Question 1

Which of the following is the correct scientific notation for the number 0.000047?

Accepted Answer

Question 2

Simplify the expression $$-21a^3b^5$ 	imes 3b$.

Accepted Answer

$$-63a^3b^6$

Question 3

Expand and simplify $$(x+6)(x+7). $$Which of the following is correct?

Accepted Answer

$$x^2 + 13x + 42$

Question 4

Factor the expression $$9x^2 - 42x + 49$.

Accepted Answer

$$(3x-7)^2$$

Question 5

Solve the quadratic equation $$x^2 + 8x + 12 = 0$.

Accepted Answer

$$x = -6, -2$$

Question 6

Which of the following is the simplified form of $$\sqrt{72}$$?

Accepted Answer

$$6\sqrt{2}$$

Question 7

Rationalize the denominator and simplify: $$\frac{5}{\sqrt{7}}.$$

Accepted Answer

$$\frac{5\sqrt{7}}{7}$$

Question 8

Given the equation $$x^2 - 4x + 8 = 15$, what are the solutions for x$?

Accepted Answer

$$x = 7, 1$$

Question 9

Which of the following is the correct factorization of $$25x^2$$ - $$9y^2$$?

Accepted Answer

$$(5x-3y)(5x+3y)$$

Question 10

A rectangle has a length $$l$$ and width $$w$$ such that $$l = 2w + 4$$ and the perimeter is $$50. $$What are the values of $$l$$ and $$w$$?

Accepted Answer

$$l = 18, w = 7$$

Question 11

Simplify the expression $$\sqrt{50x^2$}.$$

Accepted Answer

$$5x\sqrt{2}$$

Question 12

Solve for $$x$$: $$2x^2 - 8 = 0$.

Accepted Answer

$$x = \pm 2$$

Question 13

Which of the following is the correct solution to $$x^2 + 2x - 35 = 0$?

Accepted Answer

$$x = -7, 5$$

Question 14

Expand $$(3x+1)^2.$$

Accepted Answer

$$9x^2 + 6x + 1$

Question 15

A chemist mixes two solutions, one with a concentration of $$40\%$$ and another with $$50\%$$, to obtain $$90$$ liters of a $$45\%$$ solution. How many liters of each solution are used?

Accepted Answer

$$40$$ liters of $$40\%$$, $$50$$ liters of $$50\%$$

Question 16

Simplify $$\frac{2}{x^6$y}.$$

Accepted Answer

$$2x^{-6}y$$^{-1}$

Question 17

Which of the following is the correct solution for $$x in$$ $$x^2 + x - 6 = 0$?

Accepted Answer

$$x = 2, -3$$

Question 18

Given $$a^2 - 16ab$$ + $$5b^2$$, which of the following is the correct factorization?

Accepted Answer

$$(12a^2 - 16ab$$ + $$5b^2$$)$$ cannot be factored further with integer coefficients.

Question 19

Solve for $$x$$: $$x^2 - 6x + 9 = 0$.

Accepted Answer

$$x = 3$$

Exam 2 Review Guidance for Beginning-Intermediate Algebra

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