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South Central ACT Strategies and Solutions Seminar ACT Test Tips and Strategies Vertical and Horizontal Alignment Overlap Between Tennessee Math Standards and ACT 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 1. Integers 2. Rational numbers 3. Statistics 4. Probability 5. Sequences Algebra 6. Operations 7. Single Variable Equations 8. Functions 9. Word Problems 10. Inequalities 11. Matrices 12. Complex Numbers 13. Systems of equations 24 Math Skills Tested on the ACT Coordinate Geometry 14. Points 15. Lines 16. Polynomials 17. Conic Sections 18. Reflections Plane Geometry 19. Lines and Slopes 20. Triangles 21. Polygons 22. Circles Other Topics 23. Solid Geometry 24. 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: 1. Angles 2. Lengths 3. Triangles 4. Quadrilaterals 5. Circles 6. Perimeter 7. Area 8. Volume • Total: 23 questions 9 coordinate geometry questions based on: 1. Slope 2. Distance 3. Midpoint 4. Parallel 5. Perpendicular lines 6. Points of intersection 7. 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=5x2 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 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: 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