Midterm 2 Preparation

# Midterm 2: Version D

Find the solution set of the system graphically.

1. $\left\{ \begin{array}{rrrrrrr} x&-&2y&+&6&=&0 \\ x&+&y&-&6&=&0 \end{array}\right.$

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

1. $\left\{ \begin{array}{rrrrr} 3x&-&2y&=&0 \\ 2x&+&5y&=&0 \end{array}\right.$
2. $\left\{ \begin{array}{rrrrr} 2x&-&3y&=&8 \\ 3y&-&2x&=&4 \end{array}\right.$
3. $\left\{ \begin{array}{rrrrrrr} 2x&+&y&-&3z&=&-7 \\ &&-2y&+&3z&=&9 \\ 3x&&&+&z&=&6 \end{array}\right.$

Reduce the following expressions in questions 5–7.

1. $36 - \{-2x - \left[6x - 3(5 - 2x)\right]\}^0 + 3x^2$
2. $3a^2(a - 2)^2$
3. $(x^2 + 2x - 4)^2$

Divide using long division.

1. $(x^4 + 4x^3 + 4x^2 + 10x + 20) \div (x + 2)$

For problems 9–12, factor each expression completely.

1. $x^2 + 3x - 18$
2. $3x^2 + 25xy + 8y^2$
3. $125x^3 - y^3$
4. $81y^4 - 16x^4$

Solve the following word problems.

1. The sum of the ages of a boy and a girl is 18 years. Four years ago, the girl was four times the age of the boy. Find the present age of each child.
2. A purse contains $\3.50$ made up of dimes and quarters. If there are 20 coins in all, how many dimes and how many quarters were there?
3. A 60 kg blend of two different grades of tea is sold for $\218.50.$ If grade A sells for $\3.80$ per kg and grade B sells for $\3.55$ per kg, how many kg of each grade were used?

Midterm 2: Version D Answer Key