METHOD TEST PREP EDUCATIONAL SERIES Preparing for the SAT and ACT Mathematics Sections: Best Practices Evan Wessler Vice President of Education evan@methodtestprep.com

SAT vs. ACT Mathematics Sections Part I The Basics SAT vs. ACT Mathematics Sections

What’s the Difference? Parameter SAT ACT STRUCTURE 3 sections, 48 questions 25-min, 20 MC 25-min, 8 MC + 10 grid 20-min, 16 MC 1 section, 60 questions 60-min, all MC CONTENT Arithmetic Geometry Algebra I Algebra II (functions) Algebra I & II Trigonometry SCORING 200-800 MC GRIDS 1-36 CORRECT +1 raw INCORRECT –1/4 raw OMIT SCALING 1 raw pt ≈ 10 scaled pts 1-2 raw pts ≈ 1 scaled pt FORMULAS All necessary provided Most NOT Provided

The Good News Significant degree of content overlap Most colleges now accept both exams ACT favors fast test-takers who excel with content in their classes; SAT favors strong logical thinkers ACT problems are typically more straightforward Good strategy: take both, compare scores using an approved score concordance table Source: http://www.act.org/aap/concordance/

Part II Content and Strategies SAT and ACT Concepts Side-by-Side

Arithmetic and Algebra: Variables & Plugging in Numbers SAT ACT Strategy: Plugging in Numbers – one of the most crucial techniques Both problems, while ranked “medium” difficulty, can be solved easily by substituting appropriate numbers for variables Multi-case options are common on SAT, not on ACT

Arithmetic and Algebra: Word Problems and Plugging In SAT ACT Strategy: Plugging in Numbers for students with weaker algebraic reasoning skills “Easy” problems that should be givens for any student This kind of problem is common for SAT grid-in questions with definite numbers

Arithmetic and Algebra: Operations SAT ACT ACT: straightforward – similar to quiz or homework problems SAT: problems require a combination of operations Technique: laws of exponents Exponents, FOIL & factoring, radicals & roots tested on both exams Strategy example: always factor difference of perfect squares

Arithmetic and Algebra: Strange Symbols SAT ACT Technique: use position as guide. Ex. The “stuff” on the left side of the arrow goes everywhere there is an a in the formula Emphasize similarity to functions Most students are thrown by “new” operations – they must know that all that is required is to follow directions

Arithmetic and Algebra: Statistics and Probability SAT ACT Technique: stress that total # of elements must be multiple of denominator(s) “Part / Whole” concept employed in simple and difficult situations Independent events, dependent events (“without replacement” problems)

Arithmetic and Algebra: Statistics and Probability SAT ACT Technique: students must write down the formula for arithmetic mean (Avg = sum of numbers / # of terms) Strategy: encourage students to create a small set of numbers to test when necessary (this is a very useful SAT strategy) Strategy: first, phrase everything in terms of the average equation; next, cross-multiply

Geometry: Circles SAT ACT 30º P Q R SAT ACT B π A 4 θ O Technique: circle proportions and finding fractions of figures Proportionality, application of formulas involved in both problems

Geometry: Angles SAT ACT k a b x 1 m 2 8 9 yº 3 10 c 11 xº 4 n 5 6 7 12 13 14 15 d Parallel line geometry: supplements, corresponding, alternate interior, vertical angles Usually also appear in parallelograms and trapezoids (parallel sides/bases and supplementary consecutive angles)

Geometry: Area, Perimeter, Solids SAT ACT A B E C D 6 Students must integrate various principles of geometry in a single problem: area, perimeter, terminology: ACT more straightforward Technique: students MUST mark figure to maximum possible extent Common figures are quadrilaterals, right, isosceles, and equilateral triangles, circles, spheres, cubes, rectangular prisms

Coordinate Geometry SAT ACT Large emphasis on parallel/perpendicular slope relationships Substituting coordinates into equations to solve for unknown coordinates/slopes/intercepts Figures in the coordinate plane, especially circles and triangles Technique: students should be aware that if there is a question involving equations and points, they will need to plug coordinates into equations (students very typically forget they can do this)

Functions SAT ACT SAT: understanding function notation & simple operations in both algebraic and graphical contexts (i.e. points, transformations) ACT: adds in composition of functions Strategy: make sure students know notation, understand that y=f(x)

Part III Key Differences Topics Unique to the ACT

On the ACT, Not the SAT Algebra II Trigonometry Logarithms Simple matrices & operations Imaginary & complex numbers Trigonometry Basic trigonometric function calculations and graphs Reciprocal and arc trigonometric functions Laws of sines, cosines Unit circle

In Summary The SAT and ACT have some unique characteristics, but are largely similar tests Both exams are highly predictable, and are thus teachable Consistent practice with problems is essential to raising scores Teach not only math concepts, but also typical “give-aways” that indicate the problem type

Questions? evan@methodtestprep.com Thanks for Listening! Questions? evan@methodtestprep.com