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Lesson Example Discussion Quiz: Class Homework

Quiz In Class

Title: Equivalent expressions

Grade: 1400-a Lesson: S1-L5

Explanation: Hello Students, time to practice and review. Let us take next 10-15 minutes to solve the ten problems using the Quiz Sheet. Then submit the quiz to get the score. This is a good exercise to check your understanding of the concepts.

Quiz: in Class

Problem Id	Problem	Options
1	\$2/(x - 2) + 3/ (x + 5) = (rx + t) /((x -2) (x - 5))\$ The equation above is true for all x > 2, where r and t are positive constants. What is the value of rt?	A) 20 B) 60 C) 15 D) 40
2	Two workers, A and B, can complete a task together in 6 hours. Worker A alone can complete the task in 9 hours. Write an expression for the time it takes worker B to complete the task alone, and solve for it.	A) 20 hours B) 14 hours C) 18 hours D) 16 hours
3	\$(ax + b) (5x^2 - bx + 4) = 20x^3 - 9x^2 - 2x + 12\$. The equation above is true for all x, where a and b are constants. What is the value of ab?	A) 12 B) 42 C) 21 D) 24
4	\$f(x) = x^3 - 9x\$, \$g(x) = x^2 - 2x - 3\$ Which of the following expressions is equivalent to \$f(x)/g(x)\$, for x > 3?	A) \$(x(x +3))/ (x +1)\$ B) \$(x +3)/ (x -1)\$ C) \$(x(x - 3))/ (x +1)\$ D) \$(x - 3)/ (x -1)\$
5	If a and c are positive numbers, which of the following is equivalent to \$\sqrt(a + c)^3 . \sqrt(a + c)\$?	A) \$a^2 + 2ac + c^2\$ B) \$a^2 - 2ac - c^2\$ C) \$a^2 - 2ac + c^2\$ D) \$a^2 + 2ac - c^2\$
6	Simplify the expression: \$3(3x^2 - 4x + 2) + 2(2x^2 - 3)\$	A) \$13x^2 - 12x + 1\$ B) \$9x^2 - 12x + 4\$ C) \$11x^2 - 12x + 1\$ D) \$13x^2 - 12x - 6\$
7	Simplify the expression and determine if it is equivalent to \$3(x^2 − 2x + 5) − (2x^2 − 3x + 7)\$: \$3x^2 − 6x + 15 − 2x^2 + 3x − 7\$	A) \$x^2 − 3x + 8\$ B) \$x^2 − 3x + 7\$ C) \$x^2 − 3x + 6\$ D) \$x^2 − x + 8\$
8	Prove or disprove that the following expressions are equivalent: \$(6x^2 - 24)/(3x + 6)\$ and 2(x - 2)	A) Equivalent for all x B) Equivalent only if \$x ne -2\$ C) Equivalent only if \$x ne -2\$ and \$x ne 2\$ D) Not Equivalent
9	Are the expressions \$(\sqrt(x - 3)^2)\$ and x - 3 equivalent?	A) Equivalent for all x B) Equivalent only if \$x ge -3\$ C) Equivalent only if \$x ge 3\$ D) Equivalent only if \$x ge 0\$
10	Simplify the expression and determine if it is equivalent to \$5(2x^2 − 3x + 1) − 2(3x^2 + 2x − 5)\$: \$10x^2 − 15x + 5 − 6x^2 − 4x + 10\$.	A) \$4x^2 - 11x + 5\$ B) \$4x^2 - 19x + 15\$ C) \$4x^2 - 11x + 15\$ D) \$4x^2 - 19x + 5\$

Problem Id

Problem

Options

\$2/(x - 2) + 3/ (x + 5) = (rx + t) /((x -2) (x - 5))\$ The equation above is true for all x > 2, where r and t are positive constants. What is the value of rt?

A) 20

B) 60

C) 15

D) 40

Two workers, A and B, can complete a task together in 6 hours. Worker A alone can complete the task in 9 hours. Write an expression for the time it takes worker B to complete the task alone, and solve for it.

A) 20 hours

B) 14 hours

C) 18 hours

D) 16 hours

\$(ax + b) (5x^2 - bx + 4) = 20x^3 - 9x^2 - 2x + 12\$.
The equation above is true for all x, where a and b are constants. What is the value of ab?

A) 12

B) 42

C) 21

D) 24

\$f(x) = x^3 - 9x\$, \$g(x) = x^2 - 2x - 3\$
Which of the following expressions is equivalent to \$f(x)/g(x)\$, for x > 3?

A) \$(x(x +3))/ (x +1)\$

B) \$(x +3)/ (x -1)\$

C) \$(x(x - 3))/ (x +1)\$

D) \$(x - 3)/ (x -1)\$

If a and c are positive numbers, which of the following is equivalent to \$\sqrt(a + c)^3 . \sqrt(a + c)\$?

A) \$a^2 + 2ac + c^2\$

B) \$a^2 - 2ac - c^2\$

C) \$a^2 - 2ac + c^2\$

D) \$a^2 + 2ac - c^2\$

Simplify the expression:
\$3(3x^2 - 4x + 2) + 2(2x^2 - 3)\$

A) \$13x^2 - 12x + 1\$

B) \$9x^2 - 12x + 4\$

C) \$11x^2 - 12x + 1\$

D) \$13x^2 - 12x - 6\$

Simplify the expression and determine if it is equivalent to
\$3(x^2 − 2x + 5) − (2x^2 − 3x + 7)\$:
\$3x^2 − 6x + 15 − 2x^2 + 3x − 7\$

A) \$x^2 − 3x + 8\$

B) \$x^2 − 3x + 7\$

C) \$x^2 − 3x + 6\$

D) \$x^2 − x + 8\$

Prove or disprove that the following expressions are equivalent: \$(6x^2 - 24)/(3x + 6)\$ and 2(x - 2)

A) Equivalent for all x

B) Equivalent only if \$x ne -2\$

C) Equivalent only if \$x ne -2\$ and \$x ne 2\$

D) Not Equivalent

Are the expressions \$(\sqrt(x - 3)^2)\$ and x - 3 equivalent?

A) Equivalent for all x

B) Equivalent only if \$x ge -3\$

C) Equivalent only if \$x ge 3\$

D) Equivalent only if \$x ge 0\$

Simplify the expression and determine if it is equivalent to \$5(2x^2 − 3x + 1) − 2(3x^2 + 2x − 5)\$:
\$10x^2 − 15x + 5 − 6x^2 − 4x + 10\$.

A) \$4x^2 - 11x + 5\$

B) \$4x^2 - 19x + 15\$

C) \$4x^2 - 11x + 15\$

D) \$4x^2 - 19x + 5\$