Questions from Chapters 1 to 3

1. Evaluate [latex]-b-\sqrt{b^2-4ac}[/latex] if [latex]a=4,[/latex] [latex]b=6[/latex] and [latex]c=2[/latex].

For problems 2 and 3, solve for [latex]x[/latex].

2. [latex]6(x + 4) = 5(7 - x) - 4( 2 - 3x)[/latex]
3. [latex]\dfrac{x+4}{2}-\dfrac{1}{2}=\dfrac{x+2}{4}[/latex]
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 [latex]2x - 3y = 6[/latex].

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

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

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

9. The time [latex](t)[/latex] required to empty a tank varies inversely to the rate of pumping [latex](r).[/latex] 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. [latex]\left\{ \begin{array}{l} 2x + 5y = -18 \\ \phantom{2}y - 6\phantom{y} = \phantom{-}2x \end{array}\right.[/latex]
2. [latex]\left\{ \begin{array}{l} 8x+7y=51 \\ 5x+2y=20 \end{array}\right.[/latex]
3. [latex]\left\{ \begin{array}{l} \phantom{2}x+y+6z=5 \\ 2x\phantom{+3y}-3z=4 \\ \phantom{2x+}3y+4z=9 \end{array}\right.[/latex]

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

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

For problems 7 and 8, factor each expression completely.

7. [latex]3x^2 +11x + 8[/latex]
8. [latex]64x^3 - y^3[/latex]
9. A 50 kg mixture of two different grades of coffee costs [latex]\$191.25.[/latex] If grade A is worth [latex]\$3.95[/latex] per kg and grade B is worth [latex]\$3.70[/latex] 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 [latex]\$2.35,[/latex] 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. [latex]\dfrac{15s^3}{3t^2}\div \dfrac{5t}{17s^3}\div \dfrac{34s^4}{3t^3}[/latex]
2. [latex]\dfrac{2x}{x-2}-\dfrac{4x}{x-2}+\dfrac{20}{x^2-4}[/latex]
3. [latex]\dfrac{\dfrac{x^2}{y^2}-9}{\dfrac{x+3y}{y^3}}[/latex]

For questions 4–6, simplify each expression.

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

For questions 7 and 8, solve [latex]x[/latex] by any convenient method.

7. [latex]x^2 - 4x - 5 = 0[/latex]
8. [latex]\dfrac{x-3}{x}=\dfrac{x}{x-3}[/latex]

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