Prime Optional Mathematics 10

21. Find standard deviation of the observations. 0-24 0-32 0-40
Class 0-8 0-16 15 12 6

f 89

Group : D [4 × 5 = 20]
22. Maximize the function P = 3x + 2y under the constraints x + y ≤ 6, 3x – y ≤ – 2, x ≥ 0 and

y ≥ 0.
23. Find the equation of circle having radius 5 units which passes through a point (5, 3) and

centre lies in the straight line x – y = 3.
24. Prove by vector method that the line joining the center of a circle and mid-point of a

chord is perpendicular to the chord.
25. Find the co-ordinate of image of a triangle having vertices A(–2, 1), B(1, 2) and C(2, –3)

under enlargement about E[(0, –1), 2] followed by translation about T = <3F . Also plot
the object and images in graph. 4

Specification Grid for SEE Examination
referred by CDC Nepal

S.N. Containts Topics K-1 U-2 A-4 HA-5 TQ TM Periods

1 Algebra i. Function 23 2 1 8 21 35
ii. Polynomial

iii. Sequence & Series

iv. Linear Program

2 Limits and Continuity and 1 – 1 – 2 5 10
Continuity Discontinuity

3 Matrices i. Determinate 12 1 – 49 15
4 Co-ordinate 1 6 15 30
ii. Inverse
Geometry iii. Cramer's Rule

i. Angle between lines 2 2 1

ii. Homogeneous

Equation

iii. Conic Section

iv. Circle

5 Trigonometry i. Multiple angle 23 3 – 8 20 35

ii. Sub M angle

iii. Transformation F
iv. Conditional

v. Tri. Equation
vi. Heights & distance

6 Vector i. Dot Product 1 2 – 1 4 10 18
ii. Vector Geometry

7 Transformation i. Combination Tran. 1– 1 1 3 10 15
ii. Inversion Tran.
iii. Matrix Tran.

346 PRIME Opt. Maths Book - X

8 Statistics i. Quartile Deviation –12 – 3 10 12
170
ii. mean Deviation
iii. Standard
Deviation

Total Questions 10 13 11 4 38

Total Marks 10 26 44 20 100

K = Knowledge, U = Understanding, A = Application, HA = Higher ability

Model Question Set for SEE Examination

1. a. Group : A [10 × 1 = 10]
b. Define the term composite function.
In what condition x - 2 will be the factor of a polynomial p(x)?
2. a. Write down the condition of continuity of a function f(x).
b. Find the determinant of a matrix <CSoinsii CSoinsiiF
3. a. Find the slope of a straight line which is perpendicular to the another straight line
a
of slope b .

b. Prove that the line pairs of 4x2 + 6xy – 4y2 = 0 are perpendicular to each other.

4. a. Prove that Cos2A = 1 – 2Sin2A.

b. Prove that Sin(A + B) + Sin(A – B) = 2sinACosB.

5. a. If a = dx1n and b = dx2n find a.b .
y1 y2

b. Find the image of p(x, y) under FoG where F is rotation about +270 with centre
origin and G is refection about y = x.

Group : B [13 × 2 = 26]

6. a. If f-1(x) = 3x – 2 , find f(x).
b. 2
c.
Insert 3 AMs between 40 and 16.
7. a.
Write down the co-ordinate of the points on a parabola of ax2 + bx + c = 0 which are
b. the intersecting point of x - axis and the parabola.
8. a.
If D = 13, Dofx t=he39vaarniadblDeys = 26 are the determinants of the columns of two linear
b. equations x and y, find the value of 'x' and 'y'.

9. a. If –3 a is the inverse of a matrix –7 5 , find the value of 'a' and 'b'.
b. < F < F
c. –4 7 –4
b
10. a.
If angle between the line pairs of px2 – 7xy – 15y2 = 0 is 45°, find the value of 'p'.

Find the co-ordinate of a point (4, 2) under a inversion circle having center (1, 1)
and radius 20 units.

Prove that : 1 + Sini + Cosi = Cot i .
1 + sin i – Cosi 2

Prove that : 2Cos(45° + A)Sin(45° – A) = Cos2A

Solve (0 ≤ q ≤ p) : Tanq + 2Sinq = 0
If the vectors 3 i + mj and 4 i – 3j are arthogonal vectors, find the value of m.

PRIME Opt. Maths Book - X 347

b. Prove that AB2 + BC2 = AC2 by vector method in the given diagram. A
c. If third quartile of the continuous frequency distribution is 80

whose quartile deviation is 60, find the coefficient of quartile
deviation.

Group : C [11 × 4 = 44] BC
11. Solve the polynomial : 6x3 + 17x2 – 5x – 6 = 0

12. Find the number of terms of an AP whose last term is 58, sum of first four terms is 48 and

sum of last four terms is 208.

2x – 1 for x < 0

13. Determine the function f(x) = 3 for x = 0 is continuous or not.

x + 1 for x > 2

14. Solve the equations 3x 5y = 7 and 5x – 3y = 1 by matrix method.
2–3 4

15. Find the equation of diagonal AC of a square ABCD where two of the vertices are A(3, 1)
and B(–1, 7).

16. PIAfrAboov+aetBtihs+actCo:=mCoi2pns,gepctrqoow+vaeCrtodhssaettch:2qeSis+ne2CaAo-Ss+heSocir4qne2B=wCh+oeSrtie8nq2tCh–eC=ao1ntq–gl2eSoifndAeSpinreBsSsiinoCn of it from the top
of a light house is 30°. After 10 seconds depression changes to 60°. At what time the boat
17.
18.

reached to the sea-shore?

19. Find the image of unit square by using 2 × 2 matrix of a transformation where x = 2x – y
and y = x + 3y.

20. Find mean deviation from mean and its coefficient of :

Class 0-8 8-16 16-24 24-32 32-40

f 23564
21. Find root mean square deviation of :

Marks 10-18 20-28 30-38 40-48 50-58

f 4 7 12 10 7

Group : D [4 × 5 = 20]
22. Find the inequalities represented by the given feasible region. Also maximize the function
F = 4x + 3y.
23. Find the equation of circle having equation of two Y

diameters x + 2y = 5 and 3x – y = 1 which touches the 6
straight line of equation 3x + 4y + 4 = 0. 5 (1, 5)

24. Prove by vector method that the diagonals of a rhombus 4

are bisected at right angle. (0, 3) 3 (6, 0)
25. Find the co-ordinate of image of DABC having vertices A(3, 67 X
2
Pf2o)llo,lotBwt(h1ee,d–ob2by)jeaEcn2td[a0nC,d(320i,m]3.a)Agulesnsodifneinrgderanthplaehr.sgienmgleenttraanbsofuotrmE1a[0ti,o2n].
1
X'

–2 –1 O 1 2 3 4 5
–1

–2
Y'

348 PRIME Opt. Maths Book - X

Shared by :- R.P Pandey