Math’s assignMent for suMMer vacation. Class-9th
Chapter 1 Rational numbers
1. find five rational number between 3/5 and 4/5.
2. locate √2 and √3 on number line.
3. Show that 0.333.....can be expressed in the form p/q, where p and q are integers and q is not equal to zero.
4. find three Irrational between rational no 5/7 and 9/11.
5. Visualise the following numbers on number line. (a) 6.54 (b) 5.345
1
1
6. Rationalise the denominator of the following: (a)
(b)
.
√2
√7−√6
7. Simplify the following expressions: -(3+√3) (2+√2).
8. Represent √8.5 on the number line.
1
9. If x = 1-√2, then find the value of (x- 𝑥 )².
1
10. If x= 3+2√2, what is the value of x- .
𝑥
11. Simplify the following expressions: -(2+√3) (2-√3).
12. Express 1.1232323….in the form of p/q, where p and q are integers and q is not equal to zero.
13. How many irrational numbers lie between √2 and √3. Find any three irrational numbers.
3
4
5
14. Simplify √81- 8 √216 + 15 √32 + √225.
15. Show that (xa-b)a+b .(xb-c)b+c .(xc-a)c+a =1
3
6
3
6
4
4
16. Rewrite the following irrational numbers in ascending order.(a) √6,√7, √8 (b) √9, √26 ,√5
17. Add (a) 3√2 and 5√2 (b) 8√3 +2√3 + 4√3
18. Simplify √48 - √72 -√27 + 2√18 .
3
3
3
19. Simplify (a) √12 X √5
(b) √5 X √2
20. Find the value of a and b in the following question
21. Simplify
4+ √5
4−√5
+
√3− 1
=
√3+ 1
a+b √3
4−√5
4 + √5
Chapter 2 Polynomials
1. Write the following in standard forms 4x7+6x2+28 -3x3-9x.
2. Identify the following into monomials, binomials , trinomials expressions.
(a) x2 +3x (b) y3-2y +3 (c) 7
3. Write the degree of each of the following polynomials:
(a) 9x4 -6x3 + 4x2 -2.
(b) m3-2x2 +3x5 .
4. Show that 1,2and 3 are Zeros of the polynomials y3-6y2 +11y -6.
5. Divide p(x)= x4 + 1 by g(x) =x-1.Also find quotient and remainder.
6. Determine if (x+1) is a factor of x3-x2-(2+√2)x +√2.
7. If p(x)=x3-3x2+4x-12; g(x) =(x-3).Using factor theorem show that p(x)Is divisible by g (x).
8. For what value of m, if (x+3) is a factor of 3x2+mx-10.
9. Factorise x2-10x +25 by middle term split up method.
10.Use suitable identities to find the following products.
(a) (x+4)(x+10) (b)104 X 96 (c) x3 + x2-17x +15 (d) 8x3 + 64 .
ASSIGNMENT WORK FOR 1ST Formative assessment 2015-16
Objective : To obtain a square root spiral of natural numbers up to 10
Project work
1. Topic: History of 𝝅
𝝅=
𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓
Mathematicians Values of 𝜋
Archimedes
3.140845 < 𝜋 < 3.142557
Aryabhatta
3.1416
335
Chung Chi
113
Presentation should based on
 Knowledge about 𝝅 in ancient civilizations.
 Work on 𝝅 by various mathematicians and their estimation for 𝝅.
 Relation between 𝝅 and circle.
 List of formulae involving 𝝅.
The project report should contain answer of the following questions.
1. What is 𝝅?
2. Name the mathematicians who estimated the value of 𝜋.
3. What is the approximate value of 𝜋 up to 5 decimal places?
4. Why is 𝜋 an irrational number?
2.Topic: To verify that sum of the angles of a triangle is 180°.
Representation:
 Draw at least 3 different types of triangles and measure their angles .find
the sum of the angles of the triangles.
 Is there any other method of proving the angle sum property of a
triangle?
 Write at least three application of the angle sum property of a triangle .
Suggested web site
http://www.mathwarehouse.com/geometry.
http://users.mct.open.ac.uk.
Practice paper for first formative assessment.
1) The value of √20 𝑋 √5 is (a) 10
(b)2√5
(c) 20√5
(d)4 √5
4
3
2) If the polynomial 3x - 4x -3x -1 is divided by x-1, then the remainder is
a. (a) 3 (b) 5 (c) 1
(d)-5
3) Which of the following is quadratic polynomial (a) 8 (b) x2+2 (c) x3+2 (d)2x+2
4) The degree of the polynomial is 2 - y2 –y3 +2y7 is (a) 2 (b) 0 (c) 7
(d)3
5) The zeros of the polynomial 5x(x+2)(x-3) are (a) -2,0,3,5 (b) -2,3 (c) -2,3,5 (d) 0,-2,3
6) Find five rational number between 2 and 3.
7) Locate √5 on the number line.
8) Visualise 3.765 on number line, using successive magnification.
9) Without performing long division , determine which of the following rational numbers has a
terminating decimal expansion
7
3 15
, ,
13 18 45
1
,4 .
8
10) If the polynomial x3 + 3x2+ 3x +1 is divided by x+2, then find the remainder.
11) Find the product without multiplying directly. 103 x 107
12) Factories the polynomial by splitting the middle term. 6x2 +5x -6.
13) Show that 0.2353535.......can be represented in the form of p/q, where p and q are integers and q≠ 0.
14) (a) Represent √3.5 on the number line . (b) simplify (5+√7) (2+√5)
1
15) (a)Rationalize the denominator of 7+3√2. (b) multiply 6√5 X 2√5
16) Expand each of the following using suitable identities:
(a) (x +2y +4z)2
(b) (2a -3b)3
17) Factorize;- (a) 27y3 +125z3. (b) 8a3-b3-12a2b+6ab2.
18) Factorize:
x3 +13x2 +32x +20.
19) (a)Verify that x3 +y3 = (x+y)(x2 -xy +y2) .
(b)With out calculating the cubes, find the value of (7)3+(-2)3+(-5)3.
20) In which of the quadrant or on which axis do each of the points A(-2,4) , B(3,-1), C (-1,0), D(1,2),
E (-3,-5) , F(0,-2), G(0,0) lie ? Verify your answer by locating them on the Cartesian plane.
21) Give expression for the dimensions of the cuboids whose volume is 12ky2 +8ky -20k.
22) The value of 1.272727=1.27bar is (a) 10
23)
24)
25)
26)
27)
(b)1.27
127
(c) 100
14
(d)11
(d) ½
√2 𝑖𝑠 a polynomial of degree (a) 2 (b) 0 (c) 1
Which of the following is quadratic polynomial (a) x+2 (b) x2+2 (c) x3+2 (d)2x+2
The degree of the polynomial is 2 - y2 –y3 +2y7 is (a) 2 (b) 0 (c) 7
(d)3
Point (5 ,-3) lies in quadrant (a) I (b) II (c) III
(d) IV
Give possible expression for the length and breadth of the following rectangle, in which their areas are given
AREA : 25a2 -35a +12 .
28) Check whether -2 and 2 are zeros of the polynomial x +2.
Find the remainder when x3 +1 is divided by x+1.
29) Find the product using appropriate identities : (x+3) (x+3)
30) Write all the eight identities of polynomials .
Math’s assignMent for suMMer vacation. Class-8th
Chapter 1 Rational numbers
Q.1 Is zero a rational number? If yes, give two examples.
Q.2 What are the identity elements for the addition and multiplication of rational numbers?
Q.3 Write four rational numbers which are greater than - 31 and less than 4.
Q.4 Find ten rational numbers between 2 and 3. Q.5 Represent ½,4/5,6/10 on number line.
Q.6 find 3 rational number between ¼ and ½ . Q.7Write five rational number between -2/3 and 5/4.
Q.8 Write the additive inverse of -7/9 and 5/8. Q.9 Write the multiplicative inverse of -15, 12/25 ,-1.
Q.10 Multiply 6/11 by the reciprocal of -7/3.
CHAPTER – 3 UNDERSTANDING QUADRILATERALS
Q.1 What is the sum of the measures of the four angles of a quadrilateral?
Q.2 If the diagonals of a quadrilateral bisect each other at right angle, the
quadrilateral is called .............. Q.3 The adjacent angles in a parallelogram are.............
Q.4 State true or false :A pentagon is a concave polygon. Q.5 A regular polygon is both equiangular and..........
Q.6 The adjacent sides of a parallelogram are in the ratio 3:7 and its perimeter is
100 cm. Find the sides of the parallelogram.
Q.7 The angles of a quadrilateral are in the ratio 2:3:4:6. Find the measure of the angles.
Q.8 Find the number of sides of a regular polygon whose each exterior angle has a measure of 36°.
Q.9 DiagonalsAC and BD of a rectangleABCD intersect each other at point O. If OA=3cm, Find AC and BD.
Q.10 Lengths of the diagonals AC and BD of a rhombus are 6cm and 8 cm res. Find the side of the rhombus.
ASSIGNMENT WORK FOR 1ST Formative assessment 2015-16
Objective : Write the properties of different kinds of quadrilaterals , along with
figures giving examples from daily life in a tabular form . Explain about all the six
types of quadrilaterals in details and its uses in different fields like architecture,
engineering, music, science and INFORMATION TECHNOLOGY.
Project work
Topic: To verify that sum of the angles of a triangle is 180°.
Representation:
 Draw at least 3 different types of triangles and measure their angles .find
the sum of the angles of the triangles.
 Is there any other method of proving the angle sum property of a
triangle?
 Write at least three application of the angle sum property of a triangle .
Suggested web site
http://www.mathwarehouse.com/geometry.
http://users.mct.open.ac.uk.
Practice paper for first assessment class 8th
1.
2.
3.
4.
5.
6.
The rational number that does not have a reciprocal (a) 1 (b) 0 (c) 2 (d) -1
What is the multiplicative identity for rational number(a) 2 (b) 0 (c) 1
(d)½
𝑎
−𝑎
𝑎
𝑏
Additive inverse of rational number is (a)
(b) (c)
(d) a
𝑏
𝑏
𝑏
𝑎
How many diagonals does a regular hexagon have? (a) 2 (b) 9 (c) 7 (d)3
Sum of measure of exterior angles of any polygon is (a) 180° (b) 90° (c) 360° (d) 270°
−7
5
Write the additive inverse of (a)
(b)
.
9
7
−2
7. Write the multiplicative inverse of (a) -13
(b) -1 x .
5
8. (a)Express 49 as the sum of 7 odd numbers
(b)How many numbers lies between square of 12 and 13.
9. Find the square of 42 by applying (a+b) ² not by multiplication.
10.Find the square root of 9604 by prime factorization method.
11.In a parallogram RING. If measure of angle R is 70º, find all the others.
12.(a)With out adding find the sum of 1+3+5+7+9+11+13+15+17+19+21+23.
(b) Name the property under multiplication used a x b= b x a .
13. Find the number of sides of a regular polygon who’s each exterior angle has a measure of 45º.
14.Find the measure of each exterior angle of regular polygon of 9 sides.
15.Measure of two adjacent angles of a parallelogram is in the ratio 3:2. Find the measure
of each of the angles of a parallogram.
−2 −5 −9
16.(a)Represent
, , on number line. (b) In ABC, < 𝐵 =90° ,if AB=6cm, BC=8cm,
11 11 11
Find AC,
17.Find a Pythagoreans triplets in which one member is 12.
18. Find the smallest number by which 9408 must be divided so that the quotient is a
perfect square. Find the square root of the quotient.
2
4
19.(a) Find 5 rational number between and . (b) find the square root of 12.25
3
5
20.Find the length of the side of a square whose area is 441 m2.
21.Find the smallest square number that is divisible by each of the numbers 4, 9, 10.
22. The greatest negative integer is ------------------------------.
23. Zero is greater than every ----------------------------------- integer.
24. If a integer is greater than 1,It’s reciprocal is------------------1.
25. How many fourths are there in 3.
26. How much is 3/8 of a day?
27. what fraction is 25 years of a century.
28. Multiply the following decimal numbers:a) 2.3x10 b)211.04x4 c)2.5x0.5
29. Find the area of rectangle whose length is 5.7cm and breadth is 3cm?
30. Express as rupees using decimal:a) 5paise b)25rupees 5paise c)250paise d)70paise
31. Q.10 convert:32. a) 8km to m b) 12.5cm to dam c)750m to km d) 8.75kg to gram
33. Q.11 Express in kg:34. a) 2000gram b) 4580gram
Math’s assignMent for suMMer vacation. Class-7th
Q.1 The greatest negative integer is ------------------------------.
Q.2 Zero is greater than every ----------------------------------- integer.
Q.3 If a integer is greater than 1,It’s reciprocal is------------------1.
Q.4 How many fourths are there in 3.
Q.5 How much is 3/8 of a day?
Q.6 what fraction is 25 years of a century.
Q.7Multiply the following decimal numbers:a) 2.3x10 b)211.04x4 c)2.5x0.5
Q.8 Find the area of rectangle whose length is 5.7cm and breadth is 3cm?
Q.9Express as rupees using decimal:a) 5paise b)25rupees 5paise c)250paise d)70paise
Q.10 convert:a) 8km to m b) 12.5cm to dam c)750m to km d) 8.75kg to gram
Q.11 Express in kg:a) 2000gram b) 4580gram
Q.12 verify:a) (-30)x[13+(-3)]=[(-30x13)]+[(-30)x(-3)]
b) 5x[12+8]=[5x12]+[-5x8]
Q.13 An inch contains 2.54cm. how many cm will there be in 12.5 inches?
Q. 14 write multiplication table upto 20.
Q.15 . Find the Perimeter of a rectangle whose length is 28cm and breadth is 21cm
ASSIGNMENT WORK FOR 1ST Formative assessment 2015-16
Objective : write numbers upto 100. Write prime numbers , composite numbers ,
Odd numbers , even numbers , Multiple of 3, 4 , 5, 6 ,7 ,8, 9, 10, 11, 12, 13 , 14 ,15.
And also write square no. Eg; 1x1=1, 2x2=4, 3x3=9……10x10=100. and cube
numbers eg; 1x1x1=1 ,2x2x2=8,……. with in 100.
ASSIGNMENT FOR FA-2
1. In the given figure, lines AB and CD intersect at O. If
and
find ∠BOE and reflex ∠COE.
2. In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR.
Prove that
3. In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.
4. In the given figure, If AB || CD, EF ⊥ CD and ∠GED = 126º, find ∠AGE, ∠GEF and ∠FGE.
5. In the given figure, if PQ || ST, ∠PQR = 110º and ∠RST = 130º, find ∠QRS.
[Hint: Draw a line parallel to ST through point R.]
6. In the given figure, if AB || CD, ∠APQ = 50º and ∠PRD = 127º, find x and y.
7.In the given figure, if lines PQ and RS intersect at point T, such that ∠PRT = 40º,
∠RPT = 95º and ∠TSQ = 75º, find ∠SQT.
8.In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS
meet at point T, then prove that ∠QTR=½∠QPR.
9.AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD
bisects AB.
10. In the given figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
11. AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that
∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that
(i) ΔDAP ≅ ΔEBP (ii) AD = BE
12. ABC is a right angled triangle in which ∠A = 90º and AB = AC. Find ∠B and ∠C.
14. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the
triangle ABC is isosceles.
15. Show that in a right angled triangle, the hypotenuse is the longest side.
16. In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.
11. Can a triangle have all the angles less than 60°?
12. Is it possible to construct a triangle with length of its sides 5cm, 3cm and 8cm? Give reason for your answer.
13.Two points with coordinates (4,3) and (4,-2) lie on a line , parallel to which axis?
14.The base of a right-angled triangle measures 4cm and its hypotenuse measure 5cm. Find the area of the triangle.
15.If two lines intersect each other , then prove that vertically opposite angles are equal
16.Prove that angles opposite to equal sides of an isosceles triangle are equal.
18.In which quadrant or on which axis do each of the points
and
lie? Verify your
answer by locating them on the Cartesian plane.
19. BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is
isosceles.
20. Show that in a right angled triangle, the hypotenuse is the longest side.
21. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each
piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?