Two Crossing Roads Do Not Cover Their Two Areas Added
Learn to split a polygon into triangles and trapeziums, calculate a field's area from offsets along a diagonal, solve path and cross-road problems, and convert area units.
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Free study notes for CBSE & ICSE, Classes 6–12.
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The Height Is Never the Slanted Side, However It Looks
Learn the area formulas for a trapezium, parallelogram, triangle and rhombus, use the diagonals of a rhombus, and work backwards to find a missing height, side or diagonal.
Read articleEvery Circle Question Hides a Right-Angled Triangle
Learn the parts of a circle, use the radius and diameter relationship, apply the right angle in a semicircle, find tangent lengths by Pythagoras, and draw chords, sectors and segments.
Read articleTwo Reflections in a Row Are the Same as One Half Turn
Learn the coordinate rules for reflecting a point in the axes and the origin, reflecting in a line parallel to an axis, rotating about the origin, and naming the figure formed.
Read articleThe Letter S Has No Mirror Line, Yet It Is Still Symmetric
Learn to find every line of symmetry in a figure, identify point symmetry and its centre, and work out the order of rotational symmetry and the angle of rotation.
Read articleOne Equation Links the Corners, Edges and Faces of a Solid
Learn to draw and recognise nets of solids, sketch front, side and top views, count faces, edges and vertices of polyhedra, and use Euler's formula to find a missing count.
Read articleA Rhombus Needs Only Two Measurements, Not Five
Learn to construct a parallelogram from sides and an angle or from its diagonals, a rhombus from a side and a diagonal, rectangles and squares, and a trapezium.
Read articleFive Measurements Fix a Quadrilateral, and Four Never Can
Learn why a quadrilateral needs five measurements, construct one from four sides and a diagonal, from three sides and two diagonals, and from given sides and angles.
Read articleBisecting Diagonals, Equal Diagonals, Perpendicular Diagonals
Learn the side, angle and diagonal properties of a parallelogram, tell a rhombus from a rectangle and a square by their diagonals, and use trapezium and kite properties.
Read articleWalk Once Around Any Polygon and You Turn Full Circle
Learn why the exterior angles of every convex polygon total 360 degrees, calculate each angle of a regular polygon, find the number of sides from an angle, and solve ratio problems.
Read articleCount the Triangles Inside and the Angle Sum Follows
Learn to classify polygons as convex, concave or regular, count diagonals with the n(n-3)/2 formula, and find interior angle sums and missing angles.
Read articleMultiply by a Negative and the Inequality Turns Around
Learn the difference between an equation and an inequation, find solution sets over natural numbers, whole numbers and integers, apply the four rules, and draw the number line.
Read articleTurning a Paragraph of Words Into a Single Equation
Learn to choose the right variable, build equations for number and digit puzzles, solve age, money and sharing problems, and handle perimeter and angle questions.
Read articleEvery Equation Has a Solution, Except When It Does Not
Learn to move the variable to one side, clear brackets and fractions using the LCM, solve proportions by cross multiplication, and always verify your answer.
Read articleSplit the Middle Term and the Quadratic Falls Apart
Learn to factorise quadratics by splitting the middle term, handle a leading coefficient greater than one, and factorise sums and differences of cubes.
Read articleFour Terms and No Common Factor: Group Them in Pairs
Learn to take out the highest common factor, factorise four-term expressions by grouping, and recognise the difference of two squares and perfect square patterns.
Read articleCubing a Bracket Without Multiplying It Out Three Times
Learn the product identity for two brackets, the square of three terms, and the cube of a sum and difference, then use them to find cubes from a sum and a product.
Read articleSquaring 103 in Your Head, and Why It Works
Learn the square and difference identities, use them to square numbers near 100 mentally, multiply number pairs instantly, and solve problems that give you a sum and a product.
Read articleDividing One Polynomial by Another, Step by Step
Learn to multiply monomials and binomials, expand a binomial by a trinomial, divide monomials using index laws, and carry out polynomial long division with a remainder.
Read articleOnly Like Terms Can Ever Be Added Together
Learn the vocabulary of algebraic expressions, how to spot like terms, how to add and subtract expressions by collecting them, and how to substitute negative values safely.
Read articleAn Emptying Pipe Is the Only One You Ever Subtract
Learn to recognise inverse variation by a constant product, solve speed-time and workers-days problems, combine rates for people working together, and handle filling and emptying pipes.
Read articleTwo Quantities Rising Together Is Not Enough to Be Proportional
Learn what direct variation really requires, find the constant of proportionality from any pair of values, solve problems by the unitary method and by proportion, and test a table of values properly.
Read articleCompounding Twice a Year Beats the Same Rate Once a Year
Learn to build compound interest year by year, use the amount formula for any number of years, handle half-yearly compounding and changing rates, and find the difference between simple and compound interest.
Read articleA Sum Doubles in Eight Years at One Particular Rate
Learn to calculate simple interest and the amount from the formula, rearrange it to find the principal, rate or time, and handle sums lent at different rates or for part of a year.
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