MB Essential Math 40S flashcards
MB Essential Math 40S · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Simple interest formula
- I = Prt, where P is the principal, r is the annual rate written as a decimal, and t is the time in years. The total amount owed or earned is A = P(1 + rt).
- Compound interest formula
- A = P(1 + i)^n, where i is the interest rate per compounding period and n is the total number of periods. Interest is earned on previously earned interest.
- Rule of 72
- An estimate of doubling time: divide 72 by the annual percentage rate. At 6% per year, money doubles in roughly 12 years. It is a rough approximation.
- Present value
- The amount that must be invested today to reach a future value. Found by rearranging the compound interest formula: P = A ÷ (1 + i)^n.
- Amortized loan payment
- A regular equal payment covering both interest and principal. It is calculated from the principal, the periodic interest rate, and the total number of payments.
- Currency exchange rate
- The multiplier converting one currency into another. Because buy and sell rates differ, converting to another currency and back always returns less than the original amount.
- Percent change
- (new value − old value) ÷ old value × 100%. A 20% increase followed by a 20% decrease leaves 96% of the original, not 100%.
- Unit price
- Total cost divided by the quantity, expressed per gram, per litre, or per item. Convert both packages to the same unit before deciding which is cheaper.
- Mean, median, mode
- The mean is the sum divided by the count; the median is the middle of an ordered list; the mode is the most frequent value. The median resists outliers.
- Weighted mean
- The sum of each value multiplied by its weight, divided by the sum of the weights. Used when categories such as tests and assignments count for different portions of a grade.
- Standard deviation
- A measure of how far values typically sit from the mean. A small value means the data cluster tightly; a large value means they are spread out.
- z-score
- (value − mean) ÷ standard deviation. It states how many standard deviations a value lies above or below the mean, allowing comparison across different data sets.
- Interquartile range
- IQR = Q3 − Q1, the spread of the middle half of the data. Values beyond 1.5 times the IQR from the quartiles are often flagged as outliers.
- Box-and-whisker plot
- A display showing minimum, first quartile, median, third quartile, and maximum. The box spans the interquartile range and each whisker reaches an extreme value.
- Correlation versus causation
- Correlation measures how strongly two variables move together in a linear pattern. A strong correlation alone never proves that one variable causes the other.
- Sampling bias
- A distortion that occurs when the chosen sample does not represent the population. Voluntary-response and convenience samples usually over-represent people with strong opinions.
- Theoretical probability
- The number of favourable outcomes divided by the total number of equally likely outcomes. Its value always lies between 0 and 1 inclusive.
- Complement rule
- P(not A) = 1 − P(A). It is the fastest route for questions asking for the probability of at least one occurrence, since the complement is often simpler.
- Addition rule
- P(A or B) = P(A) + P(B) − P(A and B). The overlap is subtracted so outcomes counted in both events are not counted twice.
- Independent events
- Events are independent when one outcome does not change the probability of the other. For such events, P(A and B) = P(A) × P(B).
- Expected value
- The sum of each outcome multiplied by its probability. Over many repetitions, the average result approaches this value, so it measures long-run fairness.
- Odds in favour
- Written a:b, meaning a favourable outcomes for every b unfavourable ones. The matching probability is a ÷ (a + b), not a ÷ b.
- Slope as a rate
- For y = mx + b, the slope m = (y₂ − y₁) ÷ (x₂ − x₁). Its units are y-units per x-unit, such as dollars per hour or litres per minute.
- Exponential model
- y = a·b^x, where a is the starting value. If b > 1 the quantity grows by a constant percent each period; if 0 < b < 1 it decays.
- Break-even point
- The quantity at which total revenue equals total cost, so profit is zero. Producing more than this quantity yields a positive profit.
- Interpolation versus extrapolation
- Interpolation estimates a value between known data points. Extrapolation estimates beyond the known range and is far less reliable because the pattern may change.
- Scale factor and volume
- Enlarging a solid by scale factor k multiplies lengths by k, surface area by k², and volume by k³. Doubling every dimension multiplies volume by eight.
- Volume and capacity
- 1 cm³ holds 1 mL and 1000 cm³ holds 1 L. A container of 4500 cm³ therefore has a capacity of 4.5 L.
- Density
- Density = mass ÷ volume. Rearranged, mass = density × volume and volume = mass ÷ density. Units must match, such as grams per cubic centimetre.
- Trigonometric ratios
- In a right triangle: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent. Use inverse functions to recover an unknown angle.
- Sine law
- a ÷ sin A = b ÷ sin B = c ÷ sin C for any triangle. Use it when you know a side with its opposite angle plus one additional side or angle.
- Cosine law
- c² = a² + b² − 2ab·cos C. Use it with two sides and the included angle, or with all three sides to find an angle.