The short version In math, i is the imaginary unit. It’s defined as the square root of -1, so i² = -1. Imaginary numbers are multiples of i, like 3i or -7i. They let you take the square root of a negative number: √(-25) = 5i. Powers of i repeat every four steps: i, -1,…
The short version A constant term is a term in an expression that’s just a number, with no variable attached. In 3x + 7, the constant term is 7. Keep the sign. In 5x – 8, the constant term is -8. Simplify first. In 2x + 3 – 7, the constant term is -4, because…
The short version Delta in math almost always means “change in.” Δx is read “delta x” and means the final value of x minus the starting value: Δx = x2 – x1. Slope is a ratio of two deltas: Δy/Δx, the change in y divided by the change in x. From (2, 5) to (6,…
The short version Equivalent fractions are different fractions that name the same amount. 1/2, 2/4, 3/6 and 50/100 are all equal. To make an equivalent fraction, multiply or divide the numerator and denominator by the same number (not zero). 3/5 × 3/3 = 9/15. To check whether two fractions are equivalent, cross multiply. 4/6 and…
The short version The converse of an “if p, then q” statement swaps the two parts: “if q, then p.” The converse of “If a shape is a square, then it has four sides” is “If a shape has four sides, then it’s a square.” A true statement can have a false converse. One counterexample,…
The short version The domain of a function is every x value you’re allowed to put in. The range is every y value that can come out. To find the domain, start with all real numbers and remove anything that breaks the function: an x that makes a denominator 0, or an x that puts…
The short version A fraction is a number that names part of a whole, or part of a group, after it’s been split into equal parts. 3/4 means 3 of 4 equal parts. The bottom number (denominator) tells how many equal parts the whole is cut into. The top number (numerator) tells how many of…
The short version Divisibility rules are shortcuts that tell you whether one whole number divides evenly into another, with no remainder, without doing long division. The fast ones: 2 (last digit even), 5 (ends in 0 or 5), 10 (ends in 0), 3 (digit sum divisible by 3) and 9 (digit sum divisible by 9)….
The short version A rational number is any number you can write as a fraction of two integers, like 3/4, with a bottom number that isn’t 0. Whole numbers, negatives, mixed numbers, percents and square roots of perfect squares are all rational, because each one can be rewritten as a fraction. A decimal is rational…
The short version A prime number has exactly two factors: 1 and itself. 7 is prime because only 1 × 7 gives 7. There are 25 prime numbers below 100, starting 2, 3, 5, 7, 11 and ending at 97. To test a number, try dividing by the primes up to its square root. If…