Module 1 · Numbers and Operations
Chapter 1: Number System Fundamentals
Math Foundations
7 topics
What this chapter covers
The 7 topics below make up Number System Fundamentals on the Digital SAT. Click any topic to open its notes, examples and practice test.
1Place Value and Face Value
2Number Properties
3Remainders
4Unit Digit
5Number Series
6Algebraic Identities
7Number Word Problems
Study material & tests
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Formula Reference Sheet
This chapter
Sums & series
| First n natural numbers | 1+2+…+n = n(n+1)/2 |
|---|---|
| First n odd numbers | 1+3+5+… = n² |
| First n even numbers | 2+4+6+… = n(n+1) |
| Arithmetic series | sum = n × (first + last) / 2 |
Algebraic identities
| Square of a sum | (a+b)² = a² + 2ab + b² |
|---|---|
| Square of a difference | (a−b)² = a² − 2ab + b² |
| Difference of squares | a² − b² = (a+b)(a−b) |
| Useful | (a+b)² − (a−b)² = 4ab |
Remainders & digits
| Division form | number = divisor × quotient + remainder |
|---|---|
| Same remainder r | number = LCM(divisors) × k + r |
| Place value | digit × value of its position |
| Units-digit cycles | 2: 2,4,8,6 3: 3,9,7,1 7: 7,9,3,1 8: 8,4,2,6 |
Digital SAT reference
Area & Circumference
| Circle area | A = πr² |
|---|---|
| Circle circumference | C = 2πr |
| Rectangle | A = ℓw |
| Triangle | A = ½ b h |
Volume
| Rectangular box | V = ℓwh |
|---|---|
| Cylinder | V = πr²h |
| Sphere | V = 4⁄3 πr³ |
| Cone | V = 1⁄3 πr²h |
| Pyramid | V = 1⁄3 ℓwh |
Right triangles
| Pythagorean theorem | a² + b² = c² |
|---|---|
| 30°–60°–90° | sides x : x√3 : 2x |
| 45°–45°–90° | sides s : s : s√2 |
Constants
| Degrees in a circle | 360° |
|---|---|
| Radians in a circle | 2π |
| Angles of a triangle | sum = 180° |
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