Skip to main content

Proficiency Test Study Guide


Key Words and Converting Words to Equations


     Adding, subtracting, multiplying, dividing


     Writing decimals as fractions               


Reading Tables and Charts


Pre-Algebra and Algebra:

     Special notation for multiplication and division with variable

     Algebra word problems

     Order of operations

     Simplifying expressions

     Prime factorization

     Greatest common factor

     Least common multiple


     Sample algebra problems

Coordinate System:

     Grid graph

     Slope coordinates



     Squares, rectangles, circles, triangles

Math Definitions



Proof reading / spelling

Reading comprehension

Main theme of a paragraph

Logical sequence of a paragraph

Key word

English grammar

Basic word meanings



Worker roles and responsibilities

Student discipline / behavior









MDUSD Proficiency Test Study Guide / Page 2



Key Words and Converting Words to Equations


Sometimes math questions use key words to indicate what operation to perform.  Becoming familiar with these key words will help you determine what the question is asking for:


Addition Increased by; more than; combined together; total of; sum; added to.
Subtraction Decreased by; minus; less; difference between/of; less than; fewer than.
Multiplication Of; times; multiplied by; product of (For example 4 + 4 + 4 equals 4 X3).
Division Per; a; out of; ratio of; quotient of; percent (divide by 100).
Equal Is; are; was; will be; gives; yields; sold for
Per Divided by



Here are some examples of words converted to equations:


What is the sum of 8 and y? 8 + y
4 less than y y – 4
Y multiplied by 13 13y
The quotient of y and 3 y / 3
The difference of 5 and y 5 – y
The ratio of 9 more than y to y (y+9) / y
Nine less than the total of a number (y) and two (y+2) = 9 or y - 7



In order to accurately solve fraction problems it is important to distinguish between the numerator and denominator.              

Numerator:  Top number                            Denominator:  Bottom number




                    8   9/16

             -   2    4/16



    a.   10   13/16

    b.    5   13/16

    c.    6   5/16

    d.    6   13/16


           4  3/4

        + 6  3/5

          a.  11 7/20

          b.  10  2/3

         c.   11  2/3

        d.   10  7/20                                                          


       4  4/5  x  6  2/8  =                                                   

           a.    10  3/5

           b.    30

           c.    25

           d.  -24  6/8                                                        


     6  2/3   ÷   4  2/6  =   

       a.  2  1/13

       b.  28  8/9

       c.  3  2/6

       d.  1  7/13

5.  80% of what is 204?

              a.  250

              b.  240

              c.  255

              d.  260

6.    50 people went to a play. 

       3/5 of the people stayed to the end.

       How many people left?

              a.  10

              b.  30

              c.  20

              d.  40

7.  Estimate the answer:


        x  6.24             

                   a.  30

                   b.  24

                   c.  35

                   d.  28

8. What is the probability of rolling a 4 on a set of dice?

              a.  1:6

             b.  2:6

             c.  1:12

             d.  1:4


9. How many times bigger is b than a:


              a.  2 times

              b.  ½ times

              c.  3 times

              d.  1 1/2 times

              null Anull B

                  a            b

10.  Jean goes 385 miles on 14 liters of gas. What was the miles per liter?

             a.  25 miles / liter

             b.  26.3 miles / liter

             c.  27.5 miles / liter

             d. 27 miles / liter                   

Answers:  1. (C)    2.  (A    3.  (B)    4.  (D)    5.  (C)    6.  (C)    ’7. (A)   8.  (A)    9. (A)    10.  (C)

MDUSD Proficiency Test Study Guide / Page 3



 Here are some examples of special notations and what they mean:

2b means 2 x b

2(a + 5) means twice the sum of a number (a) and five

bc means b x c

4bc means 4 x b x c

d/5 means d ÷ 5


In algebra you solve problems by essentially making two groups, one for each side of an equation.  An unknown number or value is represented by a letter (for example: x).

 Basic Steps

  1. Define the variable
  2. Translate the problem into an equation and plug in known values
  3. Solve the equation
  4. Go back to the problem and plug in the new value to obtain the answer


SAMPLE A car dealership has 15 new cars and 12 used cars.  How many cars to they have?
Define the unknown variable Let x  = Total Cars
Translate the problem into an equation and plug known values in 15 + 12 = x
Solve the equation 27 = x
Answer There are 27 total cars





Two consecutive numbers have a sum of 71.  What are the numbers?

Define the unknown variables:  Since two numbers are unknown, in order to solve it you must use only one variable (such as x) in the equation.

 Let x = The First Consecutive Number

Let x + 1 = The Second Consecutive Number

Translate the problem into an equation and plug known values in.

x + (x + 1) = 71

Solve the equation

x + (x + 1) = 71

Remove parenthesis

2x + 1 = 71

Subtract 1 from each side

-1 + 2x + 1 = 71 – 1

2x = 70

Divide both sides by 2

2x = 70

2        2

x = 35

Go back to the problem and plug in new values

35 = The First Consecutive Number

35 + 1 = The Second Consecutive Number


35 & 36


MDUSD Proficiency Test Study Guide / Page 4


 Other tips for consecutive number word problems: 

  • When solving for negative consecutive numbers, ignore the negative sign and do not do anything differently.  Keep the x positive and when you have obtained your answer, add the negative sign.
  • When solving for even or odd consecutive numbers, add a space to the equation.  For example:  The next consecutive number after 15 can be found by adding 1 to it.  The next even/odd number can be found by adding 2.



 A prime number is a positive integer greater than one that can only be divided by itself and one. 

Some examples are 2, 3, 5, 7, 11, 13, 17, and 19.

 A composite number is a positive integer greater than one that has more than one divisor other than one and itself.    Some examples are 4, 6, 9. 15, and 21

 One is neither a prime nor a composite number.

 Ways to obtain the prime factor

  • Repeatedly divide by prime numbers.
  • Choose any pair of factors and split these factors until all the factors are prime.
  • Work backwards from the answers, seeing which one is BOTH only prime numbers, and produces the correct product.



   1.        15 + (- 8) =


 a.     23

 b.       7

 c.    -23

 d.     -7


  2.  Select the prime factorization

       for 84

   a.   1 x 2 x 42


   b.   2 x 2 x 21


   c.   3 x 2 x 8


   d.  2 x 2 x 3 x 7

   3.  Which answer is equivalent to:

7 – 5y < 3 (4y – 2)


a.       2y < 12y – 2


b.       -17y  <   -9


c.       7-5y   < 12 y - 6


d.       9  >  3  (9y)


4.  Evaluate the following

    when r = 2,  s = 8, and t = 5:


t + 1

          -------   + 4s


  1. 29
  2. 35
  3. 38
  4. 44




  7.  Joan’s bedroom is 25.3 feet on one side and 10.5 feet on the other.  What is the area of the bedroom?


a.  106.26

b.  139.15

c.  255.55

d.  265.65


  8.   Solve for the variable:

                   48.3   +  x = 71.2


a.  119.5

b.  23.9

c.  22.9

d.  32.9

  9. Solve for the variable:

                 12a = 60

a.  72

b.  5

c.  48

d.   5


Answers: 1.  (B)    2.  (D)    3.  (C)    4.  (B)    5.  (C)    6. (C)    7. (D)    8.  (C)    9.  (B)

MDUSD Proficiency Test Study Guide / Page 5



Main Theme of a Paragraph:

These questions ask you to first read a paragraph and then choose an answer based on the main idea of the paragraph.  The correct answer usually restates the main idea using different wording or requires that you draw a conclusion from the contents of the paragraph.


 A successful weight loss program must contain a specific plan designed to achieve healthy weight loss for an individual.  An appropriate plan, without necessary determination to carry it out, is useless.  Determination, without a well-defined plan, will only achieve partial success.

 The MAIN theme of this paragraph is

 A well-defined plan will assure the success of a weight loss program.

  1. A high degree of determination is necessary and sufficient for a highly successful weight loss program.
  2. It’s impossible to develop a successful weight loss program.
  3. Two important ingredients of a successful weight loss program are a well-defined plan and a sincere resolve to implement that plan.


Solution:  To answer this question, evaluate each choice.

 Choice (a) only contains one of the points: a well-defined plan; therefore, this choice is only partially correct.

 Choice (b) also only lists one of the points: determination; therefore, this choice is only partially correct.

 Choice (c) is not supported by evidence within the paragraph; therefore this choice is incorrect.

 Choice (d) restates the idea presented in the paragraph.  This choice is correct.

 Logical Sequence of a Paragraph:

Some questions ask you to evaluate a paragraph for a smooth, logical progression of ideas.  This is known as logical sequencing.  First, it is important to know the structure of a paragraph.  The topic sentence is the first sentence of a paragraph; it introduces the main theme.  The supporting sentences give details and develop the main theme; they usually follow the topic sentence.  The closing sentence wraps up the paragraph by restating the main theme, drawing a conclusion, or presenting a transition to another paragraph.

 Some questions to ask when evaluating a paragraph’s logical sequence are: 

  • What is the main theme of the paragraph?
  • In what order should the ideas follow?
  • Are there ideas that are an extension of the main theme?
  • Are there ideas that can’t be understood until other things are explained?

 MDUSD Proficiency Test Study Guide / Page 6



To study for questions related to the ability to assist instruction, it is important to think about the role of a Paraprofessional / Instructional Aide and to answer questions based on this role.  Paraprofessional / Instructional Aides should have knowledge of basic child guidance and development characteristics and principles and appropriate ways to manage student behavior.


Paraprofessional / Instructional Aides also need to:

  • Follow instructions provided by the teacher (verbal and written).
  • Be positive when interacting with students, parents, and school personnel.
  • Communicate and be respectful while interacting with students and families  from diverse cultures.
  • Keep student information confidential (personal information, test results, medical history, etc.)
  • Tutor students (individually and in small groups).
  • Watch and help students in other learning environments (library, computer lab).
  • Score teacher-developed tests and file information accurately.


 When communicating with parents from a different culture, it is most important to

  1. do all of the talking so they feel more comfortable
  2. be respectful of the differences between your culture and theirs
  3. realize that their level of communication is not as refined as yours
  4. point out your cultural differences at the beginning of the conversation

 Solution:  to answer this question, evaluate each choice.

 Choice (a) is incorrect.  Successful communication involves both speaking and listening.

 Choice (b) is correct.  Being respectful of cultural differences encourages open communication.

 Choice (c) is incorrect.  Being from another culture doesn’t mean that their level of communication is better or worse than yours.

 Choice (d) is incorrect.  Pointing out cultural differences may create a negative communication environment.  It is best to focus on similarities between both of you, such as concern for their child. 



Write an essay on an assigned topic.  Essay will be graded on:

  • Content
  • Grammar
  • Spelling
  • Punctuation  
  • Penmanship