MATH Exam
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36 Terms
What is the product law of exponents?
aᵐ × aⁿ = aᵐ⁺ⁿ
What is the quotient law of exponents?
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
What is the power of a power rule?
(aᵐ)ⁿ = aᵐⁿ
What is a⁰ equal to?
1
Rewrite x⁻³ with positive exponents.
1/x³
Simplify: x⁴ × x³
x⁷
Simplify: (x²)³
x⁶
What is scientific notation?
A number written as a × 10ⁿ where 1 ≤ a < 10
Convert 4,500,000 to scientific notation.
4.5 × 10⁶
Convert 0.00032 to scientific notation.
3.2 × 10⁻⁴
When do you get a negative exponent?
When the number is less than 1
Multiply: (2 × 10³)(3 × 10²)
6 × 10⁵
What is the general form of a linear equation?
y = mx + b
What does m represent?
Slope (rate of change)
What does b represent?
Y-intercept (starting value)
What is the slope formula?
(y₂ − y₁)/(x₂ − x₁)
What type of graph does a linear relation make?
A straight line
Is y = 3x + 2 increasing or decreasing?
Increasing (positive slope)
What is the general form of an exponential equation?
y = a(b)ˣ
What does a represent?
Initial value
What does b represent?
Growth/decay factor
When is it exponential growth?
When b > 1
When is it exponential decay?
When 0 < b < 1
What is the horizontal asymptote?
y = 0
Linear vs Exponential — what’s the difference?
Linear adds a constant amount; exponential multiplies by a constant factor
What is the distance formula?
√[(x₂ − x₁)² + (y₂ − y₁)²]
What is the midpoint formula?
((x₁ + x₂)/2 , (y₁ + y₂)/2)
Find midpoint of (2,4) and (6,8).
(4,6)
Find distance between (0,0) and (3,4).
5
What is the compound interest formula?
A = P(1 + r/n)ⁿᵗ
What do P, r, n, and t represent?
P=principal, r=rate (decimal), n=times per year, t=years
What is continuous compound interest formula?
A = Peʳᵗ
If $1000 grows at 5% for 1 year (annually), what is A?
$1050
What is a progressive tax system?
Income is taxed in brackets at increasing rates
Do you pay the highest tax rate on all your income?
No, only on the portion in that bracket
How do you calculate total tax?
Multiply each income portion by its rate, then add