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

2. 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

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

4. 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.

5. 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.

6. 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

7. 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

8. 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

9. 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

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

11. 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.

12. 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: ( ) / 4 = 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%

13. 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

14. 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

15. 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. 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)

17. 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 = 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 = c² = 25 c = √25 c = 5

18. 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 = 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

19. 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

20. 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

21. 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.