Questions from Chapters 1 to 3

1. Evaluate \(-b-\sqrt{b^2-4ac}\) if \(a=4,\) \(b=6\) and \(c=2\).

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

2. \(6(x + 4) = 5(7 - x) - 4( 2 - 3x)\)
3. \(\dfrac{x+4}{2}-\dfrac{1}{2}=\dfrac{x+2}{4}\)
4. Write an equation of the vertical line that passes through the point (−2, −3).
5. Find the distance between the points (−4, −2) and (2, 6).
6. Graph the relation \(2x - 3y = 6\).

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

7. \(x - 2 ( x - 5 ) \le 3 ( 6 + x )\)
8. \(\left|\dfrac{3x-2}{7}\right|<1\)

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

9. The time \((t)\) required to empty a tank varies inversely to the rate of pumping \((r).\) If a pump can empty a tank in 45 minutes at the rate of 600 kL/min, how much time will it take the pump to empty the same tank at the rate of 1000 kL/min?
10. Find two consecutive odd integers such that their sum is 12 less than four times the first integer.

Questions from Chapters 4 to 6

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

1. \(\left\{
   \begin{array}{l}
   2x + 5y = -18 \\
   \phantom{2}y - 6\phantom{y} = \phantom{-}2x
   \end{array}\right.\)
2. \(\left\{
   \begin{array}{l}
   8x+7y=51 \\
   5x+2y=20
   \end{array}\right.\)
3. \(\left\{
   \begin{array}{l}
   \phantom{2}x+y+6z=5 \\
   2x\phantom{+3y}-3z=4 \\
   \phantom{2x+}3y+4z=9
   \end{array}\right.\)

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

4. \(24 + \{-3x - \left[6x - 3(5 - 2x)\right]^0\} + 3x\)
5. \(2ab^3 (a - 4)(a + 4)\)
6. \(\left(\dfrac{xy^{-3}}{x^{-2}y^4}\right)^{-1}\)

For problems 7 and 8, factor each expression completely.

7. \(3x^2 +11x + 8\)
8. \(64x^3 - y^3\)
9. A 50 kg mixture of two different grades of coffee costs \(\$191.25.\) If grade A is worth \(\$3.95\) per kg and grade B is worth \(\$3.70\) per kg, how many kg of each type were used?
10. Kyra gave her brother Mark a logic question to solve: If she has 16 coins in her pocket worth \(\$2.35,\) and if the coins are only 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. \(\dfrac{15s^3}{3t^2}\div \dfrac{5t}{17s^3}\div \dfrac{34s^4}{3t^3}\)
2. \(\dfrac{2x}{x-2}-\dfrac{4x}{x-2}+\dfrac{20}{x^2-4}\)
3. \(\dfrac{\dfrac{x^2}{y^2}-9}{\dfrac{x+3y}{y^3}}\)

For questions 4–6, simplify each expression.

4. \(3\sqrt{25x}-2\sqrt{72x}-\sqrt{16x^3}\)
5. \(\dfrac{\sqrt{m^6n}}{\sqrt{3n}}\)
6. \(\left(\dfrac{a^0b^4}{c^8d^{-12}}\right)^{\frac{1}{4}}\)

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

7. \(x^2 - 4x - 5 = 0\)
8. \(\dfrac{x-3}{x}=\dfrac{x}{x-3}\)

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

9. The base of a right triangle is 6 cm longer than its height. If the area of this triangle is 20 cm², find the length of both the base and the height.
10. Find three consecutive even integers such that the product of the first two is 8 more than six times the third number.

Final Exam: Version A Answer Key