ACING THE ACT MATH SECTION. Seth Keene Jefferson Academy

Transcription

1 ACING THE ACT MATH SECTION Seth Keene Jefferson Academy

2 The Mathematics Test is a 60-question, 60- minute test designed to assess the mathematical skills students have typically acquired in courses taken by the end of 11th grade (Algebra 1 and 2, Geometry, Trigonometry, and Pre-Calculus). Students need knowledge of basic formulas and computational skills to answer the problems, but aren't required to know complex formulas or perform extensive computations. Calculators may be used on the Mathematics Test, but are not required as all problems can be solved without a calculator. MATH TEST OVERVIEW

3 Pre-Algebra/Elementary Algebra Pre-Algebra (14 questions) Elementary Algebra (10 questions) Intermediate Algebra/Coordinate Geometry Intermediate Algebra (9 questions) Coordinate Geometry (9 questions) Plane Geometry/Trigonometry Plane Geometry (14 questions) Trigonometry (4 questions) MATH SUB-TESTS

4 Basic operations using whole numbers, integers, fractions, decimals and percents Place Value Square roots and approximations Exponents Scientific Notation Factors Ratio, proportion, and percent Linear equations in one variable Absolute value and ordering numbers Counting techniques and simple probability Data collection, representation, and interpretation Simple descriptive statistics PRE-ALGEBRA (14)

5 Properties of exponents and square roots Evaluation of algebraic expressions through substitution Using variables to express functional relationships Understanding algebraic operations Solutions of quadratic equations by factoring ELEMENTARY ALGEBRA (10)

6 Understanding of the quadratic formula Rational and radical expressions Absolute value equations and inequalities Sequences and patterns Systems of equations Quadratic inequalities Functions and modeling Matrices Roots of polynomials Complex numbers INTERMEDIATE ALGEBRA (9)

7 Graphing points, lines, polynomials, circles, and other curves Relations between graphs and equations Graphing inequalities Slope Parallel and perpendicular lines Distance Midpoints Conics COORDINATE GEOMETRY (9)

8 Angles and relations between parallel and perpendicular lines Properties of circles, triangles, rectangles, parallelograms, and trapezoids Transformations Concept of proof and proof techniques Three dimensional shapes and volume PLANE GEOMETRY (14)

9 Trigonometric relations in right triangles Values and properties of trigonometric functions Graphing trigonometric functions Modeling with trigonometric functions Use of trigonometric identities Solving trigonometric equations TRIGONOMETRY (4)

10 Converting Raw Scores to Scale Scores (Table 1) Raw % Scale UNDERSTANDING SCORES

11 National Average 21.0 (Math) 21.1 (Composite) Middle 50% of Applicants: Ivy league, Notre Dame, Stanford: Major Public Universities: SD Board of Regents: Minimum 18 Composite $5000 Guaranteed for 24 or better* WHAT IS A GOOD SCORE?

12 #1 4+ Years of Math #2 ACT Preparation Course #3 ACT Practice Workbook Ideal Preparation Plan: 10% Understanding Test 80% Reviewing Weakest Skills 10% Test-taking Strategies TEST PREPARATION

13 Online/Self-Paced Courses: ACT Online Prep ($19.95) Career Cruising / Student Edge (FREE) Practice Books Preparing for the ACT (FREE) The Real ACT Prep Guide ($19.95) (Note: These are effective only if practice tests taken under actual test day circumstances.) Classroom Review Courses Sylvan Learning Center (FREE Practice Test) Career Learning Center My Review Class PREPARATION RESOURCES

14 Pace Yourself (Announcement only made when 5 minutes remain) Read directions before test date Read questions carefully (annotate) Answer easy questions first Answer EVERY question (no penalty for guessing) Be precise in marking answer and don t make notes on answer sheet GENERAL TEST-TAKING TIPS

15 Draw a picture if one is not provided. Figures given are not drawn to scale, so mark them with given measures or symbols (such as parallel or congruent). In square ABCE, D is the midpoint of CE. Which of the following is the ratio of the area of ADE to the area of ADB? MATH TEST-TAKING TIPS

16 Know the following translations: is means equals, of means multiply and per means divide. If 40% of a given number is 8, then what is 15% of the given number? MATH TEST-TAKING TIPS

17 Know the formulas for area and perimeter of triangles, rectangles, and circles, and volume of boxes. Formulas for all other figures will be given. Cube A has an edge length of 2 inches and Cube B has an edge length double that of Cube A. What is the volume of Cube B? What is the total surface area of a right cylinder with a base diameter of 20 cm and a height of 20 cm. (Note: The surface area of a cylinder is given by 2πr 2 + 2πrh) MATH TEST-TAKING TIPS

18 If a problem is given in terms of fractions, decimals, or percents, consider using an alternate form to find the answer. Remember that fractions represent a division problem and percents are fractions with 100 in the denominator. Simplify: (3/4)(2/9) (2/5)(5/6) MATH TEST-TAKING TIPS

19 If the question and/or answer set are given in terms of variables only, substitute simple numbers such as 1, 2, and 3 (or 100 in the case of a percent problem) to find the answer. For every positive two-digit number, x, with tens digit t and units digit u, let y be the two-digit number formed by reversing the digits of x. Which of the following expressions is equivalent to x y? a. 9(t-u) b. 9(u-t) c. 9t-u d. 9u t e. 0 MATH TEST-TAKING TIPS

20 Most answers are listed from least to greatest, so you can use a technique called backsolving to find the correct answer: start by trying the number given as choice C or H (the middle value) and then eliminate choices based on the result. Tom has taken 5 of 8 equally weighted tests for the semester and he has an average of 78.0 points. How many points does he need to earn on the 6 th test to bring his average score up to exactly 80.0 points? a. 79 b. 80 c. 82 d. 88 e. 90 MATH TEST-TAKING TIPS

21 Read each question carefully and be on the lookout for words such as not and except. To ensure you are answering the correct question, it may be a good idea to underline or circle it in your test booklet. Find the perimeter of the right triangle whose legs measure 8cm and 15cm. a.17cm b.23cm c.40cm d.60cm e. 120cm MATH TEST-TAKING TIPS

22 Do not overuse it! The test is written so that every problem can be solved without a calculator. Practice with it beforehand. It may not help to borrow a more powerful graphing calculator on the day of the test if you don t know how to use it. A good rule of thumb is: Think with your pencil. Set up the problem in your test booklet first and take a moment to consider what a reasonable answer would be. Make sure it is set on DEG (for degree) and not RAD. Know how to change the setting if needed. CALCULATOR TIPS

23 Questions? Reminders of upcoming test dates and registration deadlines Distribute materials Information Requests GO ACE THE ACT! CONCLUSION