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deepshikhasingh15
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Time ended
G7 Algebra
Math quiz helps us to enhance brains neural network.
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1) Subtract (3a − 4b + 2c) from the sum of (5a − b + c) and (2a + 3b − c).
Difference of squares: (a^2 – b^2 = (a – b)(a + b)) Here (a = 7y), (b = 6).
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2) Find the value of:
[(p − q)³(p + q)] ÷ [(p² − q²)(p² + 2pq + q²)]
when p = 4 and q = 2
Calculate: (3 times 2^2 times 3 = 36) (-2 times 2 times 3^2 = -36) (3^3 = 27) Sum: (36 – 36 + 27 = 27)
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3) Expand: (x + 2)³
Formula: ((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3) Calculate: (x^3 + 3x^2 times 2 + 3x times 4 + 8 = x^3 + 6x^2 + 12x + 8)
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4) Simplify: 9p2q + 4pq² – 5p2q + 7pq²
Combine like terms: (9p^2q – 5p^2q = 4p^2q) (4pq^2 + 7pq^2 = 11pq^2)
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5) Evaluate: 3a² – 2ab + b² for (a = 2), (b = 3)
(3a^2 = 3 times 4 = 12) (-2ab = -2 times 2 times 3 = -12) (b^2 = 9) Sum: (12 – 12 + 9 = 9)
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6) Evaluate: 2x³ – 5x² + 4 for (x = 2)
Calculate: (2 times 8 = 16) (-5 times 4 = -20) Sum: (16 – 20 + 4 = 0)
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7) A wire of total length 3x²y + 4xy+ 5y² is bent to form a triangle.Two sides of the triangle are x²y + 2xy + y² and 2x²y + xy + 2y².Find the length of the third side (in units) if x = 2 and y = 1.
Numbers that multiply to 10 and add to 7 are 5 and 2.
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8) Which of the following is true for the value of
5xy(x − y) − 4x²(y − y²) − 2y²(3x² − x) + 3xy(x − y)?
((a + b)^2 = a^2 + 2ab + b^2) Calculate: (25x^2 + 2 times 5x times 3 + 9 = 25x^2 + 30x + 9)
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9) Factorize: x² + 6x + 9
Perfect square trinomial: (x^2 + 6x + 9 = (x + 3)^2)
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10) Simplify: [ 7p2q – 2pq² + 4p2q + 5pq² ]
Combine like terms: (7p^2q + 4p^2q = 11p^2q) (-2pq^2 + 5pq^2 = 3pq^2)
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11) Find the value of:
[(x − y)²(x + y)³] ÷ [(x² − y²)(x² + y²)]
when x = 3 and y = 1.
Combine like terms: (7x^2y + 4x^2y = 11x^2y) (-3xy^2 + 6xy^2 = 3xy^2)
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12) Simplify: [ 4m2n – 7mn² + 6m2n + 2mn² ]
Combine like terms: (4m^2n + 6m^2n = 10m^2n) (-7mn^2 + 2mn^2 = -5mn^2)
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13) Expand: [ (2x – 3)(x + 5) ]
Multiply: (2x times x = 2x^2) (2x times 5 = 10x) (-3 times x = -3x) (-3 times 5 = -15) Combine like terms: (10x – 3x = 7x)
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14) Expand: (2x + 3)(x – 4)
Multiply: (2x times x = 2x^2) (2x times -4 = -8x) (3 times x = 3x) (3 times -4 = -12) Combine middle terms: (-8x + 3x = -5x) Full expression: (2x^2 – 5x – 12)
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15) If x = 3, y = −2, z = 1, then the value of3xy² + 2x²z − 5yz² + 4xyz is ____.
Difference of squares: (36y^2 – 49 = (6y)^2 – 7^2 = (6y – 7)(6y + 7))
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16) Simplify: 7xy – 3x2y + 4xy – 6x2y
Combine like terms: (7xy + 4xy = 11xy) (-3x^2y – 6x^2y = -9x^2y)
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17) Evaluate: [ 2x2y – 3xy² + y³ ] for (x = 1), (y = 2)
Step-by-step: (2x^2y = 2 times 1 times 1 times 2 = 4) (-3xy^2 = -3 times 1 times 4 = -12) (y^3 = 8) Sum: (4 – 12 + 8 = 0)
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18) What is the coefficient of x in the expression 7x − 4y + 9?
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19) What must be added to the sum of 3x² − 4x + 9, −2x² + 5x − 13, and x² − 7x + 4 to get 0?
Calculate: (4 times 8 = 32) (-3 times 4 = -12) (2 times 2 = 4) Sum: (32 – 12 + 4 – 5 = 19)
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20) Subtract (2x − 3y + z) from the sum of (4x + y − 2z) and (3x − 2y + 3z).
Use formula: ((a – b)^2 = a^2 – 2ab + b^2) Calculate: (x^2 – 2 times x times 5 + 25 = x^2 – 10x + 25)
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