Questions from Chapters 1 to 3

1. Evaluate \(-2b-\sqrt{b^2-4ac}\) if \(a=4,\) \(b=-3\) and \(c=-1\).

For problems 2 and 3, solve for \(x.\)

2. \(6(3x - 5) = 3\left[4(1 - x) - 7\right]\)
3. \(\dfrac{x+4}{2}-\dfrac{1}{3}=\dfrac{x+2}{6}\)
4. Find the equation that has a slope of \(\dfrac{2}{3}\) and passes through the point (1, 4).
5. Find the distance between the points (−4, −2) and (4, 4).
6. Graph the relation \(3x - 2y = 6\).

For problems 7 and 8, find the solution set and graph it.

7. \(3 \le 6x + 3 < 9\)
8. \(\left|\dfrac{3x+1}{4}\right|=2\)

In problems 9 and 10, set up each problem algebraically and solve. Be sure to state what your variables represent.

9. The weight (w_m) of an object on Mars varies directly with its weight (w_e) on Earth. A person who weighs 95 lb on Earth weighs 38 lb on Mars. How much would a 240 lb person weigh on Mars?
10. Find two consecutive even integers such that their sum is 20 less than the second integer.

Questions from Chapters 4 to 6

For problems 1–3, find the solution set of each system by any convenient method.

1. \(\left\{
   \begin{array}{l}
   4x - 3y = 13 \\
   6x + 5y = -9
   \end{array}\right.\)
2. \(\left\{
   \begin{array}{l}
   3x-4y=-5 \\
   \phantom{3}x+\phantom{4}y=-1
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{l}
   x+2y\phantom{-2z}=0 \\
   \phantom{x+}\phantom{2}y-2z=0 \\
   x\phantom{+2y}-4z=0
   \end{array}\right.\)

For problems 4–6, perform the indicated operations and simplify.

4. \(28 - \{5x^0 - \left[6x - 3(5 - 2x)\right]^0\} + 5x^0\)
5. \((x^2 - 3x + 8)(x - 4)\)
6. \(\left(\dfrac{x^{3n}x^{-6}}{x^{3n}}\right)^{-1}\)

For problems 7 and 8, factor each expression completely.

7. \(25y^3 - 15y^2 + 5y\)
8. \(x^3 + 8y^3\)
9. How many litres of club soda (carbonated water) must be added to 2 litres of 35% fruit juice to turn it into a carbonated drink diluted to 8% fruit juice?
10. Kyra has 14 coins with a total value of \(\$1.85.\) If all the coins are dimes and quarters, how many of each kind of coin does she have?

Questions from Chapters 7 to 9

In problems 1–3, perform the indicated operations and simplify.

1. \(\dfrac{9s^2}{7y^3}\cdot \dfrac{15t}{13s^2}\cdot \dfrac{26s}{9t}\)
2. \(\dfrac{2a}{a^2-36}-\dfrac{5}{a^2-7a+6}\)
3. \(\dfrac{1-\dfrac{8}{x}}{\dfrac{3}{x}-\dfrac{24}{x^2}}\)

For questions 4–6, simplify each expression.

4. \(\sqrt{x^5y^7}+2xy\sqrt{16xy^3}-\sqrt{xy^3}\)
5. \(\dfrac{2+x}{1-\sqrt{7}}\)
6. \(\left(\dfrac{a^6b^3}{c^0d^{-9}}\right)^{\frac{2}{3}}\)

For questions 7 and 8, solve \(x\) by any convenient method.

7. \(x^2 - 2x - 15 = 0\)
8. \(\dfrac{2x-1}{3x}=\dfrac{x-3}{x}\)

In problems 9 and 10, find the solution set of each system by any convenient method.

9. The length of a rectangle is 5 cm longer than twice the width. If the area of the rectangle is 75 cm², find its length and width.
10. Find three consecutive odd integers such that the product of the first and the second is 25 less than 8 times the third.

Final Exam: Version B