Public flashcard deck
Practice slope, quadratics, percent change, probability and geometry with public formula flashcards and checked examples.
Reviewed
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Card 1 of 12
m = (y₂ − y₁)/(x₂ − x₁). Use the same subtraction order in numerator and denominator.
Example: Between (2,7) and (5,19), m = (19 − 7)/(5 − 2) = 4.
Card 2 of 12
y − y₁ = m(x − x₁), where (x₁,y₁) lies on the line.
Example: Slope 3 through (2,5): y − 5 = 3(x − 2), or y = 3x − 1.
Card 3 of 12
x = (−b ± √(b² − 4ac))/(2a). For real roots, the discriminant b² − 4ac must be nonnegative.
Example: For x² − 5x + 6 = 0, the roots are (5 ± 1)/2, or 2 and 3.
Card 4 of 12
For y = ax² + bx + c with a ≠ 0, x = −b/(2a). Substitute to find the y-coordinate.
Example: For y = −2x² + 12x + 5, x = 3 and y = 23.
Card 5 of 12
Multiply the starting value by 1 + p/100. For a p% decrease, use 1 − p/100.
Example: A 15% increase multiplies by 1.15; $80 becomes $92.
Card 6 of 12
A(t) = A₀(1 + r)^t when r is a decimal rate and t counts those periods.
Example: A quantity starting at 200 and growing 5% per period is 200(1.05)^t.
Card 7 of 12
Add all values and divide by the number of values.
Example: The mean of 4, 7 and 10 is 21/3 = 7.
Card 8 of 12
Count only outcomes meeting the stated condition, then count favorable outcomes within that restricted group.
Example: Of 28 art students, 18 are in grade 11: P(grade 11 given art) = 18/28 = 9/14.
Card 9 of 12
(x − h)² + (y − k)² = r² gives center (h,k) and positive radius r.
Example: (x − 3)² + (y + 2)² = 25 has center (3,−2) and radius 5.
Card 10 of 12
a² + b² = c², where c is the hypotenuse opposite the right angle.
Example: Legs 8 and 15 give c² = 64 + 225 = 289, so c = 17.
Card 11 of 12
sin(θ) = opposite/hypotenuse. Identify the sides relative to the named angle.
Example: If the opposite side is 15 and the hypotenuse is 17, sin(θ) = 15/17.
Card 12 of 12
Arc length = (θ/360) × 2πr, where θ is the central angle and r is the radius.
Example: For θ = 90° and r = 6, the arc is one quarter of 12π, or 3π.
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