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ACT Resources

ACT Math Formulas
Handy formula reference sheet from ACT Prep course



ACT Math Vocabulary*

Integer ...-2, -1, 0, 1, 2, ...

Rational:  numbers that can be written as fractions (includes repeating and terminating decimals)

Irrational: numbers that can't be written as fractions (e, π, 2 )

Real numbers:  not imaginary

Prime: a number that is only divisible by 1 and itself (3, 5, 7)

Factors:  numbers that divide into a larger number (factors of 12 are 1, 2, 3, 4, 6, 12)

Multiples:  all numbers that have the same factor (multiples of 3 are 3, 6, 9, 12, 15, etc)

Divisor:  the thing that you are dividing by

Numerator:  the top of a fraction

Denominator:  the bottom of a fraction

Mixed fraction to improper:  Mixed 2 ½   verses improper 5/2

Mean:  the average of a set of numbers, add them all together and divide by the total

Median:  the number in the middle when placed in order (if there are two then average them)

Product:  the answer to a multiplication problem 

Sum:  the answer to an addition problem

Less than:  can mean subtract or <

"a number is four less than 12":  x = 12 - 4 

Coefficient:  the number in front of a variable  3x2  (3 is the coefficient)

Variable:  x or whatever letter they are choosing

Perimeter:  the sum of all of the sides of a figure

Area:  the amount of space inside a figure

Difference:  subtract

Terms:  the following has 3 terms:  3x2 + 5x - 7 

Consecutive:  one after another 

Sequence:  a pattern of numbers (2, 4, 6, 8, ...)

Add/Mult. Fractions

Add:  you need a common denominator

Mult:  multiply numerators & denominators together.



ACT Test Prep and Practice Web Sites*


This site is excellent!  It has several practice tests and gives you a score when you finish.  It also  times the test for you and has tutorials.  Everything is free.


Go to "Quick Test Prep Search" to find some free information and some materials that cost money.


A variety of test prep but it is not free, it costs but includes classes not just materials for around $75 to $100.

4. This site offers Sylvan's class, but also gives some quick tips.


This site is produced by the ACT and includes some free and some pay materials to help prepare for the test.


This site has many free testing materials for the ACT.


This site gives you information on the course offered by the University of Utah.  The course costs $185 and is offered in many locations including Bountiful.

8. This is a site for educators to help students.


This is one of the most popular test sites on the web and it is free practice for students.


This site includes software and online courses that can help students prepare for both the SAT and the ACT.  Some software is free and some cost $.


This is a pay site for "Barrons" test prep materials, includes software, online classes and much more.


This site provides helps to study and tips for increasing your score on the ACT test.


Great site!


*Math information taken from


ACT Science-Test Language/Academic Vocabulary/Important Skills



(1)    Terms and Equipment:




            --arbitrary unit






            --multiple trials





(2)    General Concepts:

            --data interpretation

            --reading information directly from tables and graphs

            --differentiating between independent and dependent variables

            --proper graphing techniques

            --meaning of a graph title

            --calculating slope and how to determine what the slope of a particular graph "means"

            --how to plot data

            --how to determine the relationship between variables

            --calculating area under a graph and how to determine what that area "means"

            --interpreting a bar graph

            --do the results support the hypothesis?

            --what is the best procedure to...?             

            --how would the results be affected if...?

            --which figure best illustrates...?

            --based on the results of the experiment...

            --which statement best explains the results of this experiment (or this data trend)?

            --from this data, we can generalize that...?

            --which best describes the relationship between...?

            --which finding can be used to counter...?

            --is the hypothesis supported by the data?

            --based on these results the student would predict...?





--biotic index                                                                                            --nuclear envelope

--E. coli                                                                                                    --cell membrane

--diversity                                                                                                 --smooth and rough ER

--pollution tolerance                                                                                   --vertical migrators

--larvae                                                                                                    --objective lens

--succession                                                                                              --magnification

--biomass                                                                                                  --aperture

--net productivity                                                                                      --resolution




--primary, secondary, tertiary, quaternary


--active shape



--random coil



--homologous chromosomes

--crossing over


--recombination frequency

--map distance

--map units





--isotope                                                                                    --solvent

--alpha decay                                                                             --mole

--beta decay                                                                              --basic organic chemistry

--isotopic notation                                                                      --octane number

--uranium series                                                                         --solid

--isotopic notation                                                                      --liquid

--concentration (and concentration measures)                              --gas

--specific gravity                                                                        --gas syringe

--percent by volume                                                                  --graduated capillary tube

--mixture                                                                                  --volume

--mixture separation                                                                  --pH

--components of mixture                                                            --organic

--filtration                                                                                 --inorganic

--ion                                                                                         --carbonates, nitrates, nitrites

--polyatomic ions                                                                      --sparker

--salts                                                                                      --simple stoichiometry

--absorbance                                                                             --atmospheric pressure

--calorimeter                                                                             --density


--vapor pressure






--unsaturated or undersaturated




--buoyant force                                                                         --trajectory

--friction                                                                                     --projectiles fired at angle

--fall time                                                                                   --blackbody

--acceleration due to gravity                                                        --wavelength

--horizontal motion

--vertical motion



--ecliptic plane

--astronomical units




--linear expansion


--visible light

--ultraviolet light

--infrared radiation

--delta (change in)

--weight in Newtons

--heat transfer rate

--cross-sectional area





--total stopping distance




--flood basalt plateaus


--pore water

--pore water conductivity





--Paleozoic Era


--calcareous ooze




ACT Reading - Test Language/Academic Vocabulary

Practice Test 1



Main purpose





Principal aim









Point of view


Context of the passage


Practice Test 2


Accurate description

Portraying characters





In comparison

Referring to

Author's proposed solution

Main function of the paragraph

Common element


Author's attitude

Aligned in spirit

Author's opinion

Author's purpose


Reasonable to conclude


Central idea


Practice Test 3


Main point

Accurately expresses

Logically inferred


Makes the claim

Expression of the belief

Considering the information

Acknowledgment by the author

Passage suggests

Passage offers as evidence


Practice Test 4


Reasonably inferred

Distinction the narrator makes

The way the paragraph functions

Passage as a whole

Narrator's view

Details suggest

Author's personal position

Attitudes expressed




ACT English - Test  Language/Academic Vocabulary

Practice Test 1

Most relevant information


Conclude (the essay)








Second-person pronouns


Practice Test 2

Preceding (sentence)

Most relevant

Most consistent

Logical placement

Parenthetical phrase




Logically placed

Subjects of an essay



Writer's goal

Related detail





Focus (of paragraph)

Writer's goal


Practice Test 3

Clearest and most logical transition

Logical and appropriate contrast

Specific transition


Conveys that message

Most effective link (transition)

Introductory phrase

Clearest example

Most effectively introduce


Main Focus

Logic and coherence



Writer's goal


Practice Test 4






Figurative description

Most specific information

Preceding sentence

Most relevant information


Fulfill the goal

Effectively introduces


Most clearly indicate

Logic and coherence


Key points





ACT English Question Stems

The greatest number of questions consists of passages with underlined portions, followed by four options to correct the passage, with one always being "NO CHANGE."

(e.g., The sentence in the reading passage reads, "Every year my high school hosts international exchange students, these teenagers join our senior class.")


    B. students, he or she is invited to

    C. students who

    D. students they


The remainder of the test utilizes the following typical question stems:


1.       Given that all of the choices are true, which one

  • provides the most relevant information with regard to...
  • provides information that is most relevant and meaningful to the essay as a whole?
  • would most effectively conclude this paragraph?
  • of the additions to the preceding sentence would be most relevant?
  • would most effectively tie together the two main subjects of this essay?
  • would most effectively lead the reader from the first sentence of this paragraph to the description that follows...
  • provides information most relevant to the main focus of this paragraph?
  • provides the most logical cause for the action described in the statement immediately following the underlined portion?
  • creates the most logical and appropriate contrast in this sentence?
  • would offer the best transition from Paragraph (#) to Paragraph (#)?
  • provides the most effective link between sentences?
  • would conclude this sentence by providing the clearest examples of...
  • provides the most specific information about...
  • most effectively introduces this sentence by describing...


2.       Three of these (word) choices indicate...Which one does NOT do so?


3.       Which of the following true sentences, if inserted here,

  • would best conclude the essay...
  • would best strengthen the assertion that...
  • would provide the best conclusion to the paragraph and is most consistent with the main focus of the essay?
  • Would both reinforce the conclusion presented in the essay and create an effective transition to the next paragraph?


4.       For the sake of logic and coherence, Sentence (#) should be placed...


5.       The author wants to add a sentence that would (further describe, etc.). Which of the following sentences would best accomplish this?


6.       The writer wants to provide a phrase here that will tie the conclusion of the essy to its beginning. Which choice does that best?


7.       Which choice most effectively guides the reader from the preceding paragraph into this new paragraph?


8.       Which choice would most effectively and appropriately lead the reader from the topic of Paragraph (#) to that of Paragraph (#)?


9.       At this point, the writer is considering deleting the following phrase from the preceding sentence: "..."  If the writer were to make this deletion, the essay would primarily lose:


10.   At this point, the writer is considering adding the following sentence: "..." Should the writer make the addition?


11.   At this point, the writer is considering adding the following parenthetical phrase:...Given that it is true, would this be a relevant addition to make here?


12.   For the sake of logic and coherence, Paragraph (#) should be placed:


13.   Which of the following alternatives to the underlined portion would be LEAST acceptable?


14.   Suppose the writer had chosen to write an essay that indicates that...Would this essay fulfill the writer's goal?


15.   Which choice is the most effective first sentence of Paragraph (X)?


16.   In this paragraph, the writer intends to...Given that all of the choices are true, which one would best accomplish the writer's intention?


17.   The most logical and effective place to add this sentence would be...


18.   Suppose the writer had decided to write an essay discussing...Would this essay successfully fulfill the writer's goal?


19.   The writer wants to balance the statement made in the earlier part of the thesis sentence with a related detail that suggests...Given that all of the choices are true, which one best accomplishes this goal?


20.   Which choice should the writer use to create the clearest and most logical transition to Paragraph (#)?


21.   Which choice would be most consistent with the figurative description provided elsewhere in this sentence?


22.   The writer has decided to divide this opening paragraph into two. The best place to add the new paragraph break would be...


23.   Which choice would most clearly indicate...


24.   Which choice would best help this sentence to summarize key points made in the essay?