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Mathematics
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Why two steps? x + 4 = 9 needs one undo. Two-step equations have a multiplier AND something added. x was multiplied by 2, then 3 was added. Undo in reverse order: the addition first. The two moves Inequalities: same moves, one extra rule So
Factors are few, multiples are endless Factors of 12: just 1, 2, 3, 4, 6, 12. Six numbers, and that's all of them. Multiples of 12 never stop. Prime, composite, and the odd one out Prime factorisation with a factor tree Split repeatedly unt
What is a table of values used for when graphing a line?
ATo measure the steepness of the lineBTo generate (x, y) points that can be plotted to draw the lineCTo rewrite the equation in a different formDTo find the line's length
Solid shapes take up space 3D shapes aren't flat on paper. They take up room, and they're everywhere once you look. Faces, edges and corners Symmetry: folding in half A shape has line symmetry if you can fold it exactly in half and both sid
Two routes to the same answers Every quadratic is ax² + bx + c = 0. You have two tools. 1. Factoring Split it into two brackets, then set each bracket to zero. 2. The quadratic formula The bit under the root, b² − 4ac, is the discriminant.
Mathematics
Mathematics · L3 · Factoring & the Quadratic Formula
Identify the family first One question sorts nearly every solid: what does its cross-section do? The formula table For cones and pyramids, l is the SLANT height along the surface, not the vertical height h. Where the one-third comes from Sa
Mathematics
Mathematics · L3 · Surface Area & Volume of Solids
Unfold it, then add up the pieces Surface area is the total area of every outside face: how much material would wrap it completely. Imagine cutting along the edges and flattening the solid into a net, then add every piece. Rectangular prism
Mathematics
Mathematics · L2 · Surface Area of Prisms & Pyramids
The parts Circumference: the distance around Divide any circle's circumference by its diameter and you always get π, about 3.14. That's where both formulas come from. Area: the space inside One circle, all three quantities
Slicing a circle two ways Central versus inscribed angles So a 90° central angle means every inscribed angle standing on that arc is 45°, wherever on the circle you put its vertex. Move the vertex all you like; the answer doesn't budge. The