While the SAT provides some basic formulas at the beginning of the math section, memorizing key formulas beforehand saves valuable time and reduces errors. Here are the essential formulas you need to master for SAT math success.
Algebra Formulas
Slope-Intercept Form: y = mx + b (where m is slope and b is y-intercept)
Slope Formula: m = (y₂ – y₁) / (x₂ – x₁)
Quadratic Formula: x = [-b ± √(b² – 4ac)] / 2a (for equations in form ax² + bx + c = 0)
Difference of Squares: a² – b² = (a + b)(a – b)
Perfect Square Trinomials: (a + b)² = a² + 2ab + b²
These algebra formulas appear frequently on the SAT, especially in the calculator and no-calculator sections. Being able to quickly identify when to use the quadratic formula or recognize factoring patterns can save you minutes on test day.
Geometry Formulas
Area of a Triangle: A = ½bh (base times height)
Area of a Circle: A = πr²
Circumference of a Circle: C = 2πr or C = πd
Pythagorean Theorem: a² + b² = c² (for right triangles)
Special Right Triangles:
- 45-45-90 triangle has sides in ratio x : x : x√2
- 30-60-90 triangle has sides in ratio x : x√3 : 2x
Volume of a Rectangular Solid: V = lwh
Volume of a Cylinder: V = πr²h
Geometry questions often combine multiple concepts, so understanding how these formulas relate to each other is crucial.
Statistics and Data Analysis
Mean (Average): Sum of all values / Number of values
Median: Middle value when data is arranged in order
Mode: Most frequently occurring value
Range: Maximum value – Minimum value
Probability: P(event) = (Number of favorable outcomes) / (Total number of possible outcomes)
Statistics questions are increasingly common on the SAT, particularly those involving data interpretation and probability calculations.
Additional Key Concepts
Percent Change: [(New Value – Original Value) / Original Value] × 100
Distance Formula: d = √[(x₂ – x₁)² + (y₂ – y₁)²]
Midpoint Formula: M = [(x₁ + x₂)/2, (y₁ + y₂)/2]
Exponential Growth/Decay: A = P(1 ± r)ᵗ (where P is initial value, r is rate, t is time)
Memorization Strategies
Don’t just memorize formulas mechanically—understand when and how to apply them. Create flashcards with formulas on one side and example problems on the other. Practice writing out all formulas from memory daily until they become second nature.
Focus especially on formulas NOT provided on the SAT formula sheet, such as the quadratic formula, slope formula, and special right triangle ratios. These are essential and appear regularly.
Finally, practice applying these formulas in various contexts. The SAT rarely asks straightforward “plug and chug” questions. Instead, you’ll need to recognize which formula applies to a given scenario and potentially combine multiple formulas to solve complex problems. Regular practice with real SAT questions is the best way to develop this skill.
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