CCSLC Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Percentage change formula

Subtract the original value from the new value, divide by the original value, then multiply by 100. Always divide by the original, not the new, amount.

Simple interest

Interest calculated only on the original principal: I = P × r × t, with r as a decimal annual rate and t in years. The principal never grows.

Compound interest

Interest charged on both the principal and previously earned interest. For annual compounding, amount = P(1 + r)^t, so growth accelerates each period.

Unit price

The cost of one item or one unit of measure, found by dividing total cost by quantity. It allows fair comparison between differently sized packs.

Map scale

The ratio of drawn length to real length. At 1 : 50 000, one centimetre on the map represents 50 000 centimetres, or half a kilometre, on the ground.

Mean, median, mode

Mean is the sum divided by the count; median is the middle value of ordered data; mode is the most frequent value. Each describes the centre differently.

Rounding decision rule

Inspect the first digit being discarded: 5 or more rounds up, 4 or less rounds down. Round only the final answer, not intermediate steps.

Currency conversion

Multiply by the exchange rate to change into the target currency; divide by the rate to convert back. Round only at the end of the calculation.

Unitary method

Find the value of a single unit by dividing, then multiply by the number of units required. Used for scaling recipes, costs, and rates.

Distance, speed, time

Distance equals speed multiplied by time. Rearranged: speed equals distance divided by time, and time equals distance divided by speed. Keep units consistent.

Ratio sharing

Add the ratio terms to get total parts, divide the amount by total parts, then multiply by each term to find each share.

Working backwards

Start from the answer options or the final condition and reverse each operation. Useful when the forward calculation is long or has several unknowns.

Estimate before calculating

Round the numbers to convenient values and compute mentally. If the exact answer is far from the estimate, an operation or unit is wrong.

Boundary value test

For conditions such as at least or at most, substitute the boundary number itself. Whether it satisfies the condition decides if it is included.

Given, unknown, constraint

Before solving, list what is supplied, what must be found, and any restriction such as a budget or time limit. This prevents answering the wrong question.

Table or diagram method

Record each quantity in a labelled row or on a sketch so every value is used exactly once. Multi-step problems become a sequence of simple operations.

Correlation versus causation

Two quantities moving together does not prove one causes the other. A third factor, or coincidence, may explain the observed pattern.

Percentage without base

A percentage change is meaningless unless the starting amount is known. A 50% rise on 10 differs greatly from 50% on 1 000.

Misleading graph axis

A vertical axis that does not start at zero exaggerates differences between bars. Check the scale before drawing conclusions from a chart.

Sample bias

Results from a small or self-selected group do not represent the whole population. Conclusions generalise only when the sample is representative.

Choosing an average

The mean is pulled by extreme values; the median resists them. For incomes and house prices, the median usually describes the typical case better.

Absolute versus relative risk

Relative risk compares two ratios; absolute risk gives the actual difference. A doubling from 1 in 10 000 is still only 0.01 percentage points.

Matching units and periods

Before comparing figures, confirm both use the same unit and the same time period. Comparing a monthly cost with an annual one distorts the choice.

Single example fallacy

One case cannot establish a general rule. A claim needs several representative cases or an explicit, testable assumption behind it.

Total cost of ownership

Purchase price plus running costs and maintenance, minus resale value, calculated over the same period for each option being compared.

Break-even point

The number of units where total revenue equals total cost: fixed costs divided by the difference between price per unit and variable cost per unit.

Successive discounts

Two discounts are not added. Multiply the remaining fractions: a 20% then 10% discount leaves 0.8 × 0.9 = 0.72, that is 28% off.

Adding and removing tax

Add tax by multiplying by one plus the rate. Remove tax already included by dividing by one plus the rate, not by subtracting the rate.

Budget surplus and deficit

Surplus is income minus expenses when positive; deficit is expenses minus income when spending exceeds earnings. Total spending must stay within income.

Risk versus return

Higher expected return normally comes with greater uncertainty. A sound decision weighs both the likely gain and the chance of loss.

Comparing loans

Compare total repayments and the annual effective interest rate across the full term, not just the monthly instalment, which can hide fees and a longer term.

Stated decision criterion

Name the basis of the choice, such as cheapest, fastest, or safest, and list the assumptions. The recommendation can then be justified and checked.