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The short version A golden rectangle is a rectangle whose long side divided by its short side equals the golden ratio, about 1.618. Its special trick: cut a square off one end and the leftover piece is another golden rectangle, forever. The exact ratio is (1 + √5) ÷ 2, which comes from solving x²…
The short version The substitution method solves a system of two equations by solving one equation for a variable, then plugging that expression into the other equation. That leaves one equation with one variable, which you solve normally. Then plug that value back in to get the second variable. Pick the variable that’s easiest to…
The short version Direct variation is a relationship where y = kx for some constant k that isn’t zero. Double x and y doubles too. To find k, divide: k = y ÷ x. If that division gives the same number for every pair, it’s direct variation. The graph is always a straight line through…
The short version A trinomial is a polynomial with exactly three terms, like x² + 5x + 6. Count terms only after combining like terms. x² + 3x + 2x looks like three terms but simplifies to x² + 5x, which is a binomial. Most trinomials in school are quadratic, written ax² + bx +…
The short version A line of reflection is the mirror line a shape flips over. Each point and its image sit the same distance from the line, on opposite sides. The segment joining a point to its image always crosses the line of reflection at a right angle, right at its midpoint. That’s how you…
The short version A dilation is a transformation that makes a figure bigger or smaller by a scale factor, measured out from a fixed center point. The shape stays the same; only the size changes. Centered at the origin, the rule is (x, y) to (kx, ky). Multiply both coordinates by the scale factor k….
The short version To round a decimal, find the place you’re rounding to and look only at the digit directly to its right. If that digit is 5 or more, round up. If it’s 4 or less, leave the digit alone. Then drop everything after it. The places after the decimal point are tenths, hundredths,…
The short version Volume is the amount of space a 3D object fills, measured in cubic units like cm³ or ft³. For boxes, prisms and cylinders, volume = area of the base × height. For pyramids and cones, take one third of that. A sphere’s volume is (4/3)πr³. Use the radius, not the diameter. Converting…
The short version The symmetric property of equality says that if a = b, then b = a. You can swap the two sides of an equation and it stays true. Its main job in algebra is putting the variable on the left: 12 = x + 5 can be rewritten as x + 5…
The short version To add or subtract decimals, line up the decimal points, not the right edges of the numbers. Fill any empty places with zeros so every number has the same count of digits after the point. 4.6 becomes 4.60 next to 3.25. Then add or subtract column by column, right to left, exactly…