SAT Math · Study & Practice
Number System Fundamentals
Strong number sense is the foundation of fast, accurate SAT Math. This chapter builds the core skills — place value, properties of integers, remainders, unit-digit cycles, series, algebraic identities and word-problem translation. Read each topic, try the problems with the hint ladder, then take the 8-question topic test.
Topics
1
Place Value and Face Value
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2
Number Properties
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3
Remainders
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4
Unit Digit
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5
Number Series
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6
Algebraic Identities
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7
Number Word Problems
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Chapter test
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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