Prime Optional Mathematics 8

Coef•icient of Q.D. = Q3 – Q1
Q3 + Q1

= 32 – 27
32 + 27

= 5
59
= 0.084.

5. If quartile deviation and its coef!icient are 11 and 0.44 respectively, !ind

the upper and lower quartiles.

Solution:

Quartile deviation (Q.D.) = 11

Coef•icient of Q.D. = 0.44.

We have,
1
Q.D. = 2 (Q3 – Q1)

or, 11 = 1 (Q3 – Q1)
2
or, 22 + Q1 = Q3 ...................•(i)
Statistics
• Again,

Coef•icient of Q.D. = 0.44
Q3 – Q1
or, Q3 + Q1 = 0.44

or, 100Q..2355.–6632(QQ231+2==0+10.5Q..446144Q)QQ=1 13=1+1.40.44.44Q4Q1Q1 1
or,
or,
or,

or, 12.32 = Q1
0.88
\ Q1 = 14•

• Putting the value of Q1 in•(i),•
•
or• QQQ333 = Q141 •++•2222
= 36
\ =

•

196 PRIME Opt. Maths Book - VIII

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•coef•icient.

• iii. If highest and lowest observations of a data are 10 and 40
respectively, •ind the range and its coef•icient.

iv. If third quartile and •irst quartile of the observations are 18 and
32•respectively, •ind the quartile deviation and its coef•icient.

v. If lowest observation of a data is 10 and its range is 30 •ind the
coef•icient•of•range.

2.• Find•the•range•and•its•coef•icient•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. 5894 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•coef•icient•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 coef•icient 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 coef•icient of the data given
below.

In•come•(thousand) 20 34 26 40 50 44

No.•of•family 132625

• iii. The range and its coef•icient are respectively 20 and 0.25, •ind

the•highest•and•lowest observations of the data.

iv. The quartile deviation and its coef•icient are 30 and 0.6

respectively, •ind the upper and lower quartiles.

v. The quartile deviation and its coef•icient are respectively 20 and

0.2,••ind•the••irst•quartile•and•3rd quartile.

5. Project work
Collect the marks obtained by 40 students of your class in optional

mathematics•in••irst•unit•test and tabulate in discrete frequency table.

Also••ind•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,•0.357•
• 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,• ind•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,• ind•the•value•of•m.

3.• a.• Find•the•quartile•deviation•of•the•observations•given below.
Marks 12 15 20 25 32 40 45
Statistics
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

Speci•ication 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, !ind the value of
‘x’.

b. If A = <12 –32F is a matrix, !ind its transpose.
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}, !ind A × B and n(A × B).

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

4. a. If A = <32 –11F and B = <13 –22F, !ind 3A – 2B.
r jc
b. Find the ratio of the angles ` 3 and 40°.

5. a. Factorise : Sin2A – 3SinA – 10.

b. If SinA = 3 , !ind 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)} ind the sets A and B.

Also• ind•B•×•A•and•show•B•×•A•in•arrow diagram.

7.• If•A = <24 13F and A + B = <32 53F ind the matrix B. Also ind the transpose
of•B.

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

origin. r jc ,
6
9.• The•frist•angle•of•a triangle is 80g and second angle is ` ind the
third•angle•in•degrees.

10.• Prove that 1 – Sin4 A = 1 + 2Tan2A
Cos4 A
11.• If•4TanA•=•3,• ind•the•value•of•Cosec2A – Cot2A.

Group : D [2 × 5 = 10] Speci•ication 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 = 1 – Sini
Cosi

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

5 Transformation i.•Re lection 1– – 1 26 6
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• + <13 12F = <193 66F, ind•the•value•of•‘x’•and•‘y’.

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

11.• Prove that = Cosec2A.

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

Speci•ication•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
Speci•ication Grid by CDC Nepal
3 Matrices i.•Introduction 11 – – 23 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.•Re lection –1 – 1 27 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

Speci•ication Grid by CDC Nepal 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 = d17n , ind•its•magnitude.

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

• b. If A + B = <13 –42F and•B•=• <13 –15F, ind•A•and•its•transpose.
4.• a.• Find• the• co-ordinate of a point which cuts the line joining the

points•(3,•2)•and•(6,•5)•in•the•ration•1:2.
• b. Convert all the trigonometrical ratios in terms of SinA.
5.• a.• If• a point A(3, 2) is translated to A’(5, 6), ind 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• irst• term and 7th term of an arithematic series are 3 and 27

respectively, ind 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, ind

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 , ind•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 re lection about x = y. Also plot
them•in•graph.
13.• If•mean•of•the•observations•is•17,• ind•the•value•of•‘m’.

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

204 PRIME Opt. Maths Book - VIII