METHOD TEST PREP EDUCATIONAL SERIES Preparing for the

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

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 II (functions) Arithmetic Geometry Algebra I & II Trigonometry 200 -800 CORRECT SCORING INCORRECT OMIT SCALING FORMULAS MC GRIDS 1 -36 MC +1 raw CORRECT – 1/4 raw 0 INCORRECT 0 0 0 OMIT 0 +1 raw pt ≈ 10 scaled pts 1 -2 raw pts ≈ 1 scaled pt 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: 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 Q A π B θ P 30º R 4 O • Technique: circle proportions and finding fractions of figures • Proportionality, application of formulas involved in both problems

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

Geometry: Area, Perimeter, Solids SAT ACT A E D • • • B 6 C 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 – 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

Thanks for Listening! Questions? evan@methodtestprep. com