Midterm 1: Version D

1. Evaluate: [latex]3b - \sqrt{b^2-4ac}[/latex] if [latex]a=4, b=4,[/latex] and [latex]c=1.[/latex]
2. Solve for [latex]x[/latex] in the equation [latex]2(x - 4)+8 = -6+3(x+3).[/latex]
3. Isolate the variable [latex]r_2[/latex] in the equation [latex]\dfrac{1}{R}=\dfrac{1}{r_1}+\dfrac{1}{r_2}.[/latex]
4. Solve for [latex]x[/latex] in the equation [latex]\dfrac{x}{15} - \dfrac{x-3}{3} = \dfrac{1}{3}.[/latex]
5. Write the equation of the horizontal line that passes through the point [latex](-2, 5).[/latex]
6. Find the equation that has a slope of [latex]\dfrac{2}{3}[/latex] and passes through the point [latex](-2, 4).[/latex]
7. Find the equation of the line passing through the points [latex](12, -7)[/latex] and [latex](8, -9).[/latex]
8. Graph the relation [latex]y=\dfrac{2}{3}x-2.[/latex]

For questions 9 to 11, find each solution set and graph it.

9. [latex]-27 \le 6x -9 \le 3[/latex]
10. [latex]\left| \dfrac{2x+2}{6}\right| = 2[/latex]
11. [latex]| 2x-1 |[/latex] > [latex]6[/latex]
12. Graph the relation [latex]y = |2x| - 1.[/latex]
13. For a given triangle, the first and second angles are equal, but the third angle is 10° less than twice the first angle. What are the measures of the three angles?
14. Find two consecutive even integers such that their sum is 20 less than the first integer.
15. [latex]y[/latex] varies jointly with [latex]m[/latex] and the square of [latex]n[/latex] and inversely with [latex]d.[/latex] If [latex]y = 16[/latex] when [latex]m = 3, n = 4,[/latex] and [latex]d = 6,[/latex] find the constant [latex]k,[/latex] then use [latex]k[/latex] to find [latex]y[/latex] when [latex]m = -2, n = 4,[/latex] and [latex]d = 8.[/latex]

Midterm 1: Version D Answer Key