Math Formulas Every Student Should Know

Shared by Aral.ai Team 20 cards 0 saves

You get your own copy to study with flashcards, the AI tutor and spaced repetition. Changes you make stay in your copy.

Try one card

Sample 1 of 5

Cards in this deck

Card 1. Pythagorean theorem: how do you find the hypotenuse c of a right triangle with legs a and b?
Answerc = √(a² + b²). Example: legs 3 and 4 give c = 5.
Card 2. What is the quadratic formula for ax² + bx + c = 0?
Answerx = (−b ± √(b² − 4ac)) / 2a. Example: x² − 5x + 6 = 0 gives x = 2 or x = 3.
Card 3. What does the discriminant b² − 4ac tell you?
AnswerPositive: two real roots. Zero: one repeated real root. Negative: no real roots (two complex roots).
Card 4. How do you find the slope of the line through (x₁, y₁) and (x₂, y₂)?
Answerm = (y₂ − y₁) / (x₂ − x₁). Example: (1, 2) and (3, 8) give m = 3.
Card 5. What is the slope-intercept form of a line?
Answery = mx + b, where m is the slope and b is the y-intercept.
Card 6. What are the area and circumference of a circle with radius r?
AnswerArea = πr²; circumference = 2πr. Example: r = 7 gives area ≈ 153.94 and circumference ≈ 43.98.
Card 7. What is the area of a triangle with base b and height h?
AnswerA = ½bh. Example: base 10, height 6 gives A = 30.
Card 8. What is the sum of the interior angles of a polygon with n sides?
Answer(n − 2) × 180°. Example: a hexagon (n = 6) has 720°.
Card 9. How do you compute simple interest?
AnswerI = Prt (principal × annual rate × years). Example: ₱10,000 at 5% for 3 years earns ₱1,500.
Card 10. How do you compute compound interest compounded n times a year?
AnswerA = P(1 + r/n)^(nt). Example: ₱10,000 at 6% compounded yearly for 2 years grows to ₱11,236.

Show the other 10 cards

Card 11. How do you find what percent a part is of a whole?
AnswerPercent = (part ÷ whole) × 100. Example: 18 out of 24 is 75%.
Card 12. How do you compute percent increase or decrease?
Answer(new − old) ÷ old × 100. Example: ₱80 to ₱100 is a 25% increase.
Card 13. What is the volume of a cylinder with radius r and height h?
AnswerV = πr²h. Example: r = 3, h = 10 gives V ≈ 282.74.
Card 14. What is the distance between points (x₁, y₁) and (x₂, y₂)?
Answerd = √((x₂ − x₁)² + (y₂ − y₁)²). Example: (0, 0) and (6, 8) are 10 units apart.
Card 15. What is the nth term of an arithmetic sequence?
Answeraₙ = a₁ + (n − 1)d. Example: 3, 7, 11, … has 10th term 3 + 9×4 = 39.
Card 16. What is the sum of the first n terms of an arithmetic sequence?
AnswerSₙ = n(a₁ + aₙ) / 2. Example: 1 + 2 + … + 100 = 5,050.
Card 17. What is the nth term of a geometric sequence?
Answeraₙ = a₁ · r^(n − 1). Example: 2, 6, 18, … has 5th term 2 × 3⁴ = 162.
Card 18. How do you find the mean, median and mode of a data set?
AnswerMean: sum ÷ count. Median: middle value when sorted. Mode: most frequent value. Example: 2, 3, 3, 5, 7 has mean 4, median 3, mode 3.
Card 19. What are the laws of exponents for multiplying and dividing powers of the same base?
Answeraᵐ · aⁿ = aᵐ⁺ⁿ and aᵐ ÷ aⁿ = aᵐ⁻ⁿ. Example: 2³ · 2⁴ = 2⁷ = 128.
Card 20. What are sine, cosine and tangent in a right triangle (SOH-CAH-TOA)?
Answersin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Example: sides 3-4-5 give sin θ = 0.6 opposite the side 3.