PrepprosMathbook 1.0 - SAT Math Question Bank - Essential Formula Sheet

Aug 25, 2026

Uploaded by Ezra

SAT Math question bank organized by key topics including linear equations and systems, quadratics and polynomials, functions and exponential models, percentages and ratios, geometry, trigonometry and the unit circle, statistics and data analysis, unit conversion and rates, plus applied word problems. Includes an essential formula sheet covering slope forms and systems, quadratic forms and discriminants, exponential growth/decay, similarity scaling, circle and triangle geometry, Pythagorean and polygon angle facts, trigonometric identities and radians, and core statistics and rate-of-change relationships.

LanguageEnglish

CategoryExam

FormatPDF

Pages76

Reading Time3 h 12 min

AccessFree to download

Topics Covered

Linear Equations & Systems

Quadratics & Polynomials

Functions & Exponential Models

Percentages, Ratios & Proportions

Geometry

Trigonometry & Unit Circle

Statistics & Data Analysis

Unit Conversion & Rates

Applied / Word Problems

Essential Formula Sheet

Linear Equations

Quadratics & Polynomials

Exponents & Exponential Functions

Percentages & Ratios

Geometry

Trigonometry

Statistics & Data Analysis

Unit Conversion

Practice Questions

Question 1 [Easy]

Question 2 [Easy]

Question 3 [Easy]

Question 4 [Medium]

Question 5 [Easy]

Question 6 [Easy]

Question 7 [Medium]

Question 8 [Easy]

Question 9 [Easy]

Question 10 [Medium]

SAT Math Question Bank Topics Covered: 1. Linear Equations & Systems 2. Quadratics & Polynomials 3. Functions & Exponential Models 4. Percentages, Ratios & Proportions 5. Geometry 6. Trigonometry & Unit Circle 7. Statistics & Data Analysis 8. Unit Conversion & Rates 9. Applied / Word Problems Essential Formula Sheet Linear Equations ❼ Slope-intercept form: y = mx + b ❼ Point-slope form: y − y 1 = m(x − x1 ) y2 − y 1 ❼ Slope: m = ~~ ~~ x2 − x 1 ❼ Standard form: Ax + By = C ❼ Parallel lines have equal slopes; perpendicular lines: m 1 · m2 = −1 ❼ System with infinitely many solutions: equations are proportional ❼ System with no solution: same slope, different intercept Quadratics & Polynomials ❼ Standard form: f (x) = ax2 + bx + c ❼ Vertex form: f (x) = a(x − h)2 + k, vertex at (h, k) −b ±√b2 − 4ac ❼ Quadratic formula: x = 2a ❼ Discriminant: ∆ = b2 − 4ac – ∆ > 0: two real solutions ∆ = 0: one solution ∆ < 0: no real solutions b ❼ Vertex x-coordinate: x = − 2a b c ❼ Sum of roots: − Product of roots: a a ❼ Difference of squares: a2 − b2 = (a + b)(a − b) ❼ Factor theorem: if f(r) = 0, then (x − r) is a factor of f(x) Exponents & Exponential Functions ❼ am · an = am+n ~~ ~~aamn = am−n (am )n = amn ❼ Exponential growth/decay: f (x) = a · bx – b > 1: growth by (b − 1) × 100% per unit – 0 < b < 1: decay by (1 − b) × 100% per unit ❼ If f(x) = a · bx/k , the quantity changes by factor b every k units Percentages & Ratios ❼ Percent increase: new = original × (1 + r) ❼ Percent decrease: new = original × (1 − r) p ❼ A is p% of B: A = · B 100 ❼ Similar figures: if scale factor is k, then area scales by k 2 , volume by k 3 Geometry ❼ Circle: area = πr2 , circumference = 2πr, arc length = 3θ60 · 2πr ❼ Equation of circle: (x − h)2 + (y − k)2 = r 2 1 1 ❼ Triangle area: A = bh = absinC 2 2 ❼ Pythagorean theorem: a2 + b2 = c2 ❼ Common triples: (3 , 4 , 5), (5 , 12 , 13), (8 , 15 , 17), (7 , 24 , 25) ❼ 45-45-90: x : x : x √2 30-60-90: x : x √3 : 2x ❼ Sum of interior angles of n-gon: (n − 2) · 180◦ 1 4 ❼ Volume: cylinder = πr2 h, cone = πr 2 h, sphere = πr3 3 3 ❼ Surface area of sphere: 4πr2 ; hemisphere volume: 23πr3 1 ❼ Pyramid volume: V = Bh (where B is base area) 3 Trigonometry ❼ sinθ = hoppositeypotenuse cosθ = hadjacentypotenuse tanθ = sincosθθ❼ Complementary angles: sin θ = cos(90◦ − θ) ❼ Unit circle: cos2 θ + sin2 θ = 1 ❼ Radians: 180◦ = π radians Statistics & Data sum of values ❼ Mean = ~~ ~~ n ❼ Margin of error decreases as sample size increases ❼ Standard deviation measures spread from the mean P (A ∩ B) ❼ Probability: P (A | B) = P (B) Unit Conversion ❼ Multiply by conversion factors so unwanted units cancel ❼ Area units scale by square of linear factor; volume by cube ∆y ❼ Rate of change:∆x 1 Linear Equations & Systems Question 1 [Easy] x y 47 + = 5 9 45 An engineer connects resistors in series, where the resistors in the series have a total resistance of ~~47~~45 ohms. In this series, there are x resistors of type A, which each have a resistance of aohms, and y resistors of type B, which each have a resistance of b ohms. The given equation represents this situation. According to this equation, what is the positive difference between the value of a and the value of b? (A) 47 (B) 4 47 (C) 45 4 (D) 45 Question 2 [Easy] A book-of-the-month club charges $17 for the first book and $13 for each additional book. Which equation gives total cost y for x books (x > 0)? (A) y = x + 17 (B) y = 13x + 17 (C) y = 13(x − 1) + 17 (D) y = (x − 1) + 17 Question 3 [Easy] 3x + 9y = 10 rx + 18y = 20 In the given system, r is a constant. The system has infinitely many solutions. What is r? (A) 2 (B) 3 (C) 6 (D) 9 Question 4 [Medium] 1 16x − 20y = 6y + 8 ty = 8x + 5 In the given system, t is a constant. If the system has no solution, what is the

FAQs

Which math topics are included in this SAT Math question bank?

It covers linear equations and systems, quadratics and polynomials, functions and exponential models, percentages/ratios/proportions, geometry, trigonometry and the unit circle, statistics and data analysis, unit conversion and rates, and applied word problems.

What key formula types are provided for linear equations and systems?

It includes slope-intercept, point-slope, and standard forms, along with slope rules for parallel and perpendicular lines and conditions for systems with infinitely many solutions or no solution.

How are exponential growth and decay described in the essential formula sheet?

The sheet gives the exponential form f(x)=a·bx and states that when b>1 it represents growth by a percentage per unit, while 0<b<1 represents decay by a percentage per unit; it also notes factor change over k units for scaled exponents.

Aug 25, 2026

Uploaded by Ezra