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

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

3. 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 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

4. 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:

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

6. 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

7. 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

8. 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

9. 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

10. 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)

11. 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

12. 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

13. Geometry: Angles SAT ACTk 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)

14. 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

15. 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)

16. 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)

17. Part III Key Differences
Topics Unique to the ACT

18. 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

19. 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

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