Algebraic Manipulations and Properties Quiz

Test your algebra skills with these 17 questions on simplifying expressions, solving equations, and finding derivatives.

Practice Learn Test

Solve the equation: 2x - 7 = 3x + 5

x = -12

x = 12

x = -6

x = 6

Expand and simplify the expression: (a - 2)(3a + 4)

3a^2 - 2a - 8

3a^2 - 2a + 8

3a^2 + 4a - 8

3a^2 + 4a + 8

Simplify the expression: (2a^2b^3)^2 / (4ab)^2

a^2b

4a^2b^2

2ab

a^2b^3

Find the value of x in the equation: 2^(3x - 1) = 8

x = 2

x = 3

x = 1

x = 4

Solve the inequality: 2x - 5 > 3x + 7

x < -12

x > -12

x < 12

x > 12

Expand and simplify the expression: (2x - 1)(x^2 + x + 1)

2x^3 - x^2 + 3x - 1

2x^3 + 3x^2 + 4x - 1

2x^3 + x^2 + 2x - 1

2x^3 + 2x^2 + x - 1

Simplify the expression: 3x + 2(x - 5) = 4(2x + 1)

x = -3

x = 3

x = 5

x = -5

Factorize the quadratic expression: x^2 - 5x + 6

(x - 2)(x - 3)

(x + 2)(x - 3)

(x - 2)(x - 1)

(x + 2)(x - 1)

Solve the system of equations:
2x + y = 8
3x - 2y = 1

x = 3, y = 2

x = 2, y = 3

x = -1, y = 6

x = 4, y = 0

#10

Factorize the following expression: 16x^2 - 9y^2

(4x - 3y)(4x + 3y)

(4x + 3y)(4x - 3y)

(2x - 3y)(2x + 3y)

(2x + 3y)(2x - 3y)

#11

Solve for x: log₂(x + 4) = 3

x = 5

x = 8

x = 9

x = 2

#12

Simplify the expression: (a^2 - b^2)/(a + b)

a - b

a + b

a^2 + b^2

a - 2b

#13

If f(x) = 2x^3 - 5x^2 + 3x + 7, find f'(x) (derivative of f(x)).

f'(x) = 6x^2 - 10x + 3

f'(x) = 6x^2 - 10x - 3

f'(x) = 6x^2 - 5x + 3

f'(x) = 6x^2 - 5x - 3

#14

If g(x) = (x^2 + 2x + 1)^3, find g'(x) (derivative of g(x)).

g'(x) = 3(x^2 + 2x + 1)^2(2x + 2)

g'(x) = 3(x^2 + 2x + 1)^2(2x + 1)

g'(x) = 3(x^2 + 2x + 1)(2x + 2)

g'(x) = 3(x^2 + 2x + 1)(2x + 1)

#15

If f(x) = 4x³ - 6x² + 2x + 1, find f''(x) (second derivative of f(x)).

f''(x) = 24x - 12

f''(x) = 12x - 6

f''(x) = 12x + 2

f''(x) = 24x + 2

#16

If h(x) = (2x^2 + 3x - 1)^4, find h'(x) (derivative of h(x)).

h'(x) = 4(2x^2 + 3x - 1)^3(4x + 3)

h'(x) = 4(2x^2 + 3x - 1)^3(2x + 3)

h'(x) = 8(2x^2 + 3x - 1)^3(4x + 3)

h'(x) = 8(2x^2 + 3x - 1)^3(2x + 3)

#17

If k(x) = (3x^2 - 4x + 1)^5, find k'(x) (derivative of k(x)).

k'(x) = 5(3x^2 - 4x + 1)^4(6x - 4)

k'(x) = 5(3x^2 - 4x + 1)^4(3x - 2)

k'(x) = 10(3x^2 - 4x + 1)^4(6x - 4)

k'(x) = 10(3x^2 - 4x + 1)^4(3x - 2)

Algebraic Manipulations and Properties Quiz

Solve the equation: 2x - 7 = 3x + 5

Expand and simplify the expression: (a - 2)(3a + 4)

Simplify the expression: (2a^2b^3)^2 / (4ab)^2

Find the value of x in the equation: 2^(3x - 1) = 8

Solve the inequality: 2x - 5 > 3x + 7

Expand and simplify the expression: (2x - 1)(x^2 + x + 1)

Simplify the expression: 3x + 2(x - 5) = 4(2x + 1)

Factorize the quadratic expression: x^2 - 5x + 6

Solve the system of equations:
2x + y = 8
3x - 2y = 1

Factorize the following expression: 16x^2 - 9y^2

Solve for x: log₂(x + 4) = 3

Simplify the expression: (a^2 - b^2)/(a + b)

If f(x) = 2x^3 - 5x^2 + 3x + 7, find f'(x) (derivative of f(x)).

If g(x) = (x^2 + 2x + 1)^3, find g'(x) (derivative of g(x)).

If f(x) = 4x³ - 6x² + 2x + 1, find f''(x) (second derivative of f(x)).

If h(x) = (2x^2 + 3x - 1)^4, find h'(x) (derivative of h(x)).

If k(x) = (3x^2 - 4x + 1)^5, find k'(x) (derivative of k(x)).

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Algebraic Manipulations and Properties Quiz

Solve the equation: 2x - 7 = 3x + 5

Expand and simplify the expression: (a - 2)(3a + 4)

Simplify the expression: (2a^2b^3)^2 / (4ab)^2

Find the value of x in the equation: 2^(3x - 1) = 8

Solve the inequality: 2x - 5 > 3x + 7

Expand and simplify the expression: (2x - 1)(x^2 + x + 1)

Simplify the expression: 3x + 2(x - 5) = 4(2x + 1)

Factorize the quadratic expression: x^2 - 5x + 6

Solve the system of equations: 2x + y = 8 3x - 2y = 1

Factorize the following expression: 16x^2 - 9y^2

Solve for x: log₂(x + 4) = 3

Simplify the expression: (a^2 - b^2)/(a + b)

If f(x) = 2x^3 - 5x^2 + 3x + 7, find f'(x) (derivative of f(x)).

If g(x) = (x^2 + 2x + 1)^3, find g'(x) (derivative of g(x)).

If f(x) = 4x³ - 6x² + 2x + 1, find f''(x) (second derivative of f(x)).

If h(x) = (2x^2 + 3x - 1)^4, find h'(x) (derivative of h(x)).

If k(x) = (3x^2 - 4x + 1)^5, find k'(x) (derivative of k(x)).

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Test Your Knowledge

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Solve the system of equations:
2x + y = 8
3x - 2y = 1