Welcome to ACT Prep Math/Science review. Introduction to the ACT What is the main purpose of the...

Welcome to ACT Prep

Math/Science review

Introduction to the ACT

• What is the main purpose of the ACT?1. Designed to help a student’s transition

from high school to college2. One piece of information that colleges

can use when making decisions regarding admission


• Are there other uses?1. Used to determine who gets

scholarship money2. Used to place students in freshman

courses– Your math score determines if you place

into College Algebra or if you have to take remedial math

– Likewise, your English score places you in English courses


• How many times can a person take the ACT?

1. Students can take the ACT test as many times as they want.

2. Colleges base their decisions on the highest composite score.


• How is the ACT scored?1. For each of the four tests (English,

Mathematics, Reading, and Science), you are given a “raw score” based on the number of questions you got right.

2. Each of the raw scores is then converted to a “scale score” ranging from 1 to 36.

3. The student’s composite score is the average of the four scaled scores.– If the average ends in .5, the composite score is

rounded up. 23.5 = 24


• Why should a student prepare?1. A higher score allows a student to be accepted by more

colleges. Higher scores open more doors.2. A higher score earns students more scholarship dollars.

Each point brings more money.3. A higher math or English score will enable you to obtain

better placement into college math and English classes. – As a matter of fact, if your math or English score is too

low, many colleges will make you take remedial courses that don’t count toward graduation!

4. The right preparation (which this class provides) will increase a student’s score. On average, students increase their scores by about 2 points, though some do even better.


• What does a student have to do to make his/her score go up?

1. The ACT rewards hard work in regular classes, as well as in test preparation.

2. What a student does to prepare for this test cannot make up for years of slack effort in high school classes, but it can help maximize what a student knows and help get a higher score. By doing the assignments in this class, a student will get the most out of this class. The homework has been designed to be as time efficient as possible!

Personal Reflection Time

• Take a couple of minutes to reflect and write down your goals:– What is your goal score on the ACT test?– What area of the test do you need the

most help with?– What is your “dream” college?– What are some things that you can do

next year to make your dreams come true?

Introduction to the Math TestI. General Information

A. There will always be 60 questions to be completed in 60 minutes

B. Questions address content through pre-calculusII. Content of the Math Test

A. Pre-Algebra (14 questions)Fractions, decimals, percents, etc.

B. Elementary Algebra (10 questions) Questions from Algebra I

C. Intermediate Algebra and Coordinate Geometry (18 questions)

Questions from Algebra II and dealing with the x- and y-axes

D. Plane Geometry (14 questions) Triangles, Polygons, Area, etc.

E. Trigonometry (4 questions)If you don’t know what this is about, don’t mess with it!

Content Guide to the ACT test– See the content guide to the ACT Math Test– This shows what areas of math each

question on the practice Math ACT tests comes from.

The ABC’s of Preparing for the Math Test

A. Review the relevant math content– This course will seem like a math class because

part of the curriculum is to review mathematics

B. Learn specific strategies that apply to the ACT

– We’ll also learn how to still get answers when you are unsure of the mathematics behind the solution

C. Connect what you know to the test by doing problems from actual ACT tests.

– Yes, we’ll do a lot of practice tests. Not only do we need to know the content on the test, but we have to practice time management since the test is timed

Specific Strategies for the Math Subtest

I. Setting the Pace (MATH)A. Key Ideas

To get your best score, you must be realistic about your goal.

In general, the questions toward the beginning are easer than the questions toward the end.

Skipping problems and going back is a good strategy for your math class where the goal is to score 90%-100%, but it is NOT a good strategy for the ACT. If you can’t do a problem, drop down levels until, as a last resort, you guess.


B. The Three Approaches1. The “20-24 approach”

– This is an average score. If math is a weak area, and you would be happy with a 20, then this is for you!

– To get a 20 all you need to know is how to do about 20 questions*

– So, move slowly on the ones you think you can get. It’s okay to spend two minutes on questions you feel you are doing correctly.

– It’s a waste of time to “play with” a question for 2 minutes, waiting for the “bolt of lightning to strike you.”

Note: 20 correct + 1/5 of the other 40 correct by guessing gives you a total of 28. This is about a 20 on most ACT’s.


B. The Three Approaches2. The “25 to 29 approach”

– If you scored between 20 and 24 on a previous ACT, or if you are a good math student, this one’s for you!

– To get a 25 on the math section, you need to know how to do about 30-35 questions correctly*Do 30-45 problems using mathUse strategies on another 10-15 questionsGuess on about 5-10 questions

Note: 35 correct + 1/5 of the other 25 correct by guessing gives a total of 40. This is about a 25 on most ACT’s


B. The Three Approaches3. The “30+approach”

– If you scored 25+ on a previous ACT and you are an exceptional math student, you want to aim for this score.

– To get a 30 or above you must be able to do most of the problems*

– You must be able to do the easier problems faster than students seeking a 20 or 25—you will need the additional time for the harder questions.

Do 45-50 questions using mathDo about 5-10 using strategiesGuess on no more than about 5 questions

Note: 50 correct + 1/5 of the other 10 correct by guessing gives you a total of 52. This is about a 30 on most ACT’s.

Putting it all together

20-24 25-29 30-33 34-36

Concentrate on

questions 1-30

Concentrate on

questions 1-40

Concentrate on

questions 1-50

Save time to go back

to the hardest

questions

Be picky on 31-50

Be picky on 41-50

Be picky on 51-60

Can’t be picky!

Hunt 51-60 Hunt 51-60 Guess on no more than 5

Do ‘em all


C. Pacing Markers1. If your goal score is 20 to 24

– You can go slower than one question per minute2. 25

– Average close to a minute/question3. Over 25

– Work faster than a minute/question– 5-10 max per minute


II. Introduction: Three ways to do Math Questions on the ACT (Use your book: Preparing for the ACT 06/07)A. (Level 1) Using Mathematics

– Just like in your math class1. One mathematical way

Do Problem #35

2. Another way Do Problem #35


II. Introduction: Three ways to do Math Questions on the ACTB. (Level 2) Using Multiple Choice Strategies

– These are ways your math teacher probably didn’t show you

1. Estimation: This is by far the most important strategy for doing questions you cannot do using standard mathematical procedure. Do Problem #35

Note: Many times estimation will only allow you to eliminate 2 or 3 choices. Pick the most reasonable answer from all viable alternatives. So, just pick the one that looks the closest.

You hope you never need them, but you’re glad to have them if you do!


II. Introduction: Three ways to do Math Questions on the ACTB. (Level 2) Using Multiple Choice Strategies

– These are ways your math teacher probably didn’t show you

2. Work backwards from the answers Do Example 8

3. Plug in numbers Do Example 47


II. Introduction: Three ways to do Math Questions on the ACTC. (Level 3) Guessing

1. Random guessing. Pick any style. On average you will get one out of 5

2. Odd-man-out. Eliminate the answer(s) which are clearly different from the others.

Have you heard the one about…

• The college student who missed every class but showed up to take the multiple-choice final?

General StrategiesIII. The General Strategies

1. Write in the test booklet2. Use “good mechanics” on every question:

Read slowly (in phrases). Reading one time slowly is better than reading twice quickly.Make sure you understand the question before you start solving.Make sure you’ve answered the question.Check each problem before you move on (no going back to check)

3. Know the directions (they’re the same as in the practice test)

4. Answer Every Question!!!

Specific StrategiesIV. Specific Level I Strategies

A. Strategies for Pre-algebra/Algebra1. Know how to go from an average to a total.

Ex. Page 23 #42 (0556A)

2. Use your calculator for computationEx #7

3. Know y = mx + b#12#26#5#4


A. Strategies for Pre-algebra/Algebra4. Know how to solve a linear equation.

#13

5. Think proportionately#28

6. Know basic probability#24

7. Remember the rules of exponents#4

8. Know how to solve a linear inequality#36

9. Know how to apply the concept of distance = rate × time#19

Specific Strategies

IV. Specific Level I Strategies B. Strategies for Geometry

1. Label all information: Start with what you are given, work toward what you want.#18

2. Draw a picture.#14, #25, #57

3. Draw the coordinate axis#37

4. Know how to apply scale factors#44, #46

5. Use the Pythagorean Theorem to find lengths or distances#14 (Be careful!)

6. Divide figures into rectangles, triangles, or circles#15

7. Know the “180-rules”#18, #39

8. Know how to apply the two special right triangles

(30-60-90 and 45-45-90)#44


C. Strategies for Advanced Algebra1. Know how to apply “FOIL”

#11

2. If given the graph of an equation you don’t recognize, find a point on the graph and plug it into the answers. The correct choice will be true for this point. If more than one choice works, try another point.#41 (0556A)

3. Know the equation of a circle (x – h)2 + (y – k)2 = r2

#59 (0556A)

4. Know when to factor#38


D. Strategies for Trigonometry1. Know how to apply SOHCAHTOA

#25, #32

2. Know the graph of sine function o f(x) = asinb(x – c) + do a = amplitude, b = 2pi /periodo c = horizontal shift, d = vertical shift

#55

3. Know how to use the identity sin2x + cos2x = 1#56

Specific StrategiesV. Specific Level 2 Strategies

– If you can’t do the problem using pure math, try these.

A. Estimation1. Eliminate unreasonable answers

#152. Use your “eyeball protractor”

#18, #453. Estimate distances using your “ruler”

#9, #30, #324. Draw your own diagram and estimate from it

#145. Approximate using your calculator

#146. Estimate by using “computational landmarks”

(e.g. .20 = 1/5, .25 = ¼, .33 = 1/3, .5 = ½, .67 = 2/3, pi = 3) #29 (0556A)



B. Work Backwards from the Answers– Start in the middle or with the easiest choice #5, #19, #24, #42, #43, #60

C. Work Backwards (start with the smallest choice)

#51



D. Make up and Substitute Numbers (plug the same numbers into the question and the choices, look for a match)

#52

E. Make up and Substitute Numbers (use numbers to help your thinking)

#17, #1

F. Do Part of the Problem Completely and Correctly It’s better to do half a problem correctly and

eliminate than to fake the whole thing #39

Specific StrategiesVI. Specific Level 3 Guessing Strategies

– This is what you should do if you have absolutely no idea how to work the problem. Remember, estimation is NOT guessing!

Random Guess. Pick your favorite strategy. On average, you get 1 out of 5 (20%) correct. Do this quickly!

Odd-Man-Out. Eliminate choices that are clearly different than the rest. (This takes a little longer, but you will get, on average, about 25%)Try #1 and #57

Specific StrategiesVII. How to get the most out of your

calculator. Use a calculator you are familiar with. A calculator is only appropriate for some

questions. If you do not now how to work a question, don’t waste time playing with it on your calculator.

Enter numbers carefully—always mentally estimate the answer to make sure that the calculator’s answer is reasonable

Make sure that you have good (perfectly new) batteries on test day.

Use your calculator to do the 4 basic math operations (#7, #21)

Use your calculator to evaluate expressions (#2, #53)

It’s Practice Test Time

• 60 minutes to do the math test• Afterwards, we’ll score the test• Then, we’ll diagnose your mistakes on

the test

Diagnosing MistakesMistake Category How to correct

You made a careless error in reading Spend more time at the beginning of each problem. Don’t begin to compute until you have fully conceptualized the problem

You made a careless error in computation Slow down on your computations and check your answers by estimation

The problem required you to use mathematics you used to understand but have forgotten

Note the content you didn’t remember and review it before the test. Put that concept in your list of “Things to Remember”

The problem required you to use mathematics you never understood

Try more level 2 approaches next time, i.e., use more multiple choice strategies

You knew the math, but the problem required you to use what you knew in a way that did not occur to you

Not much you can do about these except to keep on practicing

You ran out of time If you feel as if you could have done the problems you did not get to, then try to go a little faster. If you feel as if you could not have gotten them anyway, then your approach was correct, i.e., you ran out of time at the appropriate place.

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Welcome to ACT Prep Math/Science review. Introduction to the ACT What is the main purpose of the...

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