Q: A chemist needs to mix a $$20\%$$ saline solution with a $$50\%$$ saline solution to obtain $$10$$ liters of a $$30\%$$ solution. Let $$x be $$the amount (in liters) of the $$20\%$$ solution used. Which equation models this situation?

$$0.2x + 0.5(10 - x) = 0.3 \times 10$$

Question 1

Which of the following is the greatest common factor (GCF) of the polynomial $$12x^3y^2$ - 18x^2$y^3$$ + $$6x^4y$?

Accepted Answer

$$6x^2y$

Question 2

Factor the following trinomial completely: $$x^2 - 7x + 12$.

Accepted Answer

$$(x-3)(x-4)$$

Question 3

Which of the following is a correct factorization of the difference of squares $$16x^2 - 81$?

Accepted Answer

$$(4x-9)(4x+9)$$

Question 4

Solve the quadratic equation $$x^2 + 2x - 15 = 0$ using the zero-factor property.

Accepted Answer

$$x = 3 or$$ $$x = -5$$

Question 5

A rectangular garden has an area of $$60$$ square meters and a length that is $$4$$ meters longer than its width. Which equation can be used to find the width $$w of $$the garden?

Accepted Answer

$$w(w+4) = 60$$

Question 6

Simplify the rational expression: $$\dfrac{6x^2$ - 12x}{3x}.$$

Accepted Answer

Question 7

Multiply and simplify: $$\dfrac{x^2$ - 9}{x^2$ - x - 6} 	imes \dfrac{x - 2}{x + 3}.$$

Accepted Answer

$$\dfrac{x - 3}{x - 2}$$

Question 8

Simplify the complex fraction: $$\dfrac{\dfrac{2}{x}}{\dfrac{4}{x^2$}}.$$

Accepted Answer

Question 9

Rewrite the radical expression $$\sqrt[3]{x^5$} as an $$exponential expression.

Accepted Answer

$$x^{5/3}$$

Question 10

Solve for $$x$$: $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 11

Which of the following is the simplified form of $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$7\sqrt{2}$$

Question 12

Solve the quadratic equation by completing the square: $$x^2 + 6x + 5 = 0$.

Accepted Answer

$$x = -1 or$$ $$x = -5$$

Question 13

A chemist needs to mix a $$20\%$$ saline solution with a $$50\%$$ saline solution to obtain $$10$$ liters of a $$30\%$$ solution. Let $$x be $$the amount (in liters) of the $$20\%$$ solution used. Which equation models this situation?

Accepted Answer

$$0.2x + 0.5(10 - x) = 0.3 	imes 10$$

Question 14

Solve using the quadratic formula: $$2x^2 - 4x - 6 = 0$.

Accepted Answer

$$x = 3 or$$ $$x = -1$$

Question 15

Which of the following is the correct simplification of $$\dfrac{x^2$ - 16}{x^2$ - 8x + 16}$$?

Accepted Answer

Question 16

If $$\sqrt{a} = 7$$, what is the value of $$a$$?

Accepted Answer

$$49$$

Question 17

A car travels $$300$$ miles at a constant speed. If the trip takes $$5$$ hours, what is the speed of the car?

Accepted Answer

$$60$$ miles per hour

Question 18

Which of the following is the correct simplification of $$\dfrac{3x^2$y}{6xy^2$}$$?

Accepted Answer

$$\dfrac{x}{2y}$$

Question 19

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2 + 10x + 25$

MAT 101 Final Exam Study Guide: Factoring, Rational Expressions, Radicals, and Quadratic Equations

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