PSAT Math Formulas
Rules of Zero - Correct Answers-x/0=undefined
0*x=0
0/x=0
x⁰=1
0∧x=0
0⁰=undefined
Rules of One - Correct Answers-x/1=x
1*x=x
1∧x=1
x¹=x
Inclusive Numbers - Correct Answers-To determine inclusive numbers:
1) Subtract the smaller number from larger number
2) Add 1 to the difference
Distributive Law - Correct Answers-1. a(b+c) = ab + ac
2. (a+b)/c = (a/c)+(b/c)
BUT a/(b+c) ≠ (a/b)+(a/c)
Prime Numbers - Correct Answers-A prime number is divisible only by one & itself
1 is NOT a prime number
2 is the only even prime number
2 & 3 are the only consecutive prime numbers
The prime numbers up to 40 are: 2,3,5,7,11,13,17,19,23,29,31,37
Divisibilty Rules - Correct Answers-2 - # is even
3 - sum of digits ÷ by 3
4 - last 2 digits is # ÷ by 4
5 - # ends in 5 or 0
6 - # ÷by 2 AND 3
9 - sum of digits ÷ by 9
Given a positiv fraction x between 0 and 1 - Correct Answers-x²<x<√x
Percent Change Formula - Correct Answers-"percent increase" & "percent decrease
, =
difference/original
Key Ratio Rules - Correct Answers-1) You CANNOT + or - ratios if you do not know actual
starting number
2) You CAN × and ÷ ratios even if you do not have an actual starting number
Rates - Correct Answers-distance = rate*time
For distance problems that have one distance and two different rates and/or times
Total Distance = D₁ + D₂
D = r₁t₁ + r₂t₂
Average Speed - Correct Answers-= total distance/total time
The Group Formula - Correct Answers-2 Groups:
Total = Gr1 + Gr2 + Neither - Both
3 Groups
Total = Gr1 + Gr2 + Gr3 + Neither - Both -2(all)
Key Quadratic Equations - Correct Answers-#1: (a+b)²=(a+b)(a+b)=a²+2ab+b²
#2: (a-b)²=(a-b)(a-b)=a²-2ab+b²
#3: a²-b²=(a+b)(a-b)
Commonly Tested Square Roots - Correct Answers-√2 = 1.4
√3 = 1.7
√4 = 2
√5 = 2.2
Roots and Radical Rules - Correct Answers-√a*√b=√a*b
√a+√b=>solve
√a÷√b= √(a/b)
√a-√b=>solve
a√c+b√c=(a+b)√c
√a*√a=a
ⁿ√x=x∧(1/n)
Exponent Rules - Correct Answers-x∧a*x∧b=x∧(a+b)
(x∧a)/(x∧b)=x∧(a-b)
(xⁿ)∧b=x∧(a*b)
(xy)ⁿ=xⁿ*yⁿ
Rules of Zero - Correct Answers-x/0=undefined
0*x=0
0/x=0
x⁰=1
0∧x=0
0⁰=undefined
Rules of One - Correct Answers-x/1=x
1*x=x
1∧x=1
x¹=x
Inclusive Numbers - Correct Answers-To determine inclusive numbers:
1) Subtract the smaller number from larger number
2) Add 1 to the difference
Distributive Law - Correct Answers-1. a(b+c) = ab + ac
2. (a+b)/c = (a/c)+(b/c)
BUT a/(b+c) ≠ (a/b)+(a/c)
Prime Numbers - Correct Answers-A prime number is divisible only by one & itself
1 is NOT a prime number
2 is the only even prime number
2 & 3 are the only consecutive prime numbers
The prime numbers up to 40 are: 2,3,5,7,11,13,17,19,23,29,31,37
Divisibilty Rules - Correct Answers-2 - # is even
3 - sum of digits ÷ by 3
4 - last 2 digits is # ÷ by 4
5 - # ends in 5 or 0
6 - # ÷by 2 AND 3
9 - sum of digits ÷ by 9
Given a positiv fraction x between 0 and 1 - Correct Answers-x²<x<√x
Percent Change Formula - Correct Answers-"percent increase" & "percent decrease
, =
difference/original
Key Ratio Rules - Correct Answers-1) You CANNOT + or - ratios if you do not know actual
starting number
2) You CAN × and ÷ ratios even if you do not have an actual starting number
Rates - Correct Answers-distance = rate*time
For distance problems that have one distance and two different rates and/or times
Total Distance = D₁ + D₂
D = r₁t₁ + r₂t₂
Average Speed - Correct Answers-= total distance/total time
The Group Formula - Correct Answers-2 Groups:
Total = Gr1 + Gr2 + Neither - Both
3 Groups
Total = Gr1 + Gr2 + Gr3 + Neither - Both -2(all)
Key Quadratic Equations - Correct Answers-#1: (a+b)²=(a+b)(a+b)=a²+2ab+b²
#2: (a-b)²=(a-b)(a-b)=a²-2ab+b²
#3: a²-b²=(a+b)(a-b)
Commonly Tested Square Roots - Correct Answers-√2 = 1.4
√3 = 1.7
√4 = 2
√5 = 2.2
Roots and Radical Rules - Correct Answers-√a*√b=√a*b
√a+√b=>solve
√a÷√b= √(a/b)
√a-√b=>solve
a√c+b√c=(a+b)√c
√a*√a=a
ⁿ√x=x∧(1/n)
Exponent Rules - Correct Answers-x∧a*x∧b=x∧(a+b)
(x∧a)/(x∧b)=x∧(a-b)
(xⁿ)∧b=x∧(a*b)
(xy)ⁿ=xⁿ*yⁿ
