and comparing the result with given perimeter. 3 × 80 = 240 = Perimeter given in question. Draw this triangle on your copy and measure the angles of the triangle. What do you observe? In each of the questions 1 to 16, out of the four options, only one is correct. Write the correct answer. 1. An algebraic expression containing three terms is called a
- (a)monomial
- (b)binomial
- (c)trinomial
- (d)All of these 2. Number of terms in the expression 3x2y – 2y2z – z2x + 5 is (a) 2 (b) 3 (c) 4 (d) 5 15-04-2018 Identify the following terms as like or unlike. (a) 3x, 3y (b) 7k, – 3k (c) 2p, 2pt 3. The terms of expression 4x2 – 3xy are: (a) 4x2 and –3xy (b) 4x2 and 3xy (c) 4x2 and –xy (d) x2 and xy
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(a) monomial
(b) binomial
(c) trinomial
Factors of –5x2 y2 z are
- (a)– 5 × x × y × z
- (b)– 5 × x 2 ×y × z
- (c)– 5 × x × x × y × y × z
- (d)– 5 × x × y × z2
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(a) – 5 × x × y × z
(b) – 5 × x 2 ×y × z
Coefficient of x in – 9xy2z is
- (a)9yz
- (b)– 9yz
- (c)9y2z
- (d)– 9y2z
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Radius Diameter Circumference Foot ball 11.3 cm 22.6 cm 71 cm Basket ball 12.4 cm 24.8 cm 77.872 cm Cricket ball 3.66 cm 7.32 cm 23 cm Volley ball 10.3 cm 20.6 cm 64.684 cm Hockey ball 3.565 cm 7.13 cm 22.4 cm Lawn Tennis ball 3.175 cm
Which of the following is a pair of like terms?
- (a)–7xy2z, – 7x2yz
- (b)– 10xyz2, 3xyz2
- (c)3xyz, 3x2y2z2
- (d)4xyz2, 4x2yz
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(a) –7xy2z, – 7x2yz
(b) – 10xyz2, 3xyz2
(c) 3xyz, 3x2y2z2
(d) 4xyz2, 4x2yz
Identify the binomial out of the following:
- (a)3xy2 + 5y – x2y
- (b)x2y – 5y – x2y
- (c)xy + yz + zx
- (d)3xy2 + 5y – xy2
The sum of x4 – xy + 2y2 and –x4 + xy + 2y2 is
- (a)Monomial and polynomial in y
- (b)Binomial and Polynomial
- (c)Trinomial and polynomial
- (d)Monomial and polynomial in x
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(a) Monomial and polynomial in y
(b) Binomial and Polynomial
(c) Trinomial and polynomial
(d) Monomial and polynomial in x
The subtraction of 5 times of y from x is
- (a)5x – y
- (b)y – 5x
- (c)x – 5y
- (d)5y – x
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– b – 0 is equal to
- (a)–1 × b
- (b)1 – b – 0
- (c)0 – (–1) × b
- (d)– b – 0 – 1 15-04-2018
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The side length of the top of square table is x. The expression for perimeter is:
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The number of scarfs of length half metre that can be made from y metres of cloth is : y 1
- (a)2y
- (b)
- (c)y + 2
- (d)y + 2 2
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123x2y – 138x2y is a like term of :
- (a)10xy
- (b)–15xy
- (c)–15xy2
- (d)10x2y
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The value of 3x2 – 5x + 3 when x = 1 is
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The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
- (a)2n + 1
- (b)n – 2
- (c)5n + 2
- (d)n – 3 A variable is a letter that is used to represent one or more numbers. The numbers are the values of the variable. A variable expression is a collection of numbers, variables and operations. Here are some examples. VARIABLE EXPRESSION MEANING OPERATION 8y =8 × y = 8 (y) 8 times y Multiplication = 16 ÷ b 16 divided by b Division 4+s 4 plus s Addition 9–x 9 minus x Subtraction The expression 8y is usually not written as 8 × y because of possible confusion of symbol ‘ × ’ with the variable x. Replacing each variable in an expression by a number is called evaluating the expression. The resulting number is the value of the expression. Write the variable Substitute values Simplify the numerical → → expression for variables expression 15-04-2018
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(d) n – 3 A variable is a letter that is used to represent one or more numbers. The numbers are the values of the variable. A variable expression is a collection of numbers, variables and operations. Here are some examples. VARIABLE EXPRESSION MEANING OPERATION 8y =8 × y = 8 (y) 8 times y Multiplication = 16 ÷ b 16 divided by b Division 4+s 4 plus s Addition 9–x 9 minus x Subtraction The expression 8y is usually not written as 8 × y because of possible confusion of symbol ‘ × ’ with the variable x. Replacing each variable in an expression by a number is called evaluating the expression. The resulting number is the value of the expression. Write the variable Substitute values Simplify the numerical → → expression for variables expression 15-04-2018
The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?
- (a)2x + 16
- (b)6x + 9
- (c)8x + 3
- (d)8x + 12 In questions 17 to 32, fill in the blanks to make the statements true.
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(d) 8x + 12 In questions 17 to 32, fill in the blanks to make the statements true.
Sum or difference of two like terms is ________.
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In the formula, area of circle = πr2, the numerical constant of the expression πr2 is ________.
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3a2b and –7ba2 are ________ terms.
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–5a2b and –5b2a are ________ terms.
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In the expression 2πr, the algebraic variable is ________.
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Number of terms in a monomial is ________.
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Like terms in the expression n(n + 1) + 6 (n – 1) are ___________and ________.
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The expression 13 + 90 is a ________.
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The speed of car is 55 km/hrs. The distance covered in y hours is ________.
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x + y + z is an expression which is neither monomial nor ________. To show you understand an expression, you need to be able to explain what it means in words. You can write a word expression to represent the numeric or variable expression.
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If (x2y + y2 + 3) is subtracted from (3x2y + 2y2 + 5), then coefficient of y in the result is ________.
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– a – b – c is same as – a – ( ________ ). 15-04-2018
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The unlike terms in perimeters of following figures are___________ and __________.
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On adding a monomial _____________ to – 2x + 4y2 + z, the resulting expression becomes a binomial.
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3x + 23x2 + 6y2 + 2x + y2 + ____________ = 5x + 7y2.
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If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has _____ more toffees. In questions 33 to 52, state whether the statements given are True or False.
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1+ + x 3 is a polynomial.
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(3a – b + 3) – (a + b) is a binomial.
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A trinomial can be a polynomial.
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A polynomial with more than two terms is a trinomial.
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Sum of x and y is x + y.
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Sum of 2 and p is 2p.
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A binomial has more than two terms.
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A trinomial has exactly three terms.
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In like terms, variables and their powers are the same.
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The expression x + y + 5x is a trinomial.
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4p is the numerical coefficient of q2 in – 4pq2.
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5a and 5b are unlike terms. 15-04-2018
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Sum of x2 + x and y + y2 is 2x2 + 2y2.
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Subtracting a term from a given expression is the same as adding its additive inverse to the given expression.
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The total number of planets of Sun can be denoted by the variable n.
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In like terms, the numerical coefficients should also be the same.
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If we add a monomial and binomial, then answer can never be a monomial.
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If we subtract a monomial from a binomial, then answer is atleast a binomial.
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When we subtract a monomial from a trinomial, then answer can be a polynomial.
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When we add a monomial and a trinomial, then answer can be a monomial. Make a table that shows the number of triangles in each figure. Then tell how many triangles are in the fifth figure of the pattern. Use drawings to justify your answer. Figure 1 Figure 2 Figure 3 The table shows the number of triangles in each figure. Figure 1 2 3 4 5 The pattern is to add Number of 2 4 6 8 10 2 triangles each time. Triangles +2 +2 +2 +2 Figure 4 has 6 + 2 = 8 triangles. Figure 5 has 8 + 2 = 10 triangles. Figure 4 Figure 5 15-04-2018
This question refers to a figure in the original PDF.
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Write the following statements in the form of algebraic expressions and write whether it is monomial, binomial or trinomial.
- (a)x is multiplied by itself and then added to the product of x and y.
- (b)Three times of p and two times of q are multiplied and then subtracted from r.
- (c)Product of p, twice of q and thrice of r .
- (d)Sum of the products of a and b, b and c and c and a. (e) Perimeter of an equilateral triangle of side x. (f) Perimeter of a rectangle with length p and breadth q. (g) Area of a triangle with base m and height n. (h) Area of a square with side x. (i) Cube of s subtracted from cube of t. (j) Quotient of x and 15 multiplied by x. (k) The sum of square of x and cube of z. (l) Two times q subtracted from cube of q.
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(a) x is multiplied by itself and then added to the product of x and y.
(b) Three times of p and two times of q are multiplied and then subtracted from r.
(c) Product of p, twice of q and thrice of r .
(d) Sum of the products of a and b, b and c and c and a. (e) Perimeter of an equilateral triangle of side x. (f) Perimeter of a rectangle with length p and breadth q. (g) Area of a triangle with base m and height n. (h) Area of a square with side x. (i) Cube of s subtracted from cube of t. (j) Quotient of x and 15 multiplied by x. (k) The sum of square of x and cube of z. (l) Two times q subtracted from cube of q.
Write the coefficient of x2 in the following:
- (i)x2 – x + 4
- (ii)x3 – 2x2 + 3x + 1
- (iii)1 + 2x + 3x2 + 4x3
- (iv)y + y2x + y3x2 + y4x3
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(i) x2 – x + 4
(ii) x3 – 2x2 + 3x + 1
(iii) 1 + 2x + 3x2 + 4x3
(iv) y + y2x + y3x2 + y4x3
Find the numerical coefficient of each of the terms :
- (i)x3y2z, xy2z3, –3xy2z3, 5x3y2z, –7x2y2z2
- (ii)10xyz, –7xy2z, –9xyz, 2xy2z, 2x2y2z2
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(i) x3y2z, xy2z3, –3xy2z3, 5x3y2z, –7x2y2z2
(ii) 10xyz, –7xy2z, –9xyz, 2xy2z, 2x2y2z2
Simplify the following by combining the like terms and then write whether the expression is a monomial, a binomial or a trinomial.
- (a)3x2yz2 – 3xy2z + x2yz2 + 7xy2z
- (b)x4 + 3x3y + 3x2y2 – 3x3y – 3xy3 + y4 – 3x2y2
- (c)p3q2r + pq2r3 + 3p2qr2 – 9p2qr2
- (d)2a + 2b + 2c – 2a – 2b – 2c – 2b + 2c + 2a (e) 50x3 – 21x + 107 + 41x3 – x + 1 – 93 + 71x – 31x3 15-04-2018 Four sequences of patterns start as shown below: The four patterns are different. 1. What do the four patterns have in common? You may continue the sequence of each pattern as far as you want. 2. How many squares, dots, stars or bars will the 10th figure of each sequence have? 15-04-2018
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(a) 3x2yz2 – 3xy2z + x2yz2 + 7xy2z
(b) x4 + 3x3y + 3x2y2 – 3x3y – 3xy3 + y4 – 3x2y2
(c) p3q2r + pq2r3 + 3p2qr2 – 9p2qr2
(d) 2a + 2b + 2c – 2a – 2b – 2c – 2b + 2c + 2a (e) 50x3 – 21x + 107 + 41x3 – x + 1 – 93 + 71x – 31x3 15-04-2018 Four sequences of patterns start as shown below: The four patterns are different. 1. What do the four patterns have in common? You may continue the sequence of each pattern as far as you want. 2. How many squares, dots, stars or bars will the 10th figure of each sequence have? 15-04-2018
Add the following expressions:
- (a)p2 – 7pq – q2 and – 3p2 – 2pq + 7q2
- (b)x3 – x2y – xy2 – y3 and x3 – 2x2y + 3xy2 + 4y
- (c)ab + bc + ca and – bc – ca – ab
- (d)p2 – q + r, q2 – r + p and r2 – p + q (e) x3y2 + x2y3 +3y4 and x4 + 3x2y3 + 4y4 (f) p2qr + pq2r + pqr2 and – 3pq2r –2pqr2 (g) uv – vw, vw – wu and wu – uv (h) a2 + 3ab – bc, b2 + 3bc – ca and c2 + 3ca – ab 5 4 5 1 9 (i) p + 2 p 2 + ; –17 p + p 2 and p 5 – p 3 +7 8 8 8 8 (j) t – t2 – t3 – 14; 15t3 + 13 + 9t – 8t2; 12t2 – 19 – 24t and 4t – 9t2 + 19t3 The common properties of the four sequences of patterns on previous page are: • the first figure has 5 elements (squares, dots, stars or bars); • with each step in the row of figures, the number of elements grows by 4. So, the four sequences of patterns correspond to the same number sequence. Remark: To reach the 50th number in the strip, you need 49 steps. So take n = 49 and you find the 50th number: 5 + 4 × 49 = 201. 15-04-2018
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(a) p2 – 7pq – q2 and – 3p2 – 2pq + 7q2
(b) x3 – x2y – xy2 – y3 and x3 – 2x2y + 3xy2 + 4y
(c) ab + bc + ca and – bc – ca – ab
(d) p2 – q + r, q2 – r + p and r2 – p + q (e) x3y2 + x2y3 +3y4 and x4 + 3x2y3 + 4y4 (f) p2qr + pq2r + pqr2 and – 3pq2r –2pqr2 (g) uv – vw, vw – wu and wu – uv (h) a2 + 3ab – bc, b2 + 3bc – ca and c2 + 3ca – ab 5 4 5 1 9 (i) p + 2 p 2 + ; –17 p + p 2 and p 5 – p 3 +7 8 8 8 8 (j) t – t2 – t3 – 14; 15t3 + 13 + 9t – 8t2; 12t2 – 19 – 24t and 4t – 9t2 + 19t3 The common properties of the four sequences of patterns on previous page are: • the first figure has 5 elements (squares, dots, stars or bars); • with each step in the row of figures, the number of elements grows by 4. So, the four sequences of patterns correspond to the same number sequence. Remark: To reach the 50th number in the strip, you need 49 steps. So take n = 49 and you find the 50th number: 5 + 4 × 49 = 201. 15-04-2018
Subtract
- (a)– 7p2qr from – 3p2qr.
- (b)–a2 – ab from b2 + ab.
- (c)–4x2y – y3 from x3 + 3xy2 – x2y.
- (d)x4 + 3x3y3 + 5y4 from 2x4 – x3y3 + 7y4. (e) ab – bc – ca from – ab + bc + ca. (f) –2a2 – 2b2 from – a2 – b2 + 2ab. (g) x3y2 + 3x2y2 – 7xy3 from x4 + y4 + 3x2y2 – xy3. (h) 2 (ab + bc + ca) from –ab – bc – ca. (i) 4.5x5 – 3.4x2 + 5.7 from 5x4 – 3.2x2 – 7.3x. (j) 11 – 15y2 from y3 – 15y2 – y – 11.
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(a) – 7p2qr from – 3p2qr.
(b) –a2 – ab from b2 + ab.
(c) –4x2y – y3 from x3 + 3xy2 – x2y.
(d) x4 + 3x3y3 + 5y4 from 2x4 – x3y3 + 7y4. (e) ab – bc – ca from – ab + bc + ca. (f) –2a2 – 2b2 from – a2 – b2 + 2ab. (g) x3y2 + 3x2y2 – 7xy3 from x4 + y4 + 3x2y2 – xy3. (h) 2 (ab + bc + ca) from –ab – bc – ca. (i) 4.5x5 – 3.4x2 + 5.7 from 5x4 – 3.2x2 – 7.3x. (j) 11 – 15y2 from y3 – 15y2 – y – 11.
- (a)What should be added to x3 + 3x2y + 3xy2 + y3 to get x3 + y3?
- (b)What should be added to 3pq + 5p2q2 + p3 to get p3 + 2p2q2 + 4pq ?
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(a) What should be added to x3 + 3x2y + 3xy2 + y3 to get x3 + y3?
(b) What should be added to 3pq + 5p2q2 + p3 to get p3 + 2p2q2 + 4pq ?
- (a)What should be subtracted from 2x3 – 3x2y + 2xy2 + 3y3 to get x3 – 2x2y + 3xy2 + 4y3?
- (b)What should be subtracted from –7mn + 2m2 + 3n2 to get m2 + 2mn + n2 ?
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(a) What should be subtracted from 2x3 – 3x2y + 2xy2 + 3y3 to get x3 – 2x2y + 3xy2 + 4y3?
(b) What should be subtracted from –7mn + 2m2 + 3n2 to get m2 + 2mn + n2 ?
How much is 21a3 – 17a2 less than 89a3 – 64a2 + 6a + 16?
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How much is y4 – 12y2 + y + 14 greater than 17y3 + 34y2 – 51y + 68?
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y4 – 17y3 – 46y2 + 52y – 54
How much does 93p2 – 55p + 4 exceed 13p3 – 5p2 + 17p – 90?
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To what expression must 99x3 – 33x2 – 13x – 41 be added to make the sum zero? 1. Describe two different number patterns that begin with 3, 6, ... 2. Tell when it would be useful to make a table to help you identify and extend a pattern. 15-04-2018
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Subtract 9a2 – 15a + 3 from unity.
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Find the values of the following polynomials at a = – 2 and b = 3:
- (a)a2 + 2ab + b2
- (b)a2 – 2ab + b2
- (c)a3 + 3a2b + 3ab2 + b3
- (d)a3 – 3a2b + 3ab2 – b3 a 2 +b 2 a 2 -b 2 (e) (f) 3 3 (g) a + b (h) a2 + b2 – ab – b2 – a2
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(a) a2 + 2ab + b2
(b) a2 – 2ab + b2
(c) a3 + 3a2b + 3ab2 + b3
(d) a3 – 3a2b + 3ab2 – b3 a 2 +b 2 a 2 -b 2 (e) (f) 3 3 (g) a + b (h) a2 + b2 – ab – b2 – a2
Find the values of following polynomials at m = 1, n = –1 and p = 2:
- (a)m + n + p
- (b)m2 + n2 + p2
- (c)m3 + n3 + p3
- (d)mn + np + pm (e) m3 + n3 + p3 – 3mnp (f) m2n2 + n2p2 + p2m2
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(a) m + n + p
(b) m2 + n2 + p2
(c) m3 + n3 + p3
(d) mn + np + pm (e) m3 + n3 + p3 – 3mnp (f) m2n2 + n2p2 + p2m2
If A = 3x2 – 4x + 1, B = 5x2 + 3x – 8 and C = 4x2 – 7x + 3, then find:
- (i)(A + B) – C
- (ii)B + C – A
- (iii)A + B + C
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(i) (A + B) – C
(ii) B + C – A
(iii) A + B + C
If P = –(x – 2), Q = –2(y +1) and R = –x + 2y, find a, when P + Q + R = ax.
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From the sum of x2 – y2 – 1, y2 – x2 – 1 and 1 – x2 – y2 subtract – (1 + y2).
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Subtract the sum of 12ab –10b2 –18a2 and 9ab + 12b2 + 14a2 from the sum of ab + 2b2 and 3b2 – a2.
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Each symbol given below represents an algebraic expression: = 2x2 + 3y, = 5x2 + 3x, = 8y2 – 3x2 + 2x + 3y 15-04-2018 The symbols are then represented in the expression: + – Find the expression which is represented by the above symbols.
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Observe the following nutritional chart carefully: Food Item (Per Unit = 100g) Carbohydrates Rajma 60g Cabbage 5g Potato 22g Carrot 11g Tomato 4g Apples 14g Write an algebraic expression for the amount of carbohydrates in ‘g’ for
- (a)y units of potatoes and 2 units of rajma
- (b)2x units tomatoes and y units apples.
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(a) y units of potatoes and 2 units of rajma
(b) 2x units tomatoes and y units apples.
Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.
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Amisha has a square plot of side m and another triangular plot with base and height each equal to m. What is the total area of both plots?
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A taxi service charges 8 per km and levies a fixed charge of 50. Write an algebraic expression for the above situation, if the taxi is hired for x km. 15-04-2018
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Shiv works in a mall and gets paid 50 per hour. Last week he worked for 7 hours and this week he will work for x hours. Write an algebraic expression for the money paid to him for both the weeks.
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Sonu and Raj have to collect different kinds of leaves for science project. They go to a park where Sonu collects 12 leaves and Raj collects x leaves. After some time Sonu loses 3 leaves and Raj collects 2x leaves. Write an algebraic expression to find the total number of leaves collected by both of them.
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A school has a rectangular play ground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?
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The rate of planting the grass is x per square metre. Find the cost of planting the grass on a triangular lawn whose base is y metres and height is z metres.
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Find the perimeter of the figure given below: 15-04-2018
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In a rectangular plot, 5 square flower beds of side (x + 2) metres each have been laid (see figure given below). Find the total cost of fencing the flower beds at the cost of 50 per 100 metres:
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A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions:
- (a)How much wire is left?
- (b)If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?
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(a) How much wire is left?
(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?
Rohan's mother gave him 3xy2 and his father gave him 5(xy2+2). Out of this total money he spent (10–3xy2) on his birthday party. How much money is left with him?
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- (i)A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below: 15-04-2018
- (ii)In the given figure, the length of a green side is given by g and that of the red side is given by p. Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together. 1 2 1
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(i) A triangle is made up of 2 red sticks and 1 blue sticks . The length of a red stick is given by r and that of a blue stick is given by b. Using this information, write an expression for the total length of sticks in the pattern given below: 15-04-2018
(ii) In the given figure, the length of a green side is given by g and that of the red side is given by p. Write an expression for the following pattern. Also write an expression if 100 such shapes are joined together. 1 2 1
The sum of first n natural numbers is given by n + n . Find 2 2
- (i)The sum of first 5 natural numbers.
- (ii)The sum of first 11 natural numbers.
- (iii)The sum of natural numbers from 11 to 30. 15-04-2018
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(i) The sum of first 5 natural numbers.
(ii) The sum of first 11 natural numbers.
(iii) The sum of natural numbers from 11 to 30. 15-04-2018
The sum of squares of first n natural numbers is given by 1 1 n ( n + 1) (2n + 1) or (2 n3 + 3n 2 + n) . Find the sum of squares of the 6 6 first 10 natural numbers.
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The sum of the multiplication table of natural number ‘n’ is given by 55 × n. Find the sum of
- (a)Table of 7
- (b)Table of 10
- (c)Table of 19
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(a) Table of 7
(b) Table of 10
(c) Table of 19
If x = 2x + 3, x = x + 7 and x = x – 3, then find the value of :
- (i)2 6 + 3 – 1
- (ii)2 + 8 –3 0
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(i) 2 6 + 3 – 1
(ii) 2 + 8 –3 0
If x = x – 2 and x = x + 6, then find the value of:
- (i)10 – 4
- (ii)2 12 – 1 Translate each of the following algebraic expressions Question 91 to 94 into words.
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(i) 10 – 4
(ii) 2 12 – 1 Translate each of the following algebraic expressions Question 91 to 94 into words.
4b – 3
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Three subtracted from four times ‘b’.
8 (m + 5) 15-04-2018 93. 8–x 16
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Eight times the sum of m and five.
17 w
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Seventeen times quotient of sixteen by w. OSKNRKPNOV 1 1 n–5
- (i)Critical Thinking Write two different algebraic expressions for 1 the word phrase “ of the sum of x and 7.” 4
- (ii)What’s the Error? A student wrote an algebraic expression for “5 less than a number n divided by 3” as − 5 . What error did the student make?
- (iii)Write About it Shashi used addition to solve a word problem about the weekly cost of commuting by toll tax for 15 each day. Ravi solved the same problem by multiplying. They both got the correct answer. How is this possible?
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(i) Critical Thinking Write two different algebraic expressions for 1 the word phrase “ of the sum of x and 7.” 4
(ii) What’s the Error? A student wrote an algebraic expression for “5 less than a number n divided by 3” as − 5 . What error did the student make?
Challenge Write an expression for the sum of 1 and twice a number n. If you let n be any odd number, will the result always be an odd number?
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Critical Thinking Will the value of 11x for x = –5 be greater than 11 or less than 11? Explain.
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Match Column I with Column II in the following: Column I Column II 1. The difference of 3 and a number squared
- (a)4 – 2x 2. 5 less than twice a number squared
- (b)n2 – 3 3. Five minus twice the square of a number
- (c)2n2 – 5 4. Four minus a number multiplied by 2
- (d)5 – 2n2 5. Seven times the sum of a number and 1 (e) 3 – n2 6. A number squared plus 6 (f) 2 (n + 6) 15-04-2018 7. 2 times the sum of a number and 6 (g) 7 (n + 1) 8. Three less than the square of a number (h) n2 + 6
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(c) 2n2 – 5 4. Four minus a number multiplied by 2
(d) 5 – 2n2 5. Seven times the sum of a number and 1 (e) 3 – n2 6. A number squared plus 6 (f) 2 (n + 6) 15-04-2018 7. 2 times the sum of a number and 6 (g) 7 (n + 1) 8. Three less than the square of a number (h) n2 + 6
(a) 4 – 2x 2. 5 less than twice a number squared
(b) n2 – 3 3. Five minus twice the square of a number
At age of 2 years, a cat or a dog is considered 24 “human” years old. Each year, after age 2 is equivalent to 4 “human” years. Fill in the expression [24 + (a – 2)] so that it represents the age of a cat or dog in human years. Also, you need to determine for what ‘a’ stands for. Copy the chart and use your expression to complete it. Age [24 + (a – 2)] Age (Human Years)
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Expression : 24 + 4 (a – 2), ‘a’ stands for the present age of dog or cat Age [24 + 4(a – 2)] Age (Human Years) 2 24 + 4(2 – 2) 24 3 24 + 4(3 – 2) 28 4 24 + 4(4 – 2) 32 5 24 + 4(5 – 2) 36 6 24 + 4(6 – 2) 40
Express the following properties with variables x, y and z. (i) Commutative property of addition (ii) Commutative property of multiplication (iii) Associative property of addition (iv) Associative property of multiplication (v) Distributive property of multiplication over addition 1. Game Think of a number, multiply the number by 8, divide by 2, add 5, and then subtract 4 times the original number. 15-04-2018 No matter what number you choose the answer will always be 5. Here’s how What you say What the person Role of think Mathematics (i) Pick any number 6 (for example) n (ii) Multiply by 8 8 (6) = 48 8n (iii) Divide by 2 48 ÷ 2 = 24 8n ÷ 2 = 4n (iv) Add 5 24 + 5 = 29 4n + 5 (v) Subtract 4 times the 29 – 4 (6) = 4n + 5 – 4n = 5 original number 29 – 24 = 5 Invent your own Math magic thinking that has atleast five steps. Try it with your friend! 2. Colour the scalene triangle with Yellow, Isosceles with Green and equilateral with Red in the given adjoining figure. 15-04-2018 3. Cross Number Puzzle Rohit has to solve the given cross number puzzle to qualify for the next round of Mathematics quiz competition. Help him by evaluating the values of given expression at x = 0, y = 1, z = 2. Also help him to fill the cross number along Across and Downward with the help of given clues, (Numbers to be written in words) Across
- (a)xy + yz + zx
- (b)x2y2 + z2 – 2xyz
- (c)8 – (x+y)
- (d)x2y3 + y2z3 + z2x3 Down (e) x2 – 2xy (y–z) x3 + y 3 + z 3 (f) 3 (g) x3 + y3 + z3 – 2yz2 (h) 2x + 2y + 2z 15-04-2018
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(a) xy + yz + zx
(b) x2y2 + z2 – 2xyz
(c) 8 – (x+y)
(d) x2y3 + y2z3 + z2x3 Down (e) x2 – 2xy (y–z) x3 + y 3 + z 3 (f) 3 (g) x3 + y3 + z3 – 2yz2 (h) 2x + 2y + 2z 15-04-2018