Useful Formulas

What is a problem? A problem = a fact + a judgment. That is a simple formula that tells us something about the way the world works. Maths is full of formulas, and that can intimidate some people if they don't understand them or can't remember the right one to use. However, formulas should be our friends, as they help us to do sometimes complex calculations accurately and repeatably in a consistent and straightforward way. The following is a list of the most useful ones I've come across while teaching Maths to a variety of students at a variety of ages and at a variety of stages in their education.

Geometry

Angles around a point add up to 360º Angles on a straight line add up to 180º Opposite angles are equal, ie the two pairs of angles opposite each other when two straight lines bisect (or cross) each other Alternate angles are equal, ie the angles under the arms of a 'Z' formed by a line (or 'transversal') bisecting two parallel lines Corresponding angles are equal, ie the angles under the arms of an 'F' formed by a line (or 'transversal') bisecting two parallel lines Complementary angles add up to 90º Any straight line can be drawn using y = mx + c, where m is the gradient and c is the point where the line crosses the y-axis (the 'y-intercept') The gradient of a straight line is shown by ?y/?x (ie the difference in the y-values divided by the difference in the x-values of any two points on the line, usually found by drawing a triangle underneath it) Polygons

Number of diagonals in a polygon = (n-3)(n÷2) where n is the number of sides The sum of the internal angles of a polygon = (n-2)180º, where n is the number of sides Any internal angle of a regular polygon = (n-2)180º ÷ n, where n is the number of sides Rectangles

Perimeter of a rectangle = 2(l + w), where l = length and w = width Area of a rectangle = lw, where l = length and w = width Triangles

Area of a triangle = ½bh, where b = base and h = height Angles in a triangle add up to 180º In a right-angled triangle, a² + b² = c², ie the area of a square on the hypotenuse (or longest side) is equal to the sum of the areas of squares on the other two sides Circles

Circumference of a circle = 2?r, where r = radius Area of a circle = ?r², where r = radius ? = 3.14 to two decimal places and is sometimes given as 22/7 Spheres

Volume of a sphere = 4/3?r³, where r = radius Surface area of a sphere = 4?r², where r = radius Cuboids

Volume of a cuboid = lwh, where l is length, w is width and h is height Surface area of a cuboid = 2(lw + lh + wh), where l is length, w is width and h is height Number sequences

An arithmetic sequence (with regular intervals) = xn ± k, where x is the interval (or difference) between the values, n is the value's place in the sequence and k is a constant that is added or subtracted to make sure the sequence starts at the right number, eg the formula for 5, 8, 11, 14.etc is 3n + 2 Other

Speed = distance ÷ time Profit = sales - cost of goods sold Profit margin = profit ÷ sales Mark-up = profit ÷ cost of goods sold