Admin
14 Jun 2026 10:48
admin
#general
ACT Math Section Cheat Sheet
The ACT Math test is a 60-minute, 60-question assessment designed to measure the mathematical skills students have typically acquired in courses taken up to the beginning of grade 12. This cheat sheet provides essential concepts, formulas, and strategies to help you succeed.
Structure of the ACT Math Section
- 60 questions in 60 minutes (1 minute per question average)
- Questions increase in difficulty from 1-60
- Five topic areas with approximate percentages of questions:
- Pre-Algebra (20-25%) Questions 1-15
- Elementary Algebra (15-20%) Questions 6-20
- Intermediate Algebra (15-20%) Questions 16-40
- Coordinate Geometry (15-20%) Questions 21-50
- Plane Geometry (20-25%) Questions 26-55
- Trigonometry (5-10%) Questions 46-60
- Calculator permitted for all questions
- No formula sheet provided
Tip: The first 30 questions should be completed easily and quickly to save time for harder problems later. Don't spend more than 1-2 minutes on any question initially.
Pre-Algebra Concepts
Operations with Fractions
- Adding/subtracting: Find a common denominator
- Multiplying: Multiply numerators and denominators separately
- Dividing: Multiply by the reciprocal of the second fraction
- Simplify fractions by dividing numerator and denominator by their GCF
Operations with Decimals
- Adding/subtracting: Line up decimal points
- Multiplying: Multiply as integers, then place decimal point (sum of decimal places)
- Dividing: Move decimal in divisor to make it whole, move decimal in dividend same amount, then divide
Percentages
Percentage = (Part Whole) 100%
Part = Whole Percentage (as a decimal)
Whole = Part Percentage (as a decimal)
Proportions
a/b = c/d
Cross-multiply: ad = bc
Basic Statistics
- Mean: Sum of values number of values
- Median: Middle value when arranged in order
- Mode: Most frequently occurring value
- Range: Difference between highest and lowest values
Basic Probability
P(Event) = Favorable outcomes Total possible outcomes
P(A and B) = P(A) P(B) (for independent events)
P(A or B) = P(A) + P(B) - P(A and B)
Elementary Algebra Concepts
Variables and Expressions
- Combine like terms
- Apply distributive property: a(b + c) = ab + ac
- Evaluate expressions by substituting values
Solving Linear Equations
- Isolate the variable using inverse operations
- Remember to do the same operation to both sides
- Check your solution by substituting back
Inequalities
Warning: When multiplying or dividing an inequality by a negative number, reverse the inequality sign.
Systems of Equations
- Substitution: Solve one equation for a variable and substitute into the other
- Elimination: Add or subtract equations to eliminate one variable
Exponents
a^m a^n = a^(m+n)
(a^m)^n = a^(mn)
(ab)^n = a^n b^n
a^m a^n = a^(m-n)
a^0 = 1 (if a 0)
a^(-n) = 1/a^n
Radicals
(ab) = a b
(ab) = a b
a = |a|
Intermediate Algebra Concepts
Quadratic Equations
ax + bx + c = 0
Quadratic formula: x = (-b (b-4ac)) / 2a
Factoring: Find two numbers that multiply to ac and add to b
Vertex form: y = a(x-h) + k, where vertex is (h,k)
Functions
- Domain: Set of all possible input values (x)
- Range: Set of all possible output values (y)
- f(x) notation: f(g) means evaluate the function at x = g
- Composition: f(g(x)) means apply function g to x, then apply function f to the result
Polynomials
- Adding/subtracting: Combine like terms
- Multiplying: Use distributive property (FOIL for binomials)
- Dividing: Long division or synthetic division
Complex Numbers
i = (-1), so i = -1
a + bi form for complex numbers
(a+bi)(c+di) = ac - bd + (ad+bc)i
Sequences and Series
- Arithmetic sequence: Each term is previous term plus constant difference d
- a_n = a_1 + (n-1)d
Coordinate Geometry Concepts
Distance and Midpoint Formulas
Distance between (x, y) and (x, y): [(x-x) + (y-y)]
Midpoint between (x, y) and (x, y): ((x+x)/2, (y+y)/2)
Slope
Slope (m) = (y-y) / (x-x)
Slope-intercept form: y = mx + b
Point-slope form: y-y = m(x-x)
Parallel and Perpendicular Lines
- Parallel lines have equal slopes: m = m
- Perpendicular lines have slopes that are negative reciprocals: m m = -1
Circles in the Coordinate Plane
Standard form: (x-h) + (y-k) = r
Center: (h,k), Radius: r
Graphing
- Linear equations: Graph as straight lines
- Quadratic equations (y = ax + bx + c): Graph as parabolas
- Absolute value equations (y = |ax + b|): V-shaped graphs
Plane Geometry Concepts
Angles
- Complementary angles sum to 90
- Supplementary angles sum to 180
- Vertical angles are equal
- Angles around a point sum to 360
- Interior angles of a triangle sum to 180
Triangles
Area = (1/2) base height
Pythagorean theorem: a + b = c (for right triangles)
Special Right Triangles
- 30-60-90 triangle: sides are 1, 3, 2 (short leg opposite 30)
- 45-45-90 triangle: sides are 1, 1, 2
Triangle Classification
- Equilateral: all sides equal, all angles 60
- Isosceles: at least two sides equal, base angles equal
- Scalene: all sides different
- Right: one 90 angle
Quadrilaterals
| Shape | Properties | Area Formula |
|---|---|---|
| Rectangle | Opposite sides equal, all angles 90 | length width |
| Square | All sides equal, all angles 90 | side |
| Parallelogram | Opposite sides parallel and equal | base height |
| Trapezoid | One pair of parallel sides | (1/2) (sum of parallel sides) height |
Circles
Area = r
Arc length = (/360) 2r
Tangent line is perpendicular to radius at point of tangency
Polygons
Sum of interior angles = (n-2) 180 (where n is the number of sides)
Trigonometry Concepts
```Basic Trig Functions
sin() = opposite/hypotenuse
cos() = adjacent/hypotenuse
tan() = opposite/adjacent = sin()/cos()
Reciprocal Trig Functions
csc() = 1/sin()
sec() = 1/cos()
cot() = 1/tan() = cos()/sin()
Unit Circle Values
| Angle | 0 | 30 | 45 | 60 | 90 |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 2/2 | 3/2 | 1 |
| cos | 1 | 3/2 | 2/2 | 1/2 | 0 |
| tan | 0 | 3/3 | 1 | 3 | Undefined |
Trig Identities
sin() + cos() = 1
tan() + 1 = sec()
1 + cot() = csc()
sin(2) = 2sin()cos()
cos(2) = cos() - sin() = 1 - 2sin() = 2cos() - 1
Test-Taking Strategies
Time Management
- Spend roughly 1 minute per question
- Don't get stuck on difficult problems; mark them and return if time permits
- Set mini-time goals: Question 20 by 20 minutes, Question 40 by 40 minutes
- Answer easier questions first to build confidence
Process of Elimination
- Eliminate obviously wrong answers to improve your odds
- Use estimation to narrow down choices
- Test answer choices when appropriate (especially for algebra problems)
Problem-Solving Techniques
- Draw diagrams for geometry problems
- Substitute numbers for variables in algebra problems
- Look for patterns and relationships
- Work backwards from the answer when stuck
- Break complex problems into smaller, manageable parts
Tip: There's no penalty for wrong answers on the ACT, so never leave a question blank. Even if you can only eliminate one answer choice, you should guess from the remaining options.
Essential Formulas to Memorize
Geometric Formulas
Rectangle: Perimeter = 2(l+w); Area = lw
Square: Perimeter = 4s; Area = s
Triangle: Perimeter = a+b+c; Area = (1/2)bh
Circle: Circumference = 2r; Area = r
Cylinder (surface area): A = 2r + 2rh
Sphere (surface area): A = 4r
Rectangular Prism (volume): V = lwh
Cylinder (volume): V = rh
Sphere (volume): V = (4/3)r
Algebraic Formulas
Slope: m = (y-y)/(x-x)
Midpoint: ((x+x)/2, (y+y)/2)
Discriminant: = b - 4ac (determines number of solutions)
Trigonometric Formulas
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Tip: Practice using these formulas in context. Being able to recognize when to apply a formula is as important as knowing the formula itself.
Reference Files For ACT MATH SECTION CHEAT SHEET
Screenshoot
File Name
act_math_formula_cheat_sheet_2021.pdf
File Size
1.53 MB
File Type
PDF
File Site
Description
This file is just a reference file for ACT MATH SECTION CHEAT SHEET. Does not guarantee that the specific things you want are included in it.
Direct download (wait 10 seconds)
Authority Under Section 56(6) Of The Nursing Act, 2005 (Act 33 Of 2005) and Reference File...
Admin
2026-06-12 22:52:06
- **Sheet 1**: "harga Satuan Upah Dan Bahan" - **Sheet 2**: "pagar Beton" - **Sheet 3**:...
Admin
2026-05-30 02:15:06
Cookie Consent
We use cookies to enhance your browsing experience and analyze site traffic. By clicking 'Accept all cookies', you agree to the use of these cookies. You can manage your preferences or learn more in our [Privacy Policy/Cookie Policy.