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Essential formulas for the ACT?

Hey everyone, I'm taking the ACT pretty soon and I'm stressing a bit. Are there any essential formulas or concepts I should definitely memorize before the test? Thanks in advance!

6 months ago

Hello! It's normal to feel stressed before a big exam, but making sure you're prepared can help alleviate that stress. Here's a list of essential formulas and concepts that you should be familiar with for the ACT Math section:

1. Arithmetic formulas:

- Distance = Rate × Time

- Percent Change = [(New Value - Old Value) / Old Value] × 100

- Average (Mean) = Sum of Values / Number of Values

2. Geometry formulas:

- Area of Rectangles: A = l × w

- Area of Triangles: A = ½ × b × h

- Area of Circles: A = π × r^2

- Circumference of Circles: C = 2 × π × r

- Pythagorean Theorem: a^2 + b^2 = c^2 (for right triangles)

- SOHCAHTOA (sine, cosine, tangent ratios in right triangles)

3. Algebra:

- Slope-intercept form of a line: y = mx + b (m = slope, b = y-intercept)

- Point-slope form of a line: y - y₁ = m(x - x₁)

- Slope formula: m = (y₂ - y₁) / (x₂ - x₁)

- Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a (for ax^2 + bx + c = 0)

- Exponent rules: a^(m+n) = a^m × a^n, a^(m-n) = a^m / a^n, (a^m)^n = a^(mn)

4. Trigonometry:

- Unit Circle values (30°, 45°, 60°)

- Sine, Cosine, and Tangent functions and their inverses

- Law of Sines: (a / sin(A)) = (b / sin(B)) = (c / sin(C))

- Law of Cosines: c² = a² + b² - 2ab × cos(C)

5. Probability and statistics:

- Independent events: P(A and B) = P(A) × P(B)

- Dependent events: P(A and B) = P(A) × P(B | A)

- Complementary events: P(A') = 1 - P(A)

- Mean, median, mode, and range calculations

6. Logarithms

- Logarithm rules:

- logb(a × c) = logb(a) + logb(c)

- logb(a / c) = logb(a) - logb(c)

- logb(a^c) = c × logb(a)

These concepts should cover most of what you'll encounter on the ACT Math Section. It's a good idea to practice using these formulas in the context of real test questions. Make sure you understand how to apply the formulas, not just memorize them. And don't forget that the ACT does provide some formulas in the beginning of the Math section, but it's best not to rely solely on those. Good luck with your preparation!

6 months ago

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