Friday 30 September 2011

7th-8th maths algebraic Expressions

Algebraic Expressions
 Variables, Constants and Coefficients
Variable   A quantity which can take various numerical values is known as a variable (or a literal).
Variables can be denoted by using the letters a, b, c, x, y, z, etc.
Constant    A quantity which has a fixed numerical value is called a constant.
For example, 3, 25, and 8, 9 ,13- 12 are constants.
Numerical expression
A number or a combination of numbers formed by using the arithmetic operations is called a numerical expression or an arithmetic expression.
For example, 3 + (4 × 5), 5 – (4 × 2), (7 × 9) ÷ 5 and (3 × 4) – (4 × 5 – 7) are numerical expressions.
Algebraic Expression
An algebraic expression is a combination of variables and constants connected by arithmetic operations
Statement                                           Expressions
(i) 5 added to y                                    y + 5
(ii) 8 subtracted from n                       n – 8
(iii) 12 multiplied by x                           12 x
(iv) p divided by 3                                 p/3

Term
A term is a constant or a variable or a product of a constant and one or more  variables.
3x2, 6x and – 5 are called the terms of the expression 3x2 +   6x  + 5
A term could be
(i) a constant            
(ii) a variable
(iii) a product of constant and a variable (or variables)
(iv) a product of two or more variables
In the expression a2 + 7a + 3, 2+ + the terms are a2 , 7a and 3. The number of terms is 3.

Coefficient
The coefficient of a given variable or factor in a term is another factor whose product with the given variable or factor is the term itself.  If the coefficient is a constant, it is called a constant coefficient or a numerical coefficient.
In the term 5xy,
Coefficient of xy is 5 (numerical coefficient),
Coefficient of 5x is y,
Coefficient of 5y is x.
Like terms and Unlike terms
Terms having the same variable or product of variables with same powers are called Like terms.
Terms having different variable or product of variables with different powers are called Unlike terms.
Example 1.     (i) x, -5x, 9x are like terms as they have the same variable x
                        (ii) 4x y, 7yx 2 2 - are like terms as they have the same variable x y 2
Example 2      (i) 6x, 6y are unlike terms
                       (ii) 3xy , 5xy, 8x, 10y 2 - are unlike terms
Degree of an Algebraic expression
Consider the expression 8x2 + 6x +  7  It has 3 terms 8x2, -6x and 7.
In the term 8x2  the power of the variable x is 2.
In the term 6 x, the power of the variable x is 1.
The term 7 is called as a constant term or an independent term.
The term 7 is 7 x  1=  7x0   in which the power of the variable x is 0.
In the above expression the term 8x2 has the highest power 2. So the degree of the expression 8x2 – 6x + 7 is 2.
“ The degree of an expression of one variable is the highest value of the exponent of the variable. The degree of an expression of more than one variable is the highest value of the sum of the exponents of the variables in different terms.”
Note: The degree of a constant is 0.
Addition and subtraction of expressions is same as Adding and subtracting like terms
To fi nd the sum of two or more like terms, we add the numerical coefficient of the like terms. Similarly, to fi nd the difference between two like terms, we find the difference between the numerical coefficients of the like terms. There are two methods in finding the sum or difference between the like terms namely,
(i) Horizontal method
(ii) Vertical method
(i) Horizontal method: In this method, we arrange all the terms in a horizontal line and then add or subtract by combining the like terms.
Add 3x and 5x.

3x + 5x =( 3 + 5 )´ x = 7´ x= 7x

(ii) Vertical method: In this method, we should write the like terms vertically and then add or subtract.
          4 a
      + 7 a
----------------------
        11 a
Subtracting a term is the same as adding its inverse. For example subtracting + 3a is the same as adding – 3a.
Subtract -2xy from 9xy.
                    9 xy
                – 2 xy
               (+)                  (change of sign)
------------------------------------
                  11 xy

Notes Unlike terms cannot be added or subtracted the way like terms are added or subtracted.
For example when 7 is added to x we write it as x + 7 in which both the terms 7 and x are retained.
Similarly, if we add the unlike terms 4xy and 5, the sum is 4xy + 5. If we subtract 6 from 5pq the result is 5pq-6.
Try these
1) What should be subtracted from 4p + 6q + 14 to get -5p + 8q + 20?
2. Three sides of a triangle are 3a + 4b - 2, a - 7 and 2a - 4b + 3. What is its perimeter?
3. The sides of a rectangle are 3x + 2 and 5x + 4. Find its perimeter.
4. Ram spends 4a+3 rupees for a shirt and 8a - 5 rupees for a book. How much does he spend in all?
5. A wire is 10x - 3 metres long. A length of 3x + 5 metres is cut out of it for use. How much wire is left out?
6. (iii) If A = 8x - 3y + 9, B =- y - 9 and C = 4x - y - 9 fi nd A + B - C.

Thursday 29 September 2011

cbse math class 8th term 1 sample paper

8th maths Sample paper term -1-2011



























Tuesday 27 September 2011

National Level Science Talent Search Examination 2...

National Level Science Talent Search Examination 2011


National Level Science Talent Search Examination
NSTSE is a diagnostic test which actually helps students improve.
Unlike regular tests which try only to find out how much a child knows (or has memorized), NSTSE measures how well a student has understood concepts and gives detailed feedback on the same, to help them improve.

Thus NSTSE helps each student know whether he/she has actually understood a concept early on so that immediate action can be taken. Often students have conceptual gaps which increase as they progress and when they reach the higher classes, they develop a "phobia" for the subject.
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CBSE Maths X Ch-6 : Trigonometry Identities

1 mark questions
Q. 1 Write the value of sin 620 sin 280 – cos620 cos 280
Q. 2 Write  cot in terms of sin A.
Q. 3 Express sec790 + cot 610 in terms of trigonometrical ratios of angles between 00and 450 .
Q. 4 If 3tanθ = 4 , then write the value of tan θ + cot θ .
Q. 5 If sinq – cos θ = 0 , 00 <θ < 900 , then write the value of 'θ ' .
Q. 6 If 'q ' , then write the value of sin θ + cos 2θ .
Q. 7 Write the value of sin2 740 + sin2 160 .
Q. 8 In ΔABC, = 900 and sin C = 4/5 , what is the value of cos A?
Q. 9 If A and B are acute angles and sin = cos   , than write the value of A+B.
Q. 10 Write the value of tan2 300 + sec2 450 .
Q. 11 Write the value of 9 cosec2620 – 9 tan2 280 .
Q. 12 If sin q = 1/2, write the value of sin q – cosec Î¸ .
Q. 13 What is the value of cos2490 – sin2 410 ?
Q. 14 If q = 450  , then what is the value of 2cos ec2θ + 3sec2q ?
Q. 15 Write the value of sin ( 900 –q ) cos q + cos(900 – q) Sinq
Q. 16 If tan (3–150 ) =1, than write the value of 'x'.
Q. 17 In ΔABC, write tan (AB)/2  in terms of angle 'C'.
Q. 18 If q = 300 , then write the value of 1 – tan2 2q .
Q. 19 If tanq + cotq = 3, then what is the value of tan2θ + cot2θ ?
Q 20 Write the value of cot (35+q ) – tan (550 – q )
2/3 marks questions
Q. 21 If sin 2q = cos (q – 36)0, 2θ and (q – 360) are acute angles. Find the value of 'q ' .
Q. 22 If tan (320 +q ) = cotq , θ and (320 +q ) are acute angles, find the value of 'q '.
Q. 23 If sin ( AB) =1 and cos(A – B) = √3 /2 ,  00 ≤ ( AB) ≤ 900 , A > B, then find the values of A and B.
Q. 24 If q = 300 , then find the value of (1– tan2q)/(1+ tan2q)
Q. 25 If tan q = √2 –1, then find the value of (2 tanq) /(1+ tan2q)
Q. 26 If q = 300 , then verify : cos 3q = 4cos3q – cosq .
Q. 27 Simplify: tan 2 600 + 4cos2 450 + 3sec2 300 + 5cos2 900
Q. 28 Find the value of :-
(sin 620)/ cos 28  +  2 (tan 730)/ cot17–  (2sin 28 .sec62)/(cot170 7sec 320 – 7cot 580)
Q. 29 find the value of   
(11 sin 700 ) / ( 7 cos200 ) –  (4/7) [(cos530 .cos 370) / (tan150 .tan350 tan550 tan750)
Q. 30 Find the value of :-
3(sin2 740 sin216 )/( 4sin 620 .sec280) + 3(tan2 280 – cosec 2620 )/ tan 250 .tan 350tan 550 tan 650)

Monday 26 September 2011

10th maths Extra score questions chapter Pair of L...

10th maths Extra score questions chapter Pair of L...: Pair of Linear Equation in Two Variable HOTS By JSUNIL TUTORIAL 1 mark questions :- Q. 1 Is the pair of linear equations consistent: - x ...

Thursday 22 September 2011

Sample Paper – 2012 Class – IX Subject – Mathemati...

Sample Paper – 2012 Class – IX Subject – Mathemati...: Multiple Choice Questions (5×1)
Choose the correct answer from the given four options in the following questions:
1. Two sides of a triangle are 8cm and 11cm and its perimeter is 32cm.The third side is :
(a) 4cm (b) 13cm (c) 14cm (d) 16cm
2. The base of a triangle is 12cm and height is 8cm .Its area is:
(a) 24cm2 (b) 96cm2 (c) 48cm2 (d) none
3. The sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300m . The sides of a triangle are.
(a) 60m,100m,40m (b) 50m,80m,60m (c) 45m,75m,95m (d) none
4. What will be the area of quadrilateral ABCD if AB =3cm, BC=4cm, CD=4cm, DA=5cm and AC=5cm.
(a) 12.5cm (b) 15.2cm (c) 18.2cm (d)19.2cm
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Monday 19 September 2011

cbse maths guess 9th inequalities of triangle

1. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(A) an isosceles triangle (B) an obtuse triangle (C) an equilateral triangle (D) a right triangle

2. An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is

(A) 37+ 1/2° (B)52+ 1/2° (C) 72+ 1/2° (D) 75°

3. The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is

(A) an acute angled triangle (B) an obtuse angled triangle (C) a right triangle (D) an isosceles triangle

4 . If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be
(A) 50° (B) 65° (C) 145° (D) 155°

CBSE MATHEMATICS (Class-9) ch-Linear Equation in Two Variables



1.     Find four different solutions of the equation x+2y=6.
2.     Find two solutions for each of the following equations:
(i) 4x + 3y = 12
 
(ii) 2x + 5y = 0
(iii) 3y + 4=0
3.     Write four solutions for each of the following equations: 
(i) 2x + y = 7
 
(ii) πx + y = 9
 
(iii) x = 4y.
4.     Given the point (1, 2), find the equation of the line on which it lies. How many such equations are there?
5.     Draw the graph of the equation
(i) x + y = 7
(ii) 2y + 3 = 9
(iii) y - x = 2
(iv) 3x - 2y = 4
(v) x + y - 3 = 0
6.     Draw the graph of each of the following linear equations in two variables:
(i) x + y = 4
(ii) x - y = 2
(iii) y = 3x
 
(iv) 3 = 2x + y
(v) x - 2 = 0
(vi) x + 5 = 0
(vii) 2x + 4 = 3x + 1.
7.     If the point (3, 4) lies on the graph of the equation 3y=ax+7, find the value of ‘a’.
8.     Solve the equations 2x + 1 = x - 3, and represent the solution(s) on
(i) the number line,
(ii) the Cartesian plane.
9.     Draw a graph of the line x - 2y = 3. From the graph, find the coordinates of the point when
(i) x = - 5
 
(ii) y = 0.
10.   Draw the graph of y = x and y = - x in the same graph. Also, find the coordinates of the point where the two lines intersect.

CBSE MATHEMATICS (Class-9) ch-Surface Area and Volumes

    Section A
  1. The curved surface area of a right circular cylinder of height 14 cm is 88cm2. Find the diameter of the base of the cylinder. 
  2. Curved surface area of a right circular cylinder is 4.4m2. If the radius of the base of the cylinder is 0.7m, find its height. 
  3. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24m.Find    (i) the curved surface area and  (ii) the total surface area of a hemisphere of radius 21 cm. 
  4. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas. 

CBSE Test sample paper- IX Mathematics (Congruent triangle)

IX Mathematics (Congruent triangle)
1. If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(A) an isosceles triangle (B) an obtuse triangle (C) an equilateral triangle (D) a right triangle
2. An exterior angle of a triangle is 105° and its two interior opposite angles are  equal. Each of these equal angles is
(A) 37+ 1/2°  (B)52+ 1/2° (C) 72+ 1/2° (D) 75°
3. The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is 
(A) an acute angled triangle (B) an obtuse angled triangle  (C) a right triangle (D) an isosceles triangle
4 . If one of the angles of a triangle is 130°, then the angle between the bisectors of  the other two angles can be
(A) 50° (B) 65° (C) 145° (D) 155°
5. The sum of two angles of a triangle is equal to its third angle. Find the third angles.
(a) 900  (b) 450 (c) 600 (d) 700                                                     
                                                            Section B

CBSE :10th Real Numbers Extra score Test paper

1. Express 140 as a product of its prime factors
2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.
 3. Find the LCM and HCF of 6 and 20 by the prime factorization method.
 4. State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating decimal.
5. State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating decimal.
 6. Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.
7. Use Euclid’s division algorithm to find the HCF of 135 and 225
8.Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m
 9. Prove that √3 is irrational.
 10.Show that 5 – √3 is irrational
11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
12. An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
13. Express 156 as a product of its prime factors.
14. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.
15. Find the HCF and LCM of 12, 36 and 160, using the prime factorization method.