ°è bÉâ¸ÀÄvÀÛªÉ JAzÀÄ ¸Á¢ü¹. .......4
-- 4 --
A
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Design of the Question Paper for S.S.L.C. Examination
MATHEMATICS DIMENSION - 1 WEIGHTAGE TO CONTENT
Sl. No.
Units
Marks
l.
Real Numbers
03
2.
Sets
03
3. *
Progressions
08
4. *
Permutations and Combinations
05
5.
Probability
03
6.
Statistics
04
7.
Surds
04
8. *
Polynomials
04
9. *
Quadratic Equations
09
l0.*
Similar Triangles
06
1l.*
Pythagoras Theorem
04
l2.*
Trigonomentry
06
l3.
Co-ordinate Geometry
04
l4.*
Circle - ChordProperties and Tangent Properties
10
l5.*
Mensuration
05
l6.
Graphs and Polyhedra
02
Total
80
20% 15% 100%
Applying (Including Analysis) Skill Total
3.
4.
1x6=6
1x8=8
Skill
Total
-
1x2=2
1x6=6
Understanding -
1x4=4
1x2=2
Remembering
Applying (Including Analysis)
1 Mark Question
MCQs 1 Mark
Objectives
3 x 6 = 18
-
2x2=4 2 x 16 = 32
3x2=6
3 x 4 = 12
-
L.A. 3 Marks
2x3=6
2 x 10 = 20
2x1=2
S.A. 2 Marks
4 x 4 = 16
4x2=8
4x1=4
4x1=4
-
L.A. 4 Marks
WEIGHTAGE TO OBJECTIVES
80
12
16
44
08
Total Marks
55%
Understanding
2.
DIMENSION - 2
10%
% Marks
Remembering
Objectives
l.
Sl. No.
WEIGHTAGE TO OBJECTIVES
DIMENSION - 2
100%
15%
20%
55%
10%
Percentage
DIMENSION - 3 WEIGHTAGE TO FORM OF QUESTIONS
Sl. No.
Type of Questions
No. of Questions
Marks
l.
M.C. Questions
08
08
2.
Short Answer Type (1 Mark)
06
06
3.
Short Answer Type (2 Marks)
16
32
4.
Long Answer Type (3 Marks)
06
18
5.
Long Answer Type (4 Marks)
04
16
Total
40
80
DIMENSION - 3 ESTIMATED DIFFICULTY LEVEL
Easy
30%
Average
50%
Difficult
20%
2
- 1(1) -
7. Surds
8. Polynomials
9. Quadratic Equations
10. Similar Triangles
11. Pythagoras Theorem 1(1) 1(1)
12. Trigonomentry
13. Co-ordinate Geometry
*
*
*
*
*
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6. Statistics
-
-
2(1)
5. Probability
-
-
-
*
-
4. Permutations & Combinations
-
- 1(1) -
3.* Progressions
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
S.A.1 S.A.2 L.A.3 L.A.4
1
2. Sets
MCQ
2
3
1(1)
-
-
4
-
-
-
-
-
*
-
-
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2(1)
2(1)
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2(1)
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S.A.1 S.A.2 L.A.3 L.A.4
1
- 1(1) 2(1) -
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1(1)
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1(1)
1(1)
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MCQ
UNDERSTANDING
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MCQ
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MCQ
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S.A.1 S.A.2 L.A.3 L.A.4
1
APPLYING (INCLUDING ANALYSIS)
CORE SUBJECT BLUE PRINT
10th STANDARD MATHEMATICS
REMEMBERING
- 1(1) -
Content / Unit
1. Real Numbers
No.
Sl.
Time : 2 Hours and 45 Minutes Marks : 80
2
3
4
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S.A.1 S.A.2 L.A.3 L.A.4
1
SKILL
4
6
4
6
9
4
4
4
3
5
8
3
3
3
3
1
3
3
3
2
2
2
3
3
2
2
tions
Marks Ques-
No. of
TOTAL
Content / Unit
* -
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3
4
2
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4
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* 1(1) 2(1)
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S.A.1 S.A.2 L.A.3 L.A.4
1
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MCQ
2
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4
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MCQ
- 6(3) 6(2) 4(1) -
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S.A.1 S.A.2 L.A.3 L.A.4
1
APPLYING (INCLUDING ANALYSIS)
6(6) 2(2) 20(10) 12(4) 4(1) -
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MCQ
UNDERSTANDING
* Indicates Internal Choice Questions Unit
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2(2) 4(4) 2(1) -
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1(1)
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S.A.1 S.A.2 L.A.3 L.A.4
1
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MCQ
REMEMBERING
CORE SUBJECT BLUE PRINT
10th STANDARD MATHEMATICS
2
3
4
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2(1)
2(1)
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- 4(1)
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S.A.1 S.A.2 L.A.3 L.A.4
1
SKILL
NOTE :- (i) Numbers outside the bracket indicates Marks. (ii) Numbers inside the bracket indicates Questions. (iii) Internal choice to Questions to be given the following Units, which are comparitively have more contents for 2, 3, and 4 Marks. The Units are 3, 4, 8, 9, 10, 11, 12, 15 and 16. (iv) In case of Questions on proving theorems, the Choice Questions can be the converse of the theorems OR Corollary having equal weightage in marks. (v) In case of Questions on Riders based on theorems, choice Questions to be the Riders based on the same theorem OR Converse or Corollary.
KEY :-
Total
Polyhedra
16. Graphs and
15. Mensuration
Properties and Tangent Properties
* 14. Circle - Chord
No.
Sl.
Time : 2 Hours and 45 Minutes Marks : 80
80
2
5
10
40
1
3
4
tions
No. of
Marks Ques-
TOTAL
