I'm gearing up to take my ACT soon, and I'm focusing on improving my math score. Can anyone give me some essential math formulas that I should know for the ACT? Like, what are the most commonly used formulas that'll help me the most?
I'm happy to provide you with some essential formulas that'll be useful for the ACT Math section. Keep in mind that mastering these formulas isn't your only priority; understanding how to apply them is just as important. Here are some key formulas you should know:
1. Slope-intercept form of a linear equation: y = mx + b
m = slope
b = y-intercept
2. Point-slope form of a linear equation: y - y1 = m(x - x1)
3. Distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
4. Midpoint formula: M = ((x1 + x2)/2 , (y1 + y2)/2)
5. Quadratic formula: x = (-b ± √(b^2 - 4ac))/(2a)
6. Vertex form of a quadratic equation: y = a(x - h)^2 + k
(h, k) = vertex coordinates
7. Pythagorean theorem: a^2 + b^2 = c^2
8. Area of a triangle: A = (1/2)bh
b = base
h = height
9. Trigonometric ratios (right triangles):
Sin(θ) = opposite / hypotenuse
Cos(θ) = adjacent / hypotenuse
Tan(θ) = opposite / adjacent
10. Volume of a rectangular solid: V = lwh
l = length
w = width
h = height
11. Circle equations:
Circumference: C = 2πr or C = πd
Area: A = πr^2
12. Special triangles:
30-60-90 triangle: opposite 30° = (1/2)hypotenuse, opposite 60° = (√3/2)hypotenuse
45-45-90 triangle: legs = (1/√2)hypotenuse
Of course, this list is not exhaustive, but these formulas should give you a solid base for tackling most ACT Math problems. Make sure you practice applying them in various contexts to become familiar with using them on the test. Good luck!
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