Midterm 2 Preparation
The second midterm will be composed of fifteen questions covering chapters 5 to 7.
Twelve questions will be algebra questions, and three questions will be word problems.
- Questions 1–4 will be drawn from Chapter 5: Systems of Equations
- 5.1 Graphed Solutions
- 5.2 Substitution Solutions
- 5.3 Addition and Subtraction Solutions
- 5.4 Solving for Three Variables
- Questions 5–6 will be drawn from Chapter 6: Polynomials
- 6.1 Working with Exponents
- 6.2 Negative Exponents
- 6.3 Scientific Notation
- 6.4 Basic Operations Using Polynomials
- 6.5 Multiplication of Polynomials
- 6.6 Special Products
- 6.7 Dividing Polynomials
- Questions 9–12 will be drawn from Chapter 7: Factoring
- 7.1 Greatest Common Factor
- 7.2 Factoring by Grouping
- 7.3 Factoring Trinomials where a = 1
- 7.4 Factoring Trinomials where a ≠ 1
- 7.5 Factoring Special Products
- 7.6 Factoring Quadratics of Increasing Difficulty
- 7.7 Choosing the Correct Factoring Strategy
- 7.8 Solving Quadratic Equations by Factoring
- Questions 13–15 will be drawn from:
- 5.5 Monetary Word Problems
- 6.8 Mixture and Solution Word Problems
- 7.9 Age Word Problems
Students will be allowed to use MATQ 1099 Data Booklets & Glossaries for both Midterms and the Final Exam.
Midterm Two Review
Chapter 4: Systems of Equations (Exam Type Questions)
Find the solution set of the system of equations below graphically.
- [latex]\left\{ \begin{array}{llrllll} x&-&2y&+&4&=&3 \\ x&+&y&-&5&=&0 \end{array}\right.[/latex]
For problems 2–4, find the solution set of each system by any convenient method.
- [latex]\left\{ \begin{array}{rrrrr} 2x&-&y&=& 0 \\ 3x&+&4y&=&-22 \end{array}\right.[/latex]
- [latex]\left\{ \begin{array}{rrrrr} 2x&-&5y&=&15 \\ 3x&+&2y&=&13 \end{array}\right.[/latex]
- [latex]\left\{ \begin{array}{rrrrrrr} 5x&+&y&+&6z&=&-2 \\ &&2y&-&3z&=&3 \\ 5x&&&+&6z&=&-4 \end{array}\right.[/latex]
Chapter 5: Polynomials (Exam Type Questions)
Simplify.
- [latex](4a^2-9a+2)-(a^2-4a-5)+(9-a+3a^2)[/latex]
- [latex]2x^2(4x^2-6y^2)-3x(5xy^2+x^3)[/latex]
- [latex]6 - 2[3x - 4(5x - 2) - (1 - 7x)^0][/latex]
- [latex](5a^{-5}b^3)^2[/latex]
- [latex]8a^2(a+5)^2[/latex]
- [latex]4ab^2(a-2)(a+2)[/latex]
- [latex](x^2-4x+7)(x-3)[/latex]
- [latex](2x^2+x-3)^2[/latex]
- [latex](x^2+5x-2)(2x^2-x+3)[/latex]
- [latex](x+4)^3[/latex]
- [latex]\dfrac{(r^{-4}s^9)}{(r^3s^{-9})}[/latex]
Divide using long division.
- [latex](2x^3-7x^2+15)\div (x-2)[/latex]
Chapter 6: Factoring (Exam Type Questions)
Questions 18–19 are for review only and will not show up on exams.
- Find the prime factorization of 88.
- Find the LCM of 84 and 96.
Questions similar to 20–27 will show up on exams.
Factor each expression completely.
- [latex]5xy+6xz-15y-18z[/latex]
- [latex]x^2+x-12[/latex]
- [latex]x^3+x^2-4x-4[/latex]
- [latex]x^3-27y^3[/latex]
- [latex]x^4-35x^2-36[/latex]
Chapter 4–6 Word Problems (Exam Type Questions)
- A 70 kg mixture of two different types of nuts costs [latex]\$430.[/latex] If type A costs [latex]\$4[/latex] per kg and type B costs [latex]\$7[/latex] per kg, how many kg of each type were used?
- A wedding reception bartender is faced with a problem: how many litres of a 5% rum drink must be mixed with 2 litres of a 21% flavoured rum to make a rum punch of 11% strength?
- The sum of the ages of a boy and a girl is 16 years. Four years ago, the girl was three times the age of the boy. Find the present age of each child.