Midterm 2 Preparation

# Midterm 2: Version E

Find the solution set of the system graphically.

1. $\left\{ \begin{array}{rrrrr} x&-&y&=&-3 \\ x&+&2y&=&3 \end{array}\right.$

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

1. $\left\{ \begin{array}{rrrrr} 2x&-&5y&=&-2 \\ 3x&-&4y&=&4 \end{array}\right.$
2. $\left\{ \begin{array}{rrrrr} 4x&+&3y&=&-29 \\ 3x&+&2y&=&-21 \end{array}\right.$
3. $\left\{ \begin{array}{rrrrrrr} x&+&y&-&3z&=&0 \\ &&2y&-&2z&=&-12 \\ 2x&-&3y&&&=&16 \end{array}\right.$

Reduce the following expressions in questions 5–7.

1. $5 - 4 \left[ 2x - 2 (6x - 5)^0 - ( 7 - 2x )\right]$
2. $3ab^4(a - 5)(a + 5)$
3. $(x^2 + 3x - 6)^2$

Divide using long division.

1. $(3x^3 + 18 + 7x^2) \div (x + 3)$

For problems 9–12, factor each expression completely.

1. $x^2 + 4x - 21$
2. $4x^3 + 4x^2 - 9x - 9$
3. $8x^3 - 27y^3$
4. $x^4 - 624x^2 - 625$

Solve the following word problems.

1. The sum of the ages of a boy and a girl is 20 years. Four years ago, the girl was two times the age of the boy. Find the present age of each child.
2. How many ml of a 16% sulfuric acid solution must be added to 20 ml of a 6% solution to create a 12% solution?
3. A 60 kg blend of cereals and raisins is sold for $\213.$ If the cereal sells for $\3.40$ per kg and the raisins sells for $\3.90$ per kg, how many kg of each grade were used?

Midterm 2: Version E Answer Key 