Introduction
With just a few months left until the ACT, it’s time to intensify your preparation and leave no stone unturned. While practice and dedication are crucial, understanding the formulas tested on the ACT can give you a significant edge. This comprehensive formula sheet empowers you with the necessary mathematical knowledge to tackle the Math section with confidence.
Math Formulas for the ACT
The ACT Math section comprises 60 questions divided into three sections:
- Pre-Algebra/Elementary Algebra: 12 questions
- Intermediate Algebra/Coordinate Geometry: 26 questions
- Trigonometry/Plane Geometry: 22 questions
The formulas tested on the ACT are fundamental mathematical principles that you’ll use repeatedly throughout the exam. Having these formulas memorized and easily accessible will save you valuable time and mental energy.
Pre-Algebra/Elementary Algebra Formulas
1. Order of Operations:
* Parentheses first
* Exponents second
* Multiplication and Division (left to right)
* Addition and Subtraction (left to right)
2. Fractions:
* Simplifying: Divide the numerator and denominator by their greatest common factor.
* Multiplying: Multiply the numerators and denominators.
* Dividing: Flip the second fraction and multiply.
3. Decimals:
* Converting to fractions: Write the decimal as a fraction with a denominator of 10, 100, or 1000.
* Subtracting: Line up the decimal points and subtract.
4. Integers:
* Adding: Keep the signs the same and add the numbers.
* Subtracting: Subtract the second number from the first.
5. Absolute Value:
* Definition: The distance from zero on the number line.
* Property: |x| = x or -x (whichever is nonnegative)
Intermediate Algebra/Coordinate Geometry Formulas
1. Exponents:
* Multiplying: Multiply the bases and add the exponents.
* Dividing: Divide the bases and subtract the exponents.
* Power of a power: Raise the base to the power of the second exponent
2. Equations:
* Solving for x: Isolate x on one side of the equation.
* Quadratic formula: x = (-b ± √(b² – 4ac)) / 2a
3. Systems of Equations:
* Substitution: Solve for x in one equation and substitute it into the other.
* Elimination: Add or subtract equations to eliminate one variable.
4. Lines:
* Slope: m = (y₂ – y₁) / (x₂ – x₁)
* Point-slope form: y – y₁ = m(x – x₁)
* Slope-intercept form: y = mx + b
5. Circles:
* Equation: (x – h)² + (y – k)² = r²
* Center: (h, k)
* Radius: r
Trigonometry/Plane Geometry Formulas
1. Trigonometry:
* Sine: sin θ = opposite / hypotenuse
* Cosine: cos θ = adjacent / hypotenuse
* Tangent: tan θ = opposite / adjacent
* Pythagorean Theorem: a² + b² = c²
2. Angles:
* Supplementary: Add to 180°
* Complementary: Add to 90°
* Vertical: Opposite angles formed by intersecting lines
3. Triangles:
* Area: A = ½ bh
* Perimeter: P = a + b + c
* Law of Sines: a / sin A = b / sin B = c / sin C
* Law of Cosines: c² = a² + b² – 2ab cos C
Tables for Quick Reference
Table 1: Fraction-Decimal Equivalents
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/4 | 0.25 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
| 1/10 | 0.1 |
Table 2: Common Trig Values
| Angle | Sin | Cos | Tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | Undefined |
Table 3: Geometry Formulas
| Shape | Formula |
|---|---|
| Rectangle | Area = length × width |
| Square | Area = side² |
| Triangle | Area = ½ × base × height |
| Circle | Area = πr² |
| Sphere | Volume = (4/3)πr³ |
Table 4: Order of Operations
| Step | Operation |
|---|---|
| 1 | Parentheses |
| 2 | Exponents |
| 3 | Multiplication and Division (left to right) |
| 4 | Addition and Subtraction (left to right) |
Conclusion
The ACT Test Formula Sheet is an indispensable resource for any student preparing for the exam. By memorizing and understanding these formulas, you’ll not only save time and mental energy but also increase your confidence in tackling the math section. Whether you’re a math whiz or struggling to keep up, using these formulas to your advantage will give you a significant boost on test day. So, print this sheet out, review it regularly, and conquer the ACT Math section with ease!