Final Exam: Version B

Questions from Chapters 1 to 3

1. Evaluate [latex]-2b-\sqrt{b^2-4ac}[/latex] if [latex]a=4,[/latex] [latex]b=-3[/latex] and [latex]c=-1[/latex].

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

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

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

7. [latex]3 \le 6x + 3 < 9[/latex]
8. [latex]\left|\dfrac{3x+1}{4}\right|=2[/latex]

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

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

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

For problems 7 and 8, factor each expression completely.

7. [latex]25y^3 - 15y^2 + 5y[/latex]
8. [latex]x^3 + 8y^3[/latex]
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 [latex]\$1.85.[/latex] 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. [latex]\dfrac{9s^2}{7y^3}\cdot \dfrac{15t}{13s^2}\cdot \dfrac{26s}{9t}[/latex]
2. [latex]\dfrac{2a}{a^2-36}-\dfrac{5}{a^2-7a+6}[/latex]
3. [latex]\dfrac{1-\dfrac{8}{x}}{\dfrac{3}{x}-\dfrac{24}{x^2}}[/latex]

For questions 4–6, simplify each expression.

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

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

7. [latex]x^2 - 2x - 15 = 0[/latex]
8. [latex]\dfrac{2x-1}{3x}=\dfrac{x-3}{x}[/latex]

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