Midterm 1: Version A

1. Evaluate: [latex]-b - \sqrt{b^2 - 4ac}[/latex] if [latex]a=4,[/latex] [latex]b=-3,[/latex] and [latex]c=-1.[/latex]
2. Solve for [latex]x[/latex] in the equation [latex]2(x - 5) - 85 = 3 - 9(x + 6).[/latex]
3. Isolate the variable [latex]b[/latex] in the equation [latex]A = \dfrac{h}{B-b}[/latex].
4. Solve for [latex]x[/latex] in the equation [latex]\dfrac{x+1}{4} - \dfrac{5}{8} = \dfrac{x-1}{8}[/latex].
5. Write an equation of the vertical line that passes through the point [latex](-2, 5).[/latex]
6. Find the equation that has a slope of [latex]\dfrac{2}{5}[/latex] and passes through the point [latex](-1, -2).[/latex]
7. Find the equation of the line passing through the points [latex](-2, 0)[/latex] and [latex](6, 4)[/latex].
8. Graph the relation [latex]y = \dfrac{2}{3}x - 1[/latex].

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

9. [latex]6x - 5(1 + 6x)[/latex] > [latex]67[/latex]
10. [latex]-10 \le 4x - 2 \le 14[/latex]
11. [latex]\left| \dfrac{3x+2}{5} \right| = 2[/latex]
12. Graph the relation [latex]5x + 2y < 15.[/latex]
13. Find two numbers such that 5 times the larger number plus 3 times the smaller is 47, and 4 times the larger minus twice the smaller is 20.
14. Karl is going to cut a 36 cm cable into 2 pieces. If the first piece is to be 5 times as long as the second piece, find the length of each piece.
15. [latex]y[/latex] varies jointly with [latex]m[/latex] and [latex]n[/latex] and inversely with the square of [latex]d.[/latex] If [latex]y = 3[/latex] when [latex]m = 2,[/latex] [latex]n = 8,[/latex] and [latex]d = 4,[/latex] find the constant [latex]k,[/latex] then use [latex]k[/latex] to find [latex]y[/latex] when [latex]m = 15,[/latex] [latex]n = 10,[/latex] and [latex]d = 5.[/latex]

Midterm 1: Version A Answer Key