APES Math Questions and Answers
Multiplying Scientific Notation - answer Add exponents:
4×10³ × 5×10⁶ = 20×10¹⁸
Dividing Scientific Notation - answer Subtract exponents:
4×10³ ÷ 5×10⁶ = 4/5×10⁻³
Growth Rate - answer Growth rate = [CRUDE BIRTH RATE + immigration] -
[CRUDE DEATH RATE + emigration]
Crude Birth Rate - answer CBR = # births per 1000, per year
Crude Death Rate - answer CDR = # deaths per 1000, per year
Growth Rate % Change - answer (CBR-CDR) ÷ 10 = % change
Calculate Percent Change - answer The rate of change (percent change, growth
rate) from one period to another = [(V present - V past) ÷ V past] × 100
V = value
Annual rate of Change - answer Percent Change ÷ (V present - V past)
Percent Difference - answer {(First Value - Second Value) ÷ [(First Value + Second
Value) / 2]} × 100%
Rule of 70 (Doubling Time) - answer Doubling time = 70 / annual growth rate (in %,
not decimal)
Half-life - answer Amount remaining = (Original amount)(0.5)ⁿ
n = # of half-lives
n = time / half-life
Calculate pH using -log[H*] - answer Log₁₀x = n and 10ⁿ = x
Remember: for every one-increment change in pH, the ions change by a factor of 10
Ex: If [H*] is 10⁻⁶M, the pH is 6 and the solution is a weak acid
Graphing - answer include title and key; set consistent increments for axes; connect
dots; interpolate and extrapolate (general direction of a scatter plot)
Multiplying Scientific Notation - answer Add exponents:
4×10³ × 5×10⁶ = 20×10¹⁸
Dividing Scientific Notation - answer Subtract exponents:
4×10³ ÷ 5×10⁶ = 4/5×10⁻³
Growth Rate - answer Growth rate = [CRUDE BIRTH RATE + immigration] -
[CRUDE DEATH RATE + emigration]
Crude Birth Rate - answer CBR = # births per 1000, per year
Crude Death Rate - answer CDR = # deaths per 1000, per year
Growth Rate % Change - answer (CBR-CDR) ÷ 10 = % change
Calculate Percent Change - answer The rate of change (percent change, growth
rate) from one period to another = [(V present - V past) ÷ V past] × 100
V = value
Annual rate of Change - answer Percent Change ÷ (V present - V past)
Percent Difference - answer {(First Value - Second Value) ÷ [(First Value + Second
Value) / 2]} × 100%
Rule of 70 (Doubling Time) - answer Doubling time = 70 / annual growth rate (in %,
not decimal)
Half-life - answer Amount remaining = (Original amount)(0.5)ⁿ
n = # of half-lives
n = time / half-life
Calculate pH using -log[H*] - answer Log₁₀x = n and 10ⁿ = x
Remember: for every one-increment change in pH, the ions change by a factor of 10
Ex: If [H*] is 10⁻⁶M, the pH is 6 and the solution is a weak acid
Graphing - answer include title and key; set consistent increments for axes; connect
dots; interpolate and extrapolate (general direction of a scatter plot)
