With sample test questions
MATHEMATICS / ALGEBRA 
Key Words and Converting Words to Equations
Fractions
Adding, subtracting, multiplying, dividing
Simplifying
Writing decimals as fractions
Statistics
Reading Tables and Charts
Exponents
PreAlgebra 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
Factoring
Sample algebra problems
Coordinate System
Grid graph
Slope coordinates
Geometry
Basics
Squares, rectangles, circles, triangles
Math Definitions 
ENGLISH 
Proof reading / spelling
Reading comprehension
Main theme of a paragraph
Logical sequence of a paragraph
Key word
English grammar
Basic word meanings 
ABILITY TO ASSIST 
Worker roles and responsibilities
Student discipline / behavior 
WRITING 
Content
Format
Grammar
Spelling
Punctuation 
MDUSD Proficiency Test Study Guide / Page 2
MATH
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.
OPERATION 
OTHER WORDS WHICH INDICATE THE OPERATION 
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.
WORDS 
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 
Fractions
In order to accurately solve fraction problems it is important to distinguish between the numerator and denominator. Numerator: top number Denominator: bottom number
MATHEMATICS PRACTICE QUESTIONS 
MATHEMATICS PRACTICE QUESTIONS 
Œ
 8 9/16
 2 4/16
 10 13/16
 5 13/16
 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 
Ž
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 

80% of what is 204?
a. 250
b. 240
c. 255
d. 260 
‘
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 
’
Estimate the answer:
4.88
x 6.24 a. 30
b. 24
c. 35
d. 28 

“
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 
”
How many times bigger is b than a:
a. 2 times
b. ½ times
c. 3 times
d. 1 ½ times
a b 
• 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: Œ (C) (A Ž (B) (D) (C) ‘ (C) ’ (A) “ (A) ” (A) • (C)
MDUSD Proficiency Test Study Guide / Page 3
PREALGEBRA AND ALGEBRA
SPECIAL NOTATION FOR MULTIPLICATION AND DIVISION WITH VARIABLES.
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
ALGEBRA WORD PROBLEMS
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
 Define the variable
 Translate the problem into an equation and plug in known values
 Solve the equation
 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 
CONSECUTIVE INTEGER WORD PROBLEMS
SAMPLE 
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 
Answer 
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.
PRIME FACTORIZATION
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.
ALGEBRA PRACTICE QUESTIONS 
Œ
15 + ( 8) =
 23
 7
 23
 7

Select the prime factorization for 84
 1 x 2 x 42
 2 x 2 x 21
 3 x 2 x 8
 2 x 2 x 3 x 7

Ž Which is equivalent to
7 – 5y < 3 (4y – 2)
 a. 2y < 12y – 2
 b. 17y < 9
 c. 75y < 12 y  6
 d. 9 > 3 (9y)

Evaluate the following when r = 2,
s = 8, t = 5
t + 1
 + 4s
r
 29
 35
 38
 44

Find the area in square feet.
(A = 1/2bh)
 80
 240

120
 480
40 
‘
Find the area of the triangle in centimeters
8
 28
 112
 56
 22
14 
’ Joan’s bedroom is 25.3 feet on one side and 10.5 feet on the other. What is the area of the bedroom?
 106.26
 139.15
 255.55
 265.65

“
Solve for the variable:
 48.3 + x = 71.2
 119.5
 23.9
 22.9
 32.9

”
Solve the variable:
12a = 60
 72
 5
 48
  5

Answers: Œ (B) (D) Ž (C) (B) (C) ‘ (C) ’ (D) “ (C) ” (B)
MDUSD Proficiency Test Study Guide / Page 5
ENGLISH
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.
SAMPLE
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 welldefined plan, will only achieve partial success.
The MAIN theme of this paragraph is
A welldefined plan will assure the success of a weight loss program.
 A high degree of determination is necessary and sufficient for a highly successful weight loss program.
 It’s impossible to develop a successful weight loss program.
 Two important ingredients of a successful weight loss program are a welldefined 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 welldefined 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
ABILITY TO ASSIST
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 teacherdeveloped tests and file information accurately.
SAMPLE
When communicating with parents from a different culture, it is most important to
 do all of the talking so they feel more comfortable
 be respectful of the differences between your culture and theirs
 realize that their level of communication is not as refined as yours
 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.
WRITING
Write an essay on an assigned topic. Essay will be graded on:
 Content
 Grammar
 Spelling
 Punctuation
 Penmanship