Question 1

Solve the expression for the given values: $$|p| - 18q/(|1|/|p|)$$ where $$p = -6$$ and $$q = 1.$$

Accepted Answer

$$4$$

Question 2

For the following number written in decimal notation, rewrite in its percentage equivalent: $$0.9$$

Accepted Answer

$$90\%$$

Question 3

Write the following phrase as a simplified algebraic expression: The number $$y is $$decreased by the sum of eighteen and this number.

Accepted Answer

$$2(y+1)$$

Question 4

Determine whether the given expression is a polynomial. If it is a polynomial, indicate its degree and classify by the number of terms: $$5t^7y^4$ + (8/k^2$) - 12$

Accepted Answer

Not a polynomial

Question 5

Write the given expression after isolating the common factor with the lowest power. Assume all variables belong to $$\mathbb{Z}^+$$. $$11x^7$$ - $$33x^9$$

Accepted Answer

$$11x^7(x^2$-3)$

Question 6

Subtract these terms: $$8/\sqrt{108} - 2/\sqrt{147}$$

Accepted Answer

$$34/3$$

Question 7

Simplify the following expression: $$\sqrt[3]{41}$$

Accepted Answer

$$\sqrt[3]{41}$$

Question 8

Rationalize the denominator of the following expression: $$\frac{8}{11\sqrt{2b}/\sqrt{6}}$$

Accepted Answer

$$8\sqrt{3}/22\sqrt{b}$$

Question 9

Solve the given expression, and the answer should be written without negative exponents. (Let all the variables shown belong to $$\mathbb{Z}^+$$): $$a^{1/3}/a$$^{7/4}$

Accepted Answer

$$1/a^{5/12}$$

Question 10

Steven wins the lottery for $$500,000. 20\% of $$the total amount was deducted in taxation. He invested some of the remaining amount at $$5\%$$ and some at $$3\%. $$Find out the amount invested at each rate if the interest earned per year is $$17,000.$$

Accepted Answer

Amount invested at $$5\%$$ = $$250,000$$, Amount invested at $$3\%$$ = $$150,000$$

Question 11

The speed at which the shaft of a conveyor system rotates varies inversely as its diameter. On one end of the conveyor system, the shaft has a diameter of $$50 mm $$and it rotates at $$100$$ revolutions per minute (rpm). Calculate the speed (in rpm) at which the shaft rotates on the opposite end where the diameter is $$125 mm.$$

Accepted Answer

$$35$$ rpm

Question 12

Simplify the following expression and write the answer in standard form: $$(i^{12}$$) \cdot $$(i^{23}$$)$$

Accepted Answer

$$i$$

Question 13

Simplify the following number and express the answer in standard form: $$\sqrt{-81}$$

Accepted Answer

$$9i$$

Question 14

Perform division and express the quotient in standard form: $$119 / -i$$

Accepted Answer

$$-119i$$

Question 15

Use any method to solve the given equation: $$\sqrt{x^2$ + 8x + 15} = \sqrt{x-5} - 5\sqrt{x^2$-25}$$

Accepted Answer

$$(-1, 4)$$

Question 16

Which of the following equations represent the sides of a triangle given below? (Refer to the triangle with sides $$x$$, $$x+9$$, $$3x-3.)$$

Accepted Answer

$$(x+9)^2$$ = $$x^2$$ + $$(3x-3)^2$$

Question 17

Consider the following equations and solve for all values of $$x$$ that will satisfy them. $$z_1 = x$, z_2$ = -6/x$$ and $$z_1$$ + $$z_2 = -1$

Accepted Answer

$$(-3, 2)$$

Question 18

By using the quadratic formula, solve the following equation: $$2x^2 - x + 1 = 0$

Accepted Answer

$$x = (1 + \sqrt{-7})/4, (1 - \sqrt{-7})/4$$

College Algebra Midterm Study Guide: Key Concepts and Problem Types

Study Guide - Practice Questions

Study Guide - Flashcards