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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
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