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.
- \(\left\{
\begin{array}{llrllll}
x&-&2y&+&4&=&3 \\
x&+&y&-&5&=&0
\end{array}\right.\)
For problems 2–4, find the solution set of each system by any convenient method.
- \(\left\{
\begin{array}{rrrrr}
2x&-&y&=& 0 \\
3x&+&4y&=&-22
\end{array}\right.\) - \(\left\{
\begin{array}{rrrrr}
2x&-&5y&=&15 \\
3x&+&2y&=&13
\end{array}\right.\) - \(\left\{
\begin{array}{rrrrrrr}
5x&+&y&+&6z&=&-2 \\
&&2y&-&3z&=&3 \\
5x&&&+&6z&=&-4
\end{array}\right.\)
Chapter 5: Polynomials (Exam Type Questions)
Simplify.
- \((4a^2-9a+2)-(a^2-4a-5)+(9-a+3a^2)\)
- \(2x^2(4x^2-6y^2)-3x(5xy^2+x^3)\)
- \(6 - 2[3x - 4(5x - 2) - (1 - 7x)^0]\)
- \((5a^{-5}b^3)^2\)
- \(8a^2(a+5)^2\)
- \(4ab^2(a-2)(a+2)\)
- \((x^2-4x+7)(x-3)\)
- \((2x^2+x-3)^2\)
- \((x^2+5x-2)(2x^2-x+3)\)
- \((x+4)^3\)
- \(\dfrac{(r^{-4}s^9)}{(r^3s^{-9})}\)
Divide using long division.
- \((2x^3-7x^2+15)\div (x-2)\)
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.
- \(5xy+6xz-15y-18z\)
- \(x^2+x-12\)
- \(x^3+x^2-4x-4\)
- \(x^3-27y^3\)
- \(x^4-35x^2-36\)
Chapter 4–6 Word Problems (Exam Type Questions)
- A 70 kg mixture of two different types of nuts costs \(\$430.\) If type A costs \(\$4\) per kg and type B costs \(\$7\) 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.
