5)2+ COS2Θ= 1425+ COS2Θ= 11COS2Θ= 225215COSΘ= L E S S O N S A N D...
5
)2
+ cos2
θ= 14
2
5
+ cos2
θ= 11
cos2
θ=2
2
5
21
5
cosθ=L e s s o n s a n d P r a c t i c e Q u e s t i o n s
Familiarizing yourself with the ACT before taking the test is a great way to improve your score. If you arefamiliar with the directions, format, types of questions, and the way the test is scored, you will be more com-fortable and less anxious. This section contains ACT math test-taking strategies, information, and practicequestions and answers to apply what you learn.The lessons in this chapter are intended to refresh your memory. The 80 practice questions followingthese lessons contain examples of the topics covered here as well as other various topics you may see on theofficial ACT Assessment. If in the course of solving the practice questions you find a topic that you are notfamiliar with or have simply forgotten, you may want to consult a textbook for additional instruction.Ty p e s o f M a t h Q u e s t i o n s
Math questions on the ACT are classified by both topicand skill level. As noted earlier, the six general topicscovered are:Pre-AlgebraElementary AlgebraIntermediate AlgebraTips• The math questions start easy and get harder. Pace yourself accordingly.• Study wisely. The number of questions involving various algebra topics is significantly higher thanthe number of trigonometry questions. Spend more time studying algebra concepts.• There is no penalty for wrong answers. Make sure that you answer all of the questions, even ifsome answers are only a guess.• If you are not sure of an answer, take your best guess. Try to eliminate a couple of the answerchoices.• If you skip a question, leave that question blank on the answer sheet and return to it when youare done. Often, a question later in the test will spark your memory about the answer to a ques-tion that you skipped.• Read carefully! Make sure you understand what the question is asking.• Use your calculator wisely. Many questions are answered more quickly and easily without a cal-culator.• Most calculators are allowed on the test. However, there are some exceptions. Check the ACTwebsite (ACT.org) for specific models that are not allowed.• Keep your work organized. Number your work on your scratch paper so that you can refer backto it while checking your answers.• Look for easy solutions to difficult problems. For example, the answer to a problem that can besolved using a complicated algebraic procedure may also be found by “plugging” the answerchoices into the problem.• Know basic formulas such as the formulas for area of triangles, rectangles, and circles. ThePythagorean theorem and basic trigonometric functions and identities are also useful, and not thatcomplicated to remember.Coordinate GeometryPlane GeometryTrigonometryIn addition to these six topics, there are three skill levels: basic, application, and analysis. Basic problemsrequire simple knowledge of a topic and usually only take a few steps to solve. Application problems requireknowledge of a few topics to complete the problem. Analysis problems require the use of several topics tocomplete a multi-step problem.The questions appear in order of difficulty on the test, but topics are mixed together throughout the test.Pre-AlgebraTopics in this section include many concepts you may have learned in middle or elementary school, such asoperations on whole numbers, fractions, decimals, and integers; positive powers and square roots; absolutevalue; factors and multiples; ratio, proportion, and percent; linear equations; simple probability; using charts,tables, and graphs; and mean, median, mode, and range.N
UMBERS
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Whole numbersWhole numbers are also known as counting numbers: 0, 1, 2, 3, 4, 5, 6, . . .■
IntegersIntegers are both positive and negative whole numbers including zero: . . .−3,−2,−1, 0, 1,