South Central ACT Strategies and Solutions Seminar ACT Test Tips and Strategies

Vertical and Horizontal Alignment The following chart shows how the domains within the current Tennessee academic standards in mathematics build on one another. When you read the chart vertically, you will see which math domains students are learning each year. When you read the chart horizontally, you will see how the math domains build on one another across a student’s academic career

Overlap Between Tennessee Math Standards and ACT The navy blue areas indicate where Tennessee math standards overlap with ACT Readiness Standards within each domain.

What Determines Student Success on the ACT Mathematics Subtest? The ACT College and Career Readiness Standards for mathematics are a combination of skills taught beginning as early as grade 2 and extending through a student’s fourth year high school mathematics course. In order for a student to attain a 21 or higher, the student needs instruction focused on developing a content-rich, conceptual understanding of mathematics at all grade levels.

What Determines Student Success on the ACT Mathematics Subtest? Students need to develop an understanding of the following: which math ideas are most important, and why they are important which ideas are useful in a particular context for problem solving why and how certain key ideas aid in problem solving, which reminds us of the systematic progression of math how and why an idea or procedure is mathematically defensible how to flexibly adapt previous experience to new transfer problems.

24 Math Skills Tested on the ACT Numbers Integers Rational numbers Statistics Probability Sequences Algebra Operations Single Variable Equations Functions Word Problems Inequalities Matrices Complex Numbers Systems of equations

24 Math Skills Tested on the ACT Coordinate Geometry Points Lines Polynomials Conic Sections Reflections Plane Geometry Lines and Slopes Triangles Polygons Circles Other Topics Solid Geometry Trigonometry

Algebra 14 pre-algebra questions based on math terminology (integers, prime numbers, and so on), basic number theory (rules of zero, order of operations and so on), and manipulation of fractions and decimals 10 elementary algebra questions based on inequalities, linear equations, ratios, percents, and averages 9 intermediate algebra questions based on exponents, roots, simultaneous equations, and quadratic equations Total: 33 questions

Geometry 14 plane geometry questions based on: Angles Lengths Triangles Quadrilaterals Circles Perimeter Area Volume Total: 23 questions 9 coordinate geometry questions based on: Slope Distance Midpoint Parallel Perpendicular lines Points of intersection Graphing

Trigonometry 4 questions based on: Basic sine Cosine Tangent functions Trig identities Graphing Total: 4 questions

ACT Math Formulas The ACT does not always provide formulas at the beginning of the Math Test. This means you need to memorize relevant formulas, so you can recall them quickly as needed.

16 Most Common ACT Math Formulas 1. Arithmetic mean (average) = Sum of values / Number of values Used to calculate the mean value of a given set of numbers. Ex: (10 + 12 + 14 + 16) / 4 = 13 2. Probability = Target outcomes / Total outcomes Used to calculate the chances of something occurring from a set of possible outcomes. Ex: A jar contains five blue marbles, five red marbles, and ten white marbles. What is the probability of picking a red marble at random? 5 / 20 = .25 or 25%

16 Most Common ACT Math Formulas 3. Quadratic Formula: x = −b ± √b²-4ac/2a Used for determining the x-intercepts of a quadratic (parabolic) equation. Ex: A = 1, B = -4, C = 4 x = -4 ± √4² – 4 (1)(4) / 2(1) x = 4 ± √ 16 – 4(4) / 2 x = 4 ± √16 – 16 / 2 x = 4 ± √ 0 / 2 x = 4 / 2 x = 2

16 Most Common ACT Math Formulas 4. Distance Formula: d=√(x2 – x1)² + (y2 – y1)² Calculate the distance between two points on a coordinate plane. Ex. Find the distance between points (6, 6) and (2, 3) d=√(6 – 2)² + (6 – 3)² d=√(4)² + (3)² d=√16 + 3 d=√25 d = 5

16 Most Common ACT Math Formulas 5. Slope Formula: Slope = y₂ – y₁ / x₂ – x₁ Calculate the slope (angle) of a line that connects two points on a plane. Ex: Coordinates = (-2, -1) (4, 3) s = 3 – (-1) / 4 – (-2) s = 4 / 6 s = 2 / 3 6. Slope Intercept: y=mx+b Formula the defines a line on a plane, given a known slope and y-intercept. Ex: Slope = 2, Intercept point (0,3) y = 2x+3

16 Most Common ACT Math Formulas 7. Midpoint Formula: (x₁+x₂) / 2, (y₁+y₂) / 2 Calculates the midpoint between to points on a plane. Ex: Find the midpoint between (-1, 2) and (3, -6) (-1 + 3) / 2, (2 + -6) / 2 2 / 2, -4 / 2 Midpoint (1, -2)

16 Most Common ACT Math Formulas 8. Area of Triangle: area = (1/2) (base) (height) Calculate the total area within a triangle based on the lengths of the sides. Ex: Base = 5, Height = 8 a = 1/2 (5)(8) a = 1/2 (40) a = 20 9. Pythagorean Theorem: a²+b²=c² Used to calculate the length of an unknown side of a right triangle, given two sides are known. Ex: a = 3, b = 4 c² = 3² + 4² c² = 9 + 16 c² = 25 c = √25 c = 5

16 Most Common ACT Math Formulas 10. Area of Rectangle: area = length x width Calculates the total area within a rectangle shape. Ex: length = 5, width = 2 a = 5 x 2 a = 10 11. Area of Parallelogram: area = base x height Calculates the total area within a parallelogram. Ex: base = 6, height = 12 a = 6 x 12 a = 72

16 Most Common ACT Math Formulas 12. Area of Circle: π * r² Calculates the total area within a circle. Ex: radius = 4 a = π x 4² a = π x 16 a = 50.24 13. Circumference of Circle: circumference = 2π *  r Calculate the length of the outline of a circle. Ex: radius = 7 c = 2π x 7 c = 43.98

16 Most Common ACT Math Formulas 14. Sine (SOH): Sine = opposite / hypotenuse A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle. Ex: opposite = 2.8, hypotenuse = 4.9 s = 2.8 / 4.9 s = 0.57 15. Cosine (CAH): Cosine = adjacent / hypotenuse Ex: adjacent = 11, hypotenuse = 13 c = 11 / 13 c = 0.85

16 Most Common ACT Math Formulas 16. Tangent (TOA): Tangent = opposite / adjacent A trigonometric identity that represents the relative sizes of the sides of a triangle and can be used to calculate unknown sides or angles of the triangle. Ex: opposite = 15, adjacent = 8 t = 15 / 8 t = 1.87 Of course, there Of course, there are more formulas that might pop up on the ACT, but these ones are the most common and therefore, the most critical to know. Memorize these formulas, study, practice, and you’ll be just fine come test day.