I've heard there isn't a provided formula sheet on the ACT. Could someone please tell me which math equations or formulas are crucial to know for the test? Any help would be appreciated!
Absolutely! While the ACT doesn't provide a formula sheet, most of the essential equations you need to know are typically covered in your high school math classes. Here's a list of some important math formulas and concepts to have in mind when preparing for the ACT:
1. Basic Algebra: Make sure you're comfortable working with slopes, intercepts, and linear equations. For example, the slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
2. Quadratic Formula: The quadratic formula is essential for solving quadratic equations: x = (-b ± √(b² - 4ac)) / 2a.
3. Pythagorean Theorem: For right triangles, the Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse.
4. SOHCAHTOA: This acronym helps you remember the trigonometric ratios of sine, cosine, and tangent in right triangles. It stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.
5. Area and Circle Formulas:
- Rectangle: A = lw (length times width)
- Triangle: A = ½bh (one-half base times height)
- Circle: A = πr² (pi times radius squared)
- Circumference of a circle: C = 2πr or πd (2 times pi times radius or pi times diameter)
6. Volume Formulas:
- Rectangular Prism: V = lwh (length times width times height)
- Cylinder: V = πr²h (pi times radius squared times height)
- Sphere: V = (4/3)πr³ (four-thirds times pi times radius cubed)
7. Mean, Median, and Mode: Know how to calculate the average (mean), middle number (median), and most frequently occurring number (mode) in a set of numbers.
8. Exponents and Radicals: Understand the basic properties of exponents and radicals:
- a^n a^m = a^(n + m)
- a^n / a^m = a^(n - m)
- (a^n)^m = a^(nm)
- √(a b) = √a √b
9. Probability: Calculate probability using the formula: P(event) = Number of successful outcomes / Total possible outcomes.
10. Permutations and Combinations: Understand how to calculate permutations (when order matters) and combinations (when order doesn't matter) for arranging items or choosing items from a set.
While this list covers many key formulas and concepts for the ACT, it's still a good idea to practice various problem types so that you're prepared for any question the test might throw at you. Good luck!
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