Midterm 2 Preparation

# Midterm 2: Version A

Find the solution set of the system graphically.

1. $\left\{ \begin{array}{rrrrr} x&+&2y&=&-5 \\ x&-&y&=&-2 \end{array}\right.$

For problems 2–4, find the solution set of each system by any convenient method.

1. $\left\{ \begin{array}{rrrrr} 4x&-&3y&=&13 \\ 5x&-&2y&=&4 \end{array}\right.$
2. $\left\{ \begin{array}{rrrrr} x&-&2y&=&-5 \\ 2x&+&y&=&5 \end{array}\right.$
3. $\left\{ \begin{array}{rrrrrrr} x&+&y&+&2z&=&0 \\ 2x&&&+&z&=&1 \\ &&3y&+&4z&=&0 \end{array}\right.$

Reduce the following expressions in questions 5–7.

1. $28 - \{5x - \left[6x - 3(5 - 2x)\right]^0 \} + 5x^2$
2. $4a^2 (a - 3)^2$
3. $(x^2 + 2x + 3)^2$

Divide using long division.

1. $(2x^3 - 7x^2 + 15) \div (x - 2)$

For problems 9–12, factor each expression completely.

1. $2ab + 3ac - 4b - 6c$
2. $a^2 - 2ab - 15b^2$
3. $x^3 + x^2 - 9x - 9$
4. $x^3 - 64y^3$

Solve the following word problems.

1. The sum of a brother’s and sister’s ages is 35. Ten years ago, the brother was twice his sister’s age. How old are they now?
2. Kyra gave her brother Mark a logic question to solve: If she has 20 coins in her pocket worth $\2.75$, and if the coins are only dimes and quarters, how many of each kind of coin does she have?
3. A 50 kg blend of two different grades of tea is sold for $\191.25.$ If grade A sells for $\3.95$ per kg and grade B sells for $\3.70$ per kg, how many kg of each grade were used?

Midterm 2: Version A Answer Key