Paper by: Meghraj SapkotaTyped by: Meghraj Sapkota

PENNWOOD ACADEMYSecond Term Exams, December 18 - 27, 2012

Class: VIII Additional Mathematics FM: 100Time: 3 Hrs. PM: 40 Candidates are required to attempt all the questions in the answer sheet in their own words as far as practicable.

Group A(10×1=10)

1. (a) If A={ a, b} and B ={c, d), Find A×B.(b) Find the domain and range of the relation R= { (1,2), (2, 4), (3,6)}.

2. (a) Write the different types of polynomial.

(b) Find the degree of the polynomial, 3 x2 y2+6 xy+8.

3. (a) If the angle in degree is D, then find its value in grade, G.(b) Prove that: tan A+cot A=1

4. (a) Write the value of sin 00∧tan 300.

(b) Write the formula to calculate the midpoint between two points A(x1 ,y1)and B (x2, y2)

5. (a) Translate the point P (x, y) by the translation vector T (ab).

(b) If n is the number of observations arranged in ascending order, thenmedian is given by the formula________.

Group B (17×2=34)

6. (a) If (3 x , 8 )=(12 ,3 y−1 ) find the values of x and y.

(b) If A= {a, b, c} and B ={x, y}, find A×B, B×A and show that A × B ≠ B × A

7. (a) Represent the relation, R = {(1, 4), (2, 3), (5, 4), (5, 3)} by arrow diagramand write the inverse of it

(b) Find the product of the polynomialsf ( x )=2 x2−3 x+7∧¿g ( x )=(2x−3).

8. (a) Express 25

of a right angle into radian measure.

(b) Factorize:sin2 A−cos2 B

9. (a) Prove that: sin α . sec α

cosec α . cos α=tan2α

(b) If tanθ= 512

, find cosθ and sin θ.

10. (a) Find the value of: tan300+cot 300+sin 600

(b) Prove thatsin 100 . cos200=cos800 . sin 700.

11. (a) Find the distance between A (-2, 1) and B ( 2, -1).(b) In what ratio does a line joining the points (-1, 3) and (4, 8) divide by

the point (2,6).12. (a) Find the reflection of the points, A (2, 6) and B (-4, 9) about x-axis. (b)13. (a) Find the Arithmetic Mean from the following frequency distribution.

Pension (in Rs.): 15 25 30 35 40

No. of persons: 7 5 6 4 3(b) Find the Q1 and Q3 of the data: 7, 18, 55, 67, 41, 29, 73

14. (a) Define relation with an example.

Group C (14×4=56)

15. Find the quotient and remainder when f ( x )=4 x4−3x2+2 x−1 is divided by

g ( x )=x2−316. Express the external angle of a regular hexagon into radian.17. In a right angled triangle, right angle at C, if AC=3 cm and BC=4 cm, find

sin B, cos B, tan B.18. Find the median from the data given below.

Marks obtained:

10-20 20-30

30-40 40-50

50-60

No. of Students:

5 4 4 4 3

Paper by: Meghraj SapkotaTyped by: Meghraj Sapkota

19. Find the value of: sec2 π4

. sec2 π3 (cosec 2 π

6−cosec2 π

2 )17. Use synthetic division and find the quotient when f ( x )=4 x3+9 x2+3 x−5 is

divided by g ( x )=x+2

18. Prove that: ( x cosθ+ y sin θ )2+¿19. Solve the right angled triangle ABC if ¿ A+¿C=900 ,a=1 , c=√320. P (-1, 3), B (7, -3) and C (4, 1) are three points. Show that PQ = 2QR.21. The middle point of a line is (3, 5) and one end of the line is (4, 7). Find the

other end of the line.22. Find the locus of the point which moves such that its distance from the point

P(2, 3) is always equal to its distance from the point Q (-1, 1).23. Under the translation, a point P (5, 3) is translated to P ' (-2, 1). Where will the

point Q ( 2, -4) be translated by the same translation vector?24. Find the image of ∆ABC where vertices are A(-1, 5), B( 4, 9) and C (10, 3)

under the reflection about y-axis. Present the ∆ ABC and its image ∆ A' B' C' on the graph.

25. The following table gives the frequency distribution of weights of 80 apples. Find the mean weight.

Wt. (in gm) 110-120 120-130 130-140 140-150 150-160No. of apples 28 14 12 20 6

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