\documentclass[a4paper,12pt]{book}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{bm}
\usepackage{graphicx}
\usepackage{wrapfig}
\usepackage{fancybox}
\pagestyle{empty}
\begin{document}
Math Placement Test Practice Problems
The following problems cover material that is used on the math placement test to place students into Math 1111 College Algebra, Math 1113 Precalculus, and Math 2211 Calculus I. The problems grouped into sections by the level of the courses they are drawn from, with the lower level problems first and the higher level problems last.
Answers are provided for all problems and detailed solutions are provided for half the problems. However it is strongly recommended that you fully work a problem before looking at the answer.
First Part
1. Simplify $(2a^{3}b)^{-3}.$
2. Simplify $(-4x^{2}y^{-3})^{-2}.$
3. Simplify $\sqrt{\frac{1}{64}}.$
4. Simplify $\sqrt{3}-27.$
5. Complex numbers: Find $x$ and $y$ such that the following is correct:
$$
3x+5yi=15+5i
$$
6. Find $x$ and $y$ such that the following is correct:
$$
10x-4yi=20+\frac{1}{2}i.
$$
7. Simplify $\sqrt{27-18}.$
8. Simplify $\sqrt{\frac{-1}{25}}.$
9. Simplify $i^{15}.$
10. Simplify $i^{47}.$
11. Solve for $x$ in $3x^{2}+8x+4=0.$
12. Solve for $x$ in $x^{2}+4=0.$
13. Solve for $x$ in $x^{2}+7x+3=0.$
14. Solve for $x$ in $2x^{2}+10x-1=0.$
15. Solve for $x$ and graph the solution on a number line for $2-4x>0.$
1
16. Solve for $x$ and graph the solution on a number line for $x^{2}-2\geq 1.$
17. Solve the following equations for $x$ and $y$:
$$
3x+2y=5
$$
$$
7x-y=1\
$$
18. Solve the following equations for $w$ and $z$:
$$
w+2z=10
$$
$$
4w+z=5
$$
19. Graph the function $f(x)=x^{2}+2$ and identify $x$ and $y$ intercepts.
20. Graph the function $f(x)=3x-9$ and identify $x$ and $y$ intercepts.
21. Solve for $x$ in $0.3x+0.2=0.5.$
22. Solve for $x$ in $0.5x+0.4=1.2.$
23. Solve for $x$ in $\displaystyle \frac{x+3}{x-9}=0.$
24. Solve for $x$ in $\displaystyle \frac{x-2}{2x+1}=3.$
25. Let $f(x)=10x-5$ and find a value $x^{*}$ such that $f(x^{*})=0.$
26. Let $ f(x)=\alpha x+2\beta$ where $\alpha$ and $\beta$ are constants. Find $x^{*}$ such that $f(x^{*})=0.$
27. Find an equation of a line passing through the points
$$
(x_{0},\ y_{0})=(1,4)\ ,\ (x_{1},\ y_{1})=(2,6)\ .
$$
28. Is $y=\sin x$ one-to-one?
29. Is $y=x+2$ onto.
30. For a right triangle $ABC$ with $a=3$ and $c=5$, where $c$ is the hypotenuse, find $b.$
31. For a right triangle $ABC$ with $a=13$ and $b=14$ find the hypotenuse $c.$
32. Write in interval notation $\{x\in \mathbb{R}:10