ACT MATHEMATICS
Improving College Admission Test Scores
,Contributing Writers
Marie Haisan
L. Ramadeen
Matthew Miktus
David Hoffman
ACT is a registered trademark of ACT Inc.
Copyright 2004 by Instructivision, Inc., revised 2006, 2009, 2011, 2014
ISBN 973-156749-774-8
Printed in Canada.
All rights reserved. No part of the material protected by this copyright may be reproduced in
any form or by any means, for commercial or educational use, without permission in writing
from the copyright owner. Requests for permission to make copies of any part of the work
should be mailed to Copyright Permissions, Instructivision, Inc., P.O. Box 2004, Pine Brook,
NJ 07058.
Instructivision, Inc., P.O. Box 2004, Pine Brook, NJ 07058
Telephone 973-575-9992 or 888-551-5144; fax 973-575-9134, website: www.instructivision.com
ii
, TABLE OF CONTENTS
Introduction iv
Glossary of Terms vi
Summary of Formulas, Properties, and Laws xvi
Practice Test A 1
Practice Test B 16
Practice Test C 33
Pre Algebra
Skill Builder One 51
Skill Builder Two 57
Skill Builder Three 65
Elementary Algebra
Skill Builder Four 71
Skill Builder Five 77
Skill Builder Six 84
Intermediate Algebra
Skill Builder Seven 88
Skill Builder Eight 97
Coordinate Geometry
Skill Builder Nine 105
Skill Builder Ten 112
Plane Geometry
Skill Builder Eleven 123
Skill Builder Twelve 133
Skill Builder Thirteen 145
Trigonometry
Skill Builder Fourteen 158
Answer Forms 165
iii
, INTRODUCTION
The American College Testing Program Glossary: The glossary defines commonly used
(ACT) is a comprehensive system of data mathematical expressions and many special and
collection, processing, and reporting designed to technical words.
assist students in the transition from high school to
college. The academic tests in English, mathe- Formulas: Formulas that are commonly applied to
matics, reading, and science reasoning emphasize mathematical problems are listed in a separate
reasoning and problem-solving skills. The test section. This section can be used as a convenient
items represent scholastic tasks required to reference for formulas relating to geometric shapes
perform college level work. and algebraic functions.
ACT questions are designed to measure a
wide range of abilities and knowledge. Practice Tests: There are three full-length practice
Consequently, some of the items are difficult while tests. Under actual testing conditions, you are
others are fairly easy. A background of strong allowed 60 minutes for the entire test. The
academic courses combined with a worthwhile instructions should be followed carefully.
review will enable you to meet this challenge Skill Builders: The skill builders describe and
successfully. illustrate each of the content areas in the
Mathematics Test. The skill builders are divided
The Mathematics Test into sections, each of which relates to one of the
The Mathematics Test is a 60-question, 60- principal categories covered in the test. Each skill
minute examination that measures mathematics builder consists of a series of examples, orientation
reasoning abilities. The test focuses on the exercises, practice exercises, and a practice test.
solution of practical quantitative problems that are
encountered in high school and some college The answers to the sample tests and the skill
courses. The test uses a work-sample approach builder exercises and practice tests are not found
that measures mathematical skills in the context of in the Student Workbook. They are included in the
simple and realistic situations. Each of the Teacher Manual.
multiple-choice questions has five alternative
responses. Examine the choices, and select the How the ACT is Scored
correct response. The “raw” score of 1 point for each correct
Three subscores based on six content areas are answer will be converted to a “scale” score. The
classified in the Mathematics Test (see chart, page scale on which ACT academic test scores are
v). The 60 test questions reflect an appropriate reported is 1-36, with a mean (or average) of 18,
balance of content and skills (low, middle, and based on a nationally representative sample of
high difficulty) and range of performance. October-tested 12th grade students who plan to
Because there is no penalty for guessing, answer enter two-year or four-year colleges or
every question. There are no trick questions; In universities. The scale for each subscore is 1-18,
some problems, you may have to go through a with a mean of 9. A guidance counselor will be
number of steps in order to find the correct answer. glad to answer questions regarding the scoring
In order to perform efficiently and accurately process and the score reports.
throughout the examination, you must understand
and apply fundamental mathematical concepts. Math Strategies
Spending too much time on any one item is 1. Answer all questions. First do those problems
unwise. On the average, spend about one minute with which you are most familiar and which
on each question. Any remaining time should be seem the easiest to solve, and then answer
spent in completing unanswered questions or those you find more difficult.
reviewing previous work. 2. Practice pacing yourself. Try to solve most of
the problems in less than one minute each.
How to Use the Mathematics Workbook 3. Pay close attention to the information in each
This workbook consists of the introduction, a problem. Use the information that is important
glossary of terms, formulas, three practice tests, in solving the problem.
skill builders, and additional questions for review. 4. If you are making an educated guess, try to
eliminate any choices that seem unreasonable.
iv
Improving College Admission Test Scores
,Contributing Writers
Marie Haisan
L. Ramadeen
Matthew Miktus
David Hoffman
ACT is a registered trademark of ACT Inc.
Copyright 2004 by Instructivision, Inc., revised 2006, 2009, 2011, 2014
ISBN 973-156749-774-8
Printed in Canada.
All rights reserved. No part of the material protected by this copyright may be reproduced in
any form or by any means, for commercial or educational use, without permission in writing
from the copyright owner. Requests for permission to make copies of any part of the work
should be mailed to Copyright Permissions, Instructivision, Inc., P.O. Box 2004, Pine Brook,
NJ 07058.
Instructivision, Inc., P.O. Box 2004, Pine Brook, NJ 07058
Telephone 973-575-9992 or 888-551-5144; fax 973-575-9134, website: www.instructivision.com
ii
, TABLE OF CONTENTS
Introduction iv
Glossary of Terms vi
Summary of Formulas, Properties, and Laws xvi
Practice Test A 1
Practice Test B 16
Practice Test C 33
Pre Algebra
Skill Builder One 51
Skill Builder Two 57
Skill Builder Three 65
Elementary Algebra
Skill Builder Four 71
Skill Builder Five 77
Skill Builder Six 84
Intermediate Algebra
Skill Builder Seven 88
Skill Builder Eight 97
Coordinate Geometry
Skill Builder Nine 105
Skill Builder Ten 112
Plane Geometry
Skill Builder Eleven 123
Skill Builder Twelve 133
Skill Builder Thirteen 145
Trigonometry
Skill Builder Fourteen 158
Answer Forms 165
iii
, INTRODUCTION
The American College Testing Program Glossary: The glossary defines commonly used
(ACT) is a comprehensive system of data mathematical expressions and many special and
collection, processing, and reporting designed to technical words.
assist students in the transition from high school to
college. The academic tests in English, mathe- Formulas: Formulas that are commonly applied to
matics, reading, and science reasoning emphasize mathematical problems are listed in a separate
reasoning and problem-solving skills. The test section. This section can be used as a convenient
items represent scholastic tasks required to reference for formulas relating to geometric shapes
perform college level work. and algebraic functions.
ACT questions are designed to measure a
wide range of abilities and knowledge. Practice Tests: There are three full-length practice
Consequently, some of the items are difficult while tests. Under actual testing conditions, you are
others are fairly easy. A background of strong allowed 60 minutes for the entire test. The
academic courses combined with a worthwhile instructions should be followed carefully.
review will enable you to meet this challenge Skill Builders: The skill builders describe and
successfully. illustrate each of the content areas in the
Mathematics Test. The skill builders are divided
The Mathematics Test into sections, each of which relates to one of the
The Mathematics Test is a 60-question, 60- principal categories covered in the test. Each skill
minute examination that measures mathematics builder consists of a series of examples, orientation
reasoning abilities. The test focuses on the exercises, practice exercises, and a practice test.
solution of practical quantitative problems that are
encountered in high school and some college The answers to the sample tests and the skill
courses. The test uses a work-sample approach builder exercises and practice tests are not found
that measures mathematical skills in the context of in the Student Workbook. They are included in the
simple and realistic situations. Each of the Teacher Manual.
multiple-choice questions has five alternative
responses. Examine the choices, and select the How the ACT is Scored
correct response. The “raw” score of 1 point for each correct
Three subscores based on six content areas are answer will be converted to a “scale” score. The
classified in the Mathematics Test (see chart, page scale on which ACT academic test scores are
v). The 60 test questions reflect an appropriate reported is 1-36, with a mean (or average) of 18,
balance of content and skills (low, middle, and based on a nationally representative sample of
high difficulty) and range of performance. October-tested 12th grade students who plan to
Because there is no penalty for guessing, answer enter two-year or four-year colleges or
every question. There are no trick questions; In universities. The scale for each subscore is 1-18,
some problems, you may have to go through a with a mean of 9. A guidance counselor will be
number of steps in order to find the correct answer. glad to answer questions regarding the scoring
In order to perform efficiently and accurately process and the score reports.
throughout the examination, you must understand
and apply fundamental mathematical concepts. Math Strategies
Spending too much time on any one item is 1. Answer all questions. First do those problems
unwise. On the average, spend about one minute with which you are most familiar and which
on each question. Any remaining time should be seem the easiest to solve, and then answer
spent in completing unanswered questions or those you find more difficult.
reviewing previous work. 2. Practice pacing yourself. Try to solve most of
the problems in less than one minute each.
How to Use the Mathematics Workbook 3. Pay close attention to the information in each
This workbook consists of the introduction, a problem. Use the information that is important
glossary of terms, formulas, three practice tests, in solving the problem.
skill builders, and additional questions for review. 4. If you are making an educated guess, try to
eliminate any choices that seem unreasonable.
iv
