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1936 Carlotta Drive, Concord, CA 94519 (925) 682-8000

 Personnel Department

You are here: Mt. Diablo Unified School District > Personnel Department

PROFICIENCY TEST STUDY GUIDE 

                                           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

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

     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        

  1. 8       9/16

             -  2    4/16

 

  1. 10   13/16
  2.   5   13/16
  3.   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

 

PRE-ALGEBRA 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

  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

 

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) =

 

  1. 23
  2. 7
  3. -23
  4. -7

 



Select the prime factorization for 84

 

  1. 1 x 2 x 42
  2. 2 x 2 x 21
  3. 3 x 2 x 8
  4. 2 x 2 x 3 x 7

Ž        Which is equivalent to

7 – 5y < 3 (4y – 2)

 

  1. a.       2y < 12y – 2
  2. b.       -17y  <   -9
  3. c.       7-5y   < 12 y - 6
  4. d.       9  >  3  (9y)

 



Evaluate the following when r = 2,

s = 8, t = 5

t + 1

          -------   + 4s

r

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

 



Find the area in square feet. 

(A = 1/2bh)

 

  1. 80
  2. 240
  3. 6

    120                      
  4. 480

 

                                40

Find the area of the triangle in centimeters

                         8

 

  1. 28
  2. 112
  3. 56
  4. 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?

 

  1. 106.26
  2. 139.15
  3. 255.55
  4. 265.65

 

Solve for the variable:

    1. 48.3   +  x = 71.2

 

  1. 119.5
  2. 23.9
  3. 22.9
  4. 32.9

 

Solve the variable:

12a = 60

 

  1. 72
  2. 5
  3. 48
  4. - 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 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

  

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 teacher-developed tests and file information accurately.

             SAMPLE

 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.

 WRITING

 

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

  • Content
  • Grammar
  • Spelling
  • Punctuation  
  • Penmanship