Math Placement Practice – Stage 2: Practice

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Math Placement Practice – Stage 2: Practice

How to Complete this Work

Practice topics that are necessary for a Level 1 math placement.
Look up how to do things you have not seen in a while or have forgotten.
Practice writing out and solving the problems without a calculator.
Check your answers!
Keep in mind how you are asked to write your answer. This is to prepare for the proctored placement.
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

Arithmetic

Multiplication and Division of Integers

728(91)
452(34)
2725(324)
138 ÷ 6
9380 ÷ 35
1872 ÷ 18

Fractions

Perform the operation and write your answers as a single fraction in simplest terms.

$\frac{2}{5} + \frac{3}{5}$
$\frac{1}{3} + \frac{2}{5}$
$\frac{3}{4} + \frac{5}{6}$
Write $3 \frac{4}{9}$ as a single fraction.
Write $5 \frac{2}{7}$ as a single fraction.
$4 \frac{2}{3} + 2 \frac{1}{6}$
$3 \frac{1}{8} + 2 \frac{2}{9}$
${(\frac{2}{3})}^{2}$
${(\frac{4}{7})}^{2}$
$\frac{3}{5} (\frac{2}{7})$
$\frac{3}{25} (\frac{5}{8})$
$\frac{3}{8} (\frac{3}{4})$
$\frac{3}{7} \div \frac{2}{7}$
$\frac{3}{4} \div \frac{1}{5}$
$\frac{2}{3} \div \frac{1}{2}$
$\frac{3}{5} \div \frac{7}{9}$
Write 0.45 as a fraction in simplest terms.

Absolute Value

$| 4 |$
$| - 3 |$
$| 0 |$
$| - 11 + 5 |$
$| 18 + 24 |$
$| 17 - 36 |$
$| - 4 - 11 |$

Prealgebra and Algebra

Evaluate: (Order of operations)

$12 - 3 (2 + 9)$
$- 8 + 5 - (- 6 + 2)$
$10 + (- 4) - (- 3 + 12)$
$- 3 (4 - 7) - 2 (- 3 - 2)$

Simplify the Expression I: Write your answer in $a x + b$ form.

You will need to write answers for the value of $a$ and the value of $b$ .

Example: $3 x - 7$ means $a = 3$ , $b = - 7$

$2 x + 8 x$
$5 x - 6 - 5 x$
$- 4 x + 7 x$
$4 x + 2 x + 3 + 8$
$4 x - 3 - 5 x + 2$
$5 (2 x + 3) + 4$
$5 (2 x - 6) + 4 x - 17 x + 8$
$3 (2 x + 4) - (3 x - 1)$

Simplify the Expression II: Write your answer in $a x^{2} + b x + c$ form.

You will need to write answers for the value of $a$ , the value of $b$ , and the value of $c$ .

Example: $- x^{2} + 4 x - 9$ means $a = - 1$ , $b = 4$ , $c = - 9$

$6 x^{2} + 5 x - 9 x^{2} + 14$
$(- 3 x^{2} + 9 x - 4) + (- 8 x^{2} + 8 x - 2)$
$(- 6 x^{2} - 8 x + 5) - (- 5 x^{2} + 7 x - 8)$

Substitution: Evaluate the expression for the given value of $x$ .

$3 x - 5$ when $x = 2$
$- 5 x - 6$ when $x = 4$
$- 8 x + 11$ when $x = - 3$
$3 x^{2} + 4 x - 5$ when $x = - 1$
$- x^{2} - 5 x + 7$ when $x = - 2$

Solving equations: Find the value of $x$ .

$- 3 x = 12$
$5 x = - 30$
$x - 12 = 13$
$- x - 5 = - 7$
$8 - 2 x = 17$
$\frac{1}{4} x = 2$
$9 x = 3$
$- x + 4 = 12$
$- 3 x - 9 = 12$
$2 x - 5 = 7 + 6 x$
$2 (x - 5) + 3 x = x + 6$
$- 5 (x + 1) + 3 x + 2 = 6 x + 4$
$\frac{1}{3} (x + 1) + \frac{2}{3} (x - 4) = 3 x + 11$
$\frac{2}{5} (x - 6) + \frac{3}{5} (x + 2) = 4 x - 8$

Calculate the slope, $m$ , of the line passing through the two points.

Write your answer as a simplified fraction.

$(2, - 1), (- 5, 3)$
$(3, 1), (4, - 3)$
$(- 2, - 3), (- 1, 5)$
$(- 4, 1), (2, 6)$

Find the equation of the line passing through the two points.

Write your answer in $y = m x + b$ form, where both $m$ and $b$ are written as simplified fractions.

$(3, 4), (5, 8)$
$(5, - 2), (- 3, 14)$
$(5, - 4), (7, 2)$

Find the y-intercept.

The y-intercept is the point at which the line passes through the y-axis. At that location, the $x$ coordinate is 0. Therefore, to calculate the y-intercept plug in $x = 0$ and solve for y.

$x + 2 y = 8$
$3 x - y = 19$
$x + 2 y = 18$
$2 x - 3 y = - 19$
$2 x - 13 y = - 6$

Answers

Multiplication and Division of Integers Answers

66,248
15,368
882,900
23
268
104

Fractions Answers

$\frac{1}{1}$
$\frac{11}{15}$
$\frac{19}{12}$
$\frac{31}{9}$
$\frac{37}{7}$
$\frac{41}{6}$
$\frac{385}{72}$
$\frac{4}{9}$
$\frac{16}{49}$
$\frac{6}{35}$
$\frac{3}{40}$
$\frac{9}{32}$
$\frac{3}{2}$
$\frac{15}{4}$
$\frac{4}{3}$
$\frac{27}{35}$
$\frac{9}{20}$

Absolute Value Answers:

Evaluate Using Order of Operations Answers:

$- 21$
1
$- 3$
19

Simplify Expressions I Answers:

$a = 10$ , $b = 0$ (which means $10 x$ )
$a = 0$ , $b = - 6$ (which means $- 6$ )
$a = 3$ , $b = 0$ (which means $3 x$ )
$a = 6$ , $b = 11$ (which means $6 x + 11$ )
$a = - 1$ , $b = - 1$ (which means $- x - 1$ )
$a = 10$ , $b = 19$ (which means $10 x + 19$ )
$a = - 3$ , $b = - 22$ (which means $- 3 x - 22$ )
$a = 3$ , $b = 13$ (which means $3 x + 13$ )

Simplify Expressions II Answers:

$a = - 3$ , $b = 5$ , $c = 14$
(which means $- 3 x^{2} + 5 x + 14$ )
$a = - 11$ , $b = 17$ , $c = - 6$
(which means $- 11 x^{2} + 17 x - 6$ )
$a = - 1$ , $b = - 15$ , $c = 13$
(which means $- x^{2} - 15 x + 13$ )

Substitution Answers:

1
$- 26$
35
$- 6$
13

Solving Equations Answers:

$x = - 4$
$x = - 6$
$x = 25$
$x = 2$
$x = \frac{- 9}{2}$
$x = 8$
$x = \frac{1}{3}$
$x = - 8$
$x = - 7$
$x = - 3$
$x = 4$
$x = \frac{- 7}{8}$
$x = \frac{- 20}{3}$
$x = \frac{34}{15}$

Slope Answers: (Must be written as a fraction)

$m = \frac{- 4}{7}$
$m = \frac{- 4}{1}$
$m = \frac{8}{1}$
$m = \frac{5}{6}$

Equation of Line Answers:

$m = \frac{2}{1}$ , $b = \frac{- 2}{1}$ (which means $y = 2 x - 2$ )
$m = \frac{- 2}{1}$ , $b = \frac{8}{1}$ (which means $y = - 2 x + 8$ )
$m = \frac{3}{1}$ , $b = \frac{- 19}{1}$ (which means $y = 3 x - 19$ )

Y-Intercept Answers:

$y = 4$ (when $x = 0$ )
$y = - 19$ (when $x = 0$ )
$y = 9$ (when $x = 0$ )
$y = \frac{19}{3}$ (when $x = 0$ )
$y = \frac{6}{13}$ (when $x = 0$ )

If you have answered many questions incorrectly, you may consider more practice on those topics before moving onto the next practice guide.

If you’d like to meet with one of our peer tutors in the Math Learning Lab, you can schedule tutoring using the link: WCOnline. You will need to register for an account before your first visit using your RIC email address. Once you have account, log into the Math and Computer Science Schedule, use the “limit to” menu to select Math Placement, select an open timeslot, and fill out the appointment form. If you have any questions about this process, email Megan at mdibonaventura@ric.edu.

We also have workshops available beginning in June 2026!