Optional Math 8

Exercise 8.3

1. i. What is dispersion? Write down with example.
ii. What is quartile deviation? Write down the formula of Q.D. and

its coefficient.
iii. If highest and lowest observations of a data are 10 and 40

respectively, find the range and its coefficient.
iv. If first quartile and third quartile of the observations are 18 and

32 respectively, find the quartile deviation and its coefficient.
v. If lowest observation of a data is 10 and its range is 30 find the

coefficient of range.

2. Find the range and its coefficient from the followings.
i. 13, 15, 18, 12, 30, 23, 48, 36

ii. 108, 102, 112, 142, 130, 148, 130, 120

Marks 32 36 42 45 48
2
iii. No of students 5 7 12 3 Statistics
18
Age of 12 14 15 16 2

iv. No of students 5 8 9 4 5.4
9
Height (ft) 4.4 4.6 5 5.6 5.2

v. No. of persons 43627

3. Find the quartile deviation and its coefficient of the followings.
i. 12, 14, 16, 18, 20, 22, 24.
ii. 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60.
iii. 18, 12, 6, 34, 28, 24, 46, 40.
iv. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Marks 42 48 54 60 70 80

v. No. of students 4 5 8 10 7 6

4. i. Find the quartile deviation and its coefficient of the data given
below.

Weight 40 45 50 55 60 65

No. of persons 4 8 10 12 9 7

PRIME Opt. Maths Book - VIII 197

ii. Find the quartile deviation and its coefficient of the data given
below.

In come (thousand) 20 34 26 40 50 44

No. of family 132625

iii. The range and its coefficient are respectively 20 and 0.25, find

the highest and lowest observations of the data.
iv. The quartile deviation and its coefficient are 30 and 0.6

respectively, find the upper and lower quartiles.
v. The quartile deviation and its coefficient are respectively 20 and
0.2, find the first quartile and 3rd quartile.

5. Project work

Collect the marks obtained by 40 students of your class in optional
mathematics in first unit test and tabulate in discrete frequency table.
Also find the quartile deviation.

Statistics Answer

1. i. Show to your teacher.

ii. Show to your teacher.

iii. 30, 0.6 iv. 7, 0.28 v. 0.6
iii. 16, 0.2
2. i. 36, 0.6 ii. 46, 0.184 iii. 12.5, 0.48
iv. 6, 0.2 v. 1.2, 0. 12 iii. 50 , 30

3. i. 4, 0.22 ii. 12, 0.3
iv. 27.5, 0.5 v. 8, 0. 129

4. i. 5, 0.0909 ii. 5, 0.128
iv. 20, 80 v. 80, 120

198 PRIME Opt. Maths Book - VIII

Statistics

Unit Test - 1
Time : 30 minutes

[1 × 1 + 3 × 2 + 2 × 4 + 1 × 5 = 20]

Attempt all the questions:

1. What type of measure of partition value is the quartiles?
2. a. If arithmetic mean of 12, 16, x, 34, 38 is 24, find the value of ‘x’.
b. Find the 7th decile of the observations 15, 18, 21, 24, 12, 9, 33, 30,

27.

c. If median of the observations taken in order of 10, 15, 18, 20+ m,
28, 32, 36, 40 is 26, find the value of m.

3. a. Find the quartile deviation of the observations given below. Statistics
Marks 12 15 20 25 32 40 45
f 3 6 9 12 10 8 2

b. Find the arithmetic mean of the observations.

Age 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50

f 3 8 13 9 7

4. Find the 6th decile and 3rd decile of the observations given below.
x 15 20 14 30 36 24 10 40
f 9 10 2 8 5 12 7 3

PRIME Opt. Maths Book - VIII 199

Proposed Syllabus with Grid for
First Terminal Examination

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

1 Algebra i. Order Pairs 11 1 – 37 5
ii. Cartesian Product

2 Matrices i. Introduction 111 – 37 5
ii. Addition
iii. Transpose

3 Co-ordinate i. Distance Formula 1 1 1 1 4 12 4
Geometry

4 Trigonometry i. Measurement of 13 3 1 8 24 12
angle
ii. Trigonometric
Ratios
iii. Conversion of TR

Specification Grid by CDC Nepal Total Questions 4 6 6 2 18

Total Marks 4 12 24 10 50 26

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

Model Question Set for First Terminal Examination

Group : A [4 × 1 = 4]
1. a. If ordered pairs (x + 2, 6) and (2x, 6) are equal, find the value of

‘x’.

2 3 is a matrix, find its transpose.
b. If A = < F
1
–2

2. a. Write down the co-ordinate of points on x-axis and y-axis

respectively.

b. What is trigonometry ? Write down its importance.

Group : B [6 × 2 = 12]
3. a. If A = {1, 2} and B = {3, 4, 5}, find A × B and n(A × B).

b. Find the distance between the points (2, –1) and (5, 3)

2 1 3 2 , find 3A – 2B.
4. a. If A = < F and B = < F
3 –1 1
–2

b. Find the ratio of the angles ` r c and 40°.
3
j

5. a. Factorise : Sin2A – 3SinA – 10.

b. If SinA = 3 , find the value of TanA and SecA.
5

200 PRIME Opt. Maths Book - VIII

Group : C [6 × 4 = 24]
6. If A × B = {(a, p), (b, p), (c, p), (a, q), (b, q), (c, q)} find the sets A and B.
Also find B × A and show B × A in arrow diagram.

2 33 5 find the matrix B. Also find the transpose
7. If A = < F and A + B = < F
of B. 4 1 2
3

8. Prove that the points (4, 3), (5, 0) and (3, –4) are equidistant from the

origin. r c
6
9. The first angle of a triangle is 80g and second angle is ` j , find the

third angle in degrees.

10. Prove that 1 – Sin4 A = 1 + 2Tan2A
Cos4 A

11. If 4TanA = 3, find the value of Cosec2A – Cot2A.

Group : D [2 × 5 = 10] Specification Grid by CDC Nepal

12. Prove that the points A(3, 2), B(3, –3) and C(8, –3) are the vertices of

isosceles right angled triangle.

13. Prove that Tani + Tani = 2 – Cosecq
Seci – 1 Seci + 1

Proposed Syllabus with Grid for
Second Terminal Examination

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

1 Algebra i. Polynomial 11 1 – 37 6

ii. Sequence & Series

2 Matrices – 111 – 37 –

3 Co-ordinate i. Section Formula –11 – 26 4
Geometry

4 Trigonometry i. Standard Angles 1 2 3 – 6 17 12
ii. Complimentary
Angle 1– – 1 26 6

5 Transformation i. Reflection
ii. Rotation

6 Statistics i. Central Tendency –1 – 1 27 6
ii. Partition Values

First Term Review 6

Total Questions 4 6 6 2 18

Total Marks 4 12 24 10 50 40

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

PRIME Opt. Maths Book - VIII 201

Speci�ication Grid by CDC Nepal Model Question Set for Second Terminal Examination
Group : A [4 × 1 = 4]

1. a. What is ordered pair? Write down with an example.
b. If A = <12 12F and B = <–21 10F, �ind A + B.

2. a. What is the image of a point (0, 4) under re�lection about x-axis?
b. Convert 5° 12’ 15’’ into seconds.

Group : B [6 × 2 = 12]
3. a. If p(x) = x3 + 2x2 – 3x + 2 and q(x) = x3 – x2 – x + 1. Find p(x) + q(x).

b. Find the mid-point of line joining the points (1, 3) and (5, 7).
4. a. If aij = 2i + j, �ind 2 × 2 matrix.

b. Factorise : Sin8A – Cos8A
5. a. Find the value of : 4Sin230° – 4Sin260° + Tan260°

b. If 22.5 is the median of the observations 12, 15, 18, x – 4, x – 1,
27, 30 and 33 taken in order, �ind the value of x.

Group : C [6 × 4 = 24]

6. Find the 12th term of the sequence 4, 10, 16, 22, ....................

7. If =x2+z2 y–1G + <13 12F = <193 66F, �ind the value of ‘x’ and ‘y’.
5

8. Prove that the points A(–2, 3), B(3, 3), C(3, –2) and D(–2, –2) are the
vertices of a square.

9. Find the angles of a triangle in degrees where two of the angles are in
the ratio 4:5 and the third angle is 80g.

10. Prove that 1 – SinA = SecA – TanA.
1 + SinA
Sec (90°–A) Co sec (90°–A)
11. Prove that Sin (90°–A) . Tan (90°–A) . Cos (90°–A) = Cosec2A.
Cot (90°–A)

Group : D [2 × 5 = 10]
12. Find the image of triangle having vertices A(1, 2), B(3, 5) and C(4, –3)

under re�lection about y-axis followed by translation about T = <32F .
Also plot the object and images in graph.

202 PRIME Opt. Maths Book - VIII

13. Find the 9th decile of the observations.
x 12 18 24 30 36 42 48
f 3 5 7 13 10 8 4

Specification Grid for
Final Examination referred by CDC Nepal

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

1 Algebra i. Order Pairs 11 1 – 37 16

ii. Cartesian Product

iii. Polynomial

iv. Sequence & Series

2 Limits and Limit and Continuity – – 1 – 1 4 4
Continuity
Specification Grid by CDC Nepal
3 Matrices i. Introduction 1 1 – – 2 3 10
ii. Addition
iii. Transpose

4 Co-ordinate i. Distance Formula –11 – 26 10
Geometry ii. Section Formula

5 Trigonometry i. Measurement of 11 2 – 4 11 20
Angle
ii. Trigonometric
Ratios
iii. Conversion of TR
iv. Standard Angles
v. Complimentary
Angle

6 Vector i. Introduction 1– 1 – 25 4

5 Transformation i. Reflection – 1 – 1 2 7 10
ii. Rotation

iii. Translation

6 Statistics i. Central Tendency –1 – 1 27 6
ii. Partition Values

First Term Review 4

Second Term Review 4

Total Questions 466 2 16

Total Marks 4 12 24 10 50 80

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

PRIME Opt. Maths Book - VIII 203

Model Question Set for Final Terminal Examination

Group : A [4 × 1 = 4]

1. a. Write down one difference between sequence and series.

b. What do you mean by transpose of a matrix?

2. a. Prove that Sin35° = Cos55°

b. If a = 1 , find its magnitude.
dn
7

Group : B [6 × 2 = 12]
3. a. If A = {1, 2, 3}, find A × A and n(A × A).

3 –2 1 –5 , find A and its transpose.
b. If A + B = < 4 F and B = < F
1 3
1

4. a. Find the co-ordinate of a point which cuts the line joining the

points (3, 2) and (6, 5) in the ratio 1:2.

Specification Grid by CDC Nepal b. Convert all the trigonometrical ratios in terms of SinA.
5. a. If a point A(3, 2) is translated to A’(5, 6), find the translation

vertor T.

b. Find 7th decile of the observations 20, 14, 8, 36, 30, 24, 50, 44, 40

Group : C [6 × 4 = 24]
6. If the first term and 7th term of an arithematic series are 3 and 27

respectively, find the common difference.

7. Evaluate : lim x2 – 4
x"2 x–2

8. If distance between any two points (a, – 3) and (8, 5) is 10 units, find

the value of ‘a’.

9. Prove that (1 + TanA)2 + (1 – TanA)2 = 2Sec2A
r r r r r
10. If xSin 6 + Sin 4 .Cos 2 .Sin 3 = Sin 3 , find the value of ‘x’.

11. If A(1, 3), B(5, 1), P(–1, 1) and Q(3, –1) are the four points, prove that

AB = PQ

Group : D [2 × 5 = 10]
12. Find the image of triangle having vertices A(–2, 1), B(1, 5) & C(2, –1)

under rotation about +90° followed by reflection about x-axis. Also
plot them in graph.
13. If mean of the observations is 17, find the value of ‘m’.

x 5 10 15 20 25 30
f 2 5 10 m 4 2

204 PRIME Opt. Maths Book - VIII