Advanced Math Placement Practice

Only use this practice if you are seeking a higher placement than Level 1.

How to Complete This Work

• Put away your notes and other practice materials.
• Try these problems in one sitting without a calculator.
• Check your answers!
• If you would like to print these questions you can do so by going to File > Print in your current browser.
• If you have questions about this practice work please email Megan at mdibonaventura@ric.edu.

Questions

1. Calculate $31-(-11)-(6-9)$
2. Calculate $11-3(21-16)$
3. Calculate $|-24+17|$
4. Calculate and express your answer as a fraction in lowest terms: ${\left(\frac{3}{5}\right)}^2$
5. Add the fractions and express your answer as a single fraction in lowest terms: $\frac{2}{3}+\frac{5}{11}$
6. Divide the fractions and express your answer as a fraction in lowest terms: $\frac{13}{5}÷\frac{10}{3}$
7. Calculate and express your answer as a fraction in lowest terms: $(\frac{1}{2}·\frac{-4}{5})+(\frac{-1}{3}·\frac{3}{4})$
8. Simplify the expression to one of the form $ax+b$: $4(3x+1)-(2x-6)$
   (Note: You need numerical values for $a$ and $b$)
9. Solve for $x$ and write your answer as a fraction: $5x+2=-3x+4$
10. Simplify the expression to one of the form $a{x}^2+bx+c$: $(2x^2+x-5)-(5x^2-6x-2)$
    (Note: You need numerical values for $a$, $b$, and $c$)
11. Calculate the slope of the line going through the points $(-5,6)$ and $(2,3)$. Write your answer as a fraction.
12. Solve for $x$ and write your answer as a fraction: $2(x-3)=1-4(2x+5)$
13. Evaluate the expression $x^2-2x+6$ for $x=-1$.
14. Solve for $x$ and write your answers in either order: $x^2-11x=-28$
15. Simplify: $\frac{20x^3{y}^4}{2x^6{y}^3}$. Enter the values for $a$, $b$, and $c$ for your answer to be written in the form $a{x}^b{y}^c$.
16. Find the two roots of the quadratic equation and write your answers in either order: $x^2-8x+12=0$
17. Solve for $x$ and write your answer as a fraction: $\frac{2}{x}-\frac{1}{4}=\frac{1}{7}$
18. Solve for $x$ and write your answers in either order: $|4x+1|+3=6$
19. If $f\left(x\right)=-3x+7$, calculate and simplify $\frac{f(4+h)-f\left(4\right)}{h}$. Enter the values of $a$ and $b$ where your answer is in the form $ah+b$.
20. The graph of $y=\frac{1}{x+2}+9$ is the graph of $y=\frac{1}{x}$ with what transformations?
    1. shifted left 9 units and down 2 units
    2. shifted left 2 units and up 9 units
    3. shifted left 2 units and down 9 units
    4. shifted right 2 units and up 9 units
    5. shifted left 9 units and up 2 units
21. A right triangle has sides A, B, and C, where C is the hypotenuse. Side A has length 18, side B has length 24, and side C has length 30. If $\theta$ is the angle between sides A and C, what is the value of $\sin \left(\theta \right)$? Enter your answer as a simplified fraction.
22. Which of the following is the inverse of $f\left(x\right)={(x-10)}^3$?
    1. $f^{-1}\left(x\right)={(x-10)}^{\frac{1}{3}}$
    2. $f^{-1}\left(x\right)={(x-10)}^{\frac{1}{3}}+10$
    3. $f^{-1}\left(x\right)=x^{\frac{1}{3}}-10$
    4. $f^{-1}\left(x\right)=x^{\frac{1}{3}}+10$
    5. $f^{-1}\left(x\right)=x^3+10$
23. Solve for $x$ and enter the values for $a$, $b$, and $c$ where your answer is in the form $x={log}_{b}a+c$: $7^{x+6}=2$
24. Evaluate: $\ln \left(e^{43}\right)$.
25. Find the equation of the curve formed by vertically stretching the graph of $y=\sin \left(x\right)$ by 2 and then shifting it right by 7 units. Enter the values of $a$, $b$, $c$, and $d$ where your answer is of the form $y=a·\sin (bx+c)$.
26. Use the method of completing the square to write $x^2+6x-2$ in the form ${(x+a)}^2+b$. Enter the values for $a$ and $b$.

Answers

1. 45 (Order of operations)
2. $\frac{-4}{1}$ (Order of operations)
3. 7 (Adding integers and absolute value)
4. $\frac{9}{25}$ (Rules of exponents)
5. $\frac{37}{33}$ (Adding fractions)
6. $\frac{39}{50}$ (Dividing fractions)
7. $\frac{-13}{20}$ (Order of operations with fractions)
8. $a=10$, $b=10$ (Simplify expressions, distributive property)
9. $x=\frac{1}{4}$ (Solve a linear equation in one variable)
10. $a=-3$, $b=7$, $c=-3$ (Simplifying expressions, subtracting polynomials)
11. $m=\frac{-3}{7}$ (Slope of a line)
12. $x=\frac{-13}{10}$ (Solve a linear equation in one variable)
13. 9 (Substitution)
14. $x=4$ and $x=7$ (Solving a quadratic equation)
15. $a=10$, $b=-3$, $c=1$ (Rules of exponents)
16. $x=2$ and $x=6$ (Solving a quadratic equation)
17. $x=\frac{56}{11}$ (Solving a linear equation in one variable where $x\ne 0$)
18. $x=\frac{1}{2}$ and $x=\frac{-1}{1}$ (Solving absolute value equations)
19. $a=0$, $b=-3$ (Difference quotient, evaluating a function)
20. b (Function transformations)
21. $\frac{4}{5}$ (Basic trigonometry)
22. d (Inverse functions)
23. $a=2$, $b=7$, $c=-6$ (Converting between logarithmic and exponential form)
24. 43 (Natural logarithm and $e$ are inverse functions, rules of natural log)
25. $a=2$, $b=1$, $c=-7$, $d=0$ (Transformations of trig functions)
26. $a=3$, $b=-11$ (Completing the square)