This chapter contains several sections that will help prepare for the midterm exam:

Midterm Three Composition

The third midterm will be composed of fifteen questions covering chapters 7 to 9. Twelve questions will be algebra questions, and three questions will be word problems.

• Questions 1–4 will be drawn from Chapter 8: Rational Expressions
  • 8.1 Reducing Rational Expressions
  • 8.2 Multiplication and Division of Rational Expressions
  • 8.3 Least Common Denominators
  • 8.4 Addition and Subtraction of Rational Expressions
  • 8.5 Reducing Complex Fractions
  • 8.6 Solving Complex Fractions
  • 8.7 Solving Rational Equations
• Questions 5–8 will be drawn from Chapter 9: Radicals
  • 9.1 Reducing Square Roots
  • 9.2 Reducing Higher Power Roots
  • 9.3 Adding and Subtracting Radicals
  • 9.4 Multiplication and Division of Radicals
  • 9.5 Rationalizing Denominators
  • 9.6 Radicals and Rational Exponents
  • 9.8 Radicals of Mixed Index
  • 9.9 Complex Numbers (Optional)
• Questions 9–12 will be drawn from Chapter 10: Quadratics
  • 10.1 Solving Radical Equations
  • 10.2 Solving Exponential Equations
  • 10.3 Completing the Square
  • 10.4 The Quadratic Equation
  • 10.5 Solving Quadratic Equations Using Substitution
  •  10.6 Graphing Quadratic Equations—Vertex and Intercept Method
  • 10.7 Quadratic Word Problems: Age and Numbers
  • 10.8 Construct a Quadratic Equation from its Roots
• Questions 13–15 will be three word problems drawn from:
  • 8.8 Rate Word Problems: Speed, Distance and Time
  • 9.10 Rate Word Problems: Work and Time
  • 10.7 Quadratic Word Problems: Age and Numbers

Students will be allowed to use MATQ 1099 Data Booklets & Glossaries for both Midterms and the Final Exam.

Midterm Three Review

Chapter 7: Rational Expressions (Exam Type Questions)

In the problems below, perform the indicated operations and simplify.

1. \(\dfrac{6a-6b}{a^3+b^3}\div \dfrac{a^2-b^2}{a^2-ab+b^2}\)
2. \(\dfrac{x}{x^2-25} - \dfrac{2}{x^2-6x+5}\)
3. \(\dfrac{1-\dfrac{6}{x}}{\dfrac{4}{x}-\dfrac{24}{x^2}}\)

Solve for \(x\).

4. \(\dfrac{4}{x+4}-\dfrac{5}{x-2}=5\)

Chapter 8: Radicals (Exam Type Questions)

Questions 5–6 are for review only and will not show up on exams.

5. \(\sqrt[3]{-64}=-4 \text{ (true or false)}\)
6. \(\sqrt[6]{-64}=-2\text{ (true or false)}\)

Questions similar to 7–13 will show up on exams.

For questions 7–10, simplify each expression.

7. \(4\sqrt{36}+3\sqrt{72}+\sqrt{16}\)
8. \(\dfrac{\sqrt{300a^5b^2}}{3ab^2}\)
9. \(\dfrac{12}{3-\sqrt{6}}\)
10. \(\left(\dfrac{a^0b^3}{c^6d^{-12}}\right)^{\frac{1}{3}}\)

For questions 11–13, solve for \(x\).

11. \(\sqrt{5x-6}=x\)
12. \(\sqrt{2x+9}+3=x\)
13. \(\sqrt{x-3}=\sqrt{2x-5}\)

Chapter 9: Quadratics (Exam Type Questions)

Use the quadratic discriminant to determine the nature of the roots of each equation.

14. \(\phantom{1}\)
    1. \(2x^2 + 4x + 3 = 0\)
    2. \(3x^2-2x-8=0\)

For the questions below, find the solution set by any convenient method.

15. \(\phantom{1}\)
    1. \(3x^2 = 27\)
    2. \(2x^2=16x\)
16. \(\phantom{1}\)
    1. \(x^2-x-12=0\)
    2. \(x^2+9x=-8\)
17. \(\dfrac{x-3}{2}+\dfrac{6}{x+3}=1\)
18. \(\dfrac{x-2}{x}=\dfrac{x}{x+4}\)

Chapter 7–9 Word Problems (Exam Type Questions)

19. The length of a rectangle is 3 cm longer than twice the width. If the area of the rectangle is 65 cm², find its length and width.
20. Find three consecutive even integers such that the product of the first and the second is 68 more than the third integer.
21. A boat cruises upriver for 8 hours and returns to its starting point in 6 hours. If the speed of the river is 4 km/h, find the speed of this boat in still water.
22. The base of a right triangle is 8 m longer than its height. If the area of the triangle is 330 m², what are its base and height measurements?

Midterm 3: Prep Questions Answer Key