Record your answers then check the answer key.

1

Find the solution of the equation \(2(1-x)=x+8\\\)

  1. \(-3\\\)
  2. \(6\\\)
  3. \(-2\\\)
  4. \(4\\\)

2

Find all real solutions of the equation \(x^2+3x-10=0\\\).

  1. \(2\\\)
  2. \(-5,2\\\)
  3. \(5,-2\\\)
  4. \(5\\\)

3

Simplify the expression: \(x-3\cdot x+3\\\)

  1. \(-2x+3\\\)
  2. \(x^2-9\\\)
  3. \(x^2-6x+9\\\)
  4. \(x^2-6x-9\\\)

4

Find all complex solutions of the equation \(x^2-2x+5=0\\\).

  1. \(2\pm i\\\)
  2. \(0,2\\\)
  3. \(\dfrac{x^2+5}{2}\\\)
  4. \(1\pm 2i\\\)

5

Simplify the expression \( \dfrac{(x^2)^3}{x^2x^3} \\\)

  1. \(1\\\)
  2. \(x\\\)
  3. \(x^2\\\)
  4. \(x^{-1}\\\)

6

Solve the literal equation for \(P\): \(A-P=\dfrac{A+P}{B}\\\)

  1. \(P=\dfrac{A(B-1)}{B+1}\\\)
  2. \( P=-A\\\)
  3. \(P=1\\\)
  4. \(P=-\dfrac{P}{B}\\\)

7

Solve the inequality \(2-x>10\\\)

  1. \(x<-8\\\)
  2. \(x<-12\\\)
  3. \(x>-5\\\)
  4. \(x>-8\\\)

8

Perform the operations and simplify:\( \dfrac{1}{\frac{1}{x}+\frac{1}{y}}\\\)

  1. \(x+y\\\)
  2. \(\dfrac{x+y}{xy}\\ \)
  3. \( \dfrac{xy}{x+y}\\ \)
  4. \( \dfrac{1}{x}+\dfrac{1}{y}\\\)

9

Simplify the expression: \( \dfrac{12m^4n}{15mn^2}\\\)

  1. \( \dfrac{12m^3}{15n}\\\)
  2. \(\dfrac{4m^3n}{5n^2}\\\)
  3. \(\dfrac{4m^3}{5}\\\)
  4. \(\dfrac{4m^3}{5n}\\\)

10

Simplify the expression by rationalizing the denominator: \(\dfrac{1+\sqrt{15}}{4-\sqrt{15}}\\\)

  1. \(1+\sqrt{15}\\\)
  2. \(19+5\sqrt{15}\\\)
  3. \(\frac{2}{3}\\\)
  4. \(\frac{1}{4}\\\)

11

What is the slope of the line through the points \((3,-1)\) and \((5,7)\\\)?

  1. \(3\\\)
  2. \(\frac{1}{4}\\\)
  3. \(4\\\)
  4. \(1\\\)

12

How would the following set be written in interval notation? \( \left\{x\,|\,-2 < x\le1\right\}\\\)

  1. \( (-2,1)\\\)
  2. \( (-2,1]\\\)
  3. \( (-\infty,-2)\cup[1,\infty)\\\)
  4. \( [-1,2)\\\)

13

Find the product of the complex numbers \((2-3i)(1+2i)\\\)

  1. \( 8+i\\\)
  2. \( 2-6i\\\)
  3. \( -4+i\\\)
  4. \( 8\\\)

14

Find a value of \(c\) so that the quadratic expression will be a perfect square: \(x^2-6x+c\\\)

  1. \( 36\\\)
  2. \( -9\\\)
  3. \( 9\\\)
  4. \( -36\\\)

15

Add the following fractions: \(\dfrac{2}{x}+\dfrac{x-1}{x+1}\\\)

  1. \( \dfrac{x^2+x+2}{x^2+x}\\\)
  2. \( \dfrac{x+1}{2x+1}\\\)
  3. \( 2\\\)
  4. \( \dfrac{2-x}{x}\\\)

16

Simplify the following expression: \(\dfrac{x^3-x^2-2x}{x^3+4x^2+3x}\\\)

  1. \( -\dfrac{1}{4}\\\)
  2. \( \dfrac{x-2}{x+3}\\\)
  3. \( -\dfrac{2}{3}\\\)
  4. \( -\dfrac{3}{7}\\\)

17

For what value of \(x\) is the following expression undefined? \(\dfrac{x-3}{2-x}\\\)

  1. \( 3\\\)
  2. \( 3\) and \(2\\\)
  3. \( 2\\\)
  4. It is defined for all values of \(x\\\).

18

Find the solution of the equation: \(| 1-x | =5\\\)

  1. \( 6\\\)
  2. \( 4\\\)
  3. \( -4\\\)
  4. \( 6\) and \(-4\\\)

9

\(\sqrt{(-4)^2}=\\\)

  1. \( -4\\\)
  2. \( -2\\\)
  3. \( 2\\\)
  4. \( 4\\\)

20

Perform the indicated operations and simplify the result: \(\dfrac{2a^2b}{b^2}\div\dfrac{6a^3}{b}\\\)

  1. \( \dfrac{12a^5}{b^2}\\\)
  2. \( \dfrac{1}{3a}\\\)
  3. \( \dfrac{1}{3a^2}\\\)
  4. \( \dfrac{1}{3ab}\\\)