UPDATED GCSE Maths CLASS ACTIVITY 2023

Finding the LCM of two numbers when you have the prime factors - - List all the prime factors out - If a factor appears more than once, list it that many times, e.g. 2, 2, 2, 3, 4 and 2, 2, 3, 4 would be 2, 2, 2, 3, 4 - Multiply these together Finding the HCF of two numbers when you have the prime factors - - List all the prime factors that appear in both numbers - Multiply these together Multiplying fractions - Multiply the top and bottom separately Dividing fractions - Turn the second fraction upside down then multiply Rule for terminating and recurring decimals - If the denominator has prime factors of only 2 or 5, it is a terminal decimal Turning a recurring decimal into a fraction - - Name the decimal with an algebraic letter - Multiply by a power of ten to get the one loop of repeated numbers past the decimal point - Subtract the larger value from the single value to get an integer - Rearrange - *Simplify* Turning a recurring fraction into a decimal when the recurring decimal is not immediately after the decimal, e.g. r = 0.16666... - - Name the decimal with an algebraic letter e.g. r = 0.16666... - Multiply by a power of ten to get the non-repeating part out of the bracket e.g. 10r = 1.6666... - Multiply to get the repeating part out of the bracket e.g. 100r = 16.6666... - Take away the larger value from the smaller one (to get an integer) e.g. 100r - 10r = 90r = 15 r = 15/90 - *Simplify* e.g. 15/90 = 1/6 Turning a fraction into a decimal - - Make the fraction have all nines at the bottom - The number on the top is the recurring part, the number of nines is the number of recurring decimals there are Significant figures - The first number which isn't a zero. This is rounded. Rules for calculating with significant digits - Estimating square roots - - Find two numbers either side of the number in the root - Make a sensible estimate depending on which one it is closer to Truncated units - When a measurement is truncated, the actual measurement can be up to a whole unit bigger but no smaller, e.g. 2.4 truncated to 1 d.p. is 2.4 ≤ x 2.5 Multiplying and dividing standard form - - Convert both numbers to standard form - Separate the power of ten and the other number - Do each calculation separately Adding and subtracting standard form - - Convert both numbers into standard form - Make both powers of 10 the same in each bracket - Add the two numbers and multiply by whatever power of ten; they are to the same power so this can be done Negative powers - 1 over whatever the number to the power was, e.g. 7⁻² = 1 / 7² = 1 / 49 a⁻⁴ = 1 / a⁴ If the number is a fraction, then it is swapped around, e.g. (3/5)⁻² = (5/3)² = 25 / 9 Fractional powers - Something to the power of 1/2 means square root Something to the power of 1/3 means cube root Something to the power of 1/4 means fourth root, e.g. 25^½ = √25 = 5 Two-stage fractional powers - When there is a fraction with a numerator higher than one, spilt it into a fraction and a power and do the root first, then power, e.g. 64^5/6 = (64^1/6)⁵ = (2)⁵ = 32 Difference between two squares - a²-b²=(a+b)(a-b) Simplifying surds - Split the number in the root into a square number and the lowest other number possible, e.g. √250 = √(25 × 10) = 5√10 Rationalising the denominator - This is done to get rid of a surd on the denominator. You multiply by the same fraction of the surd, but with the operation the other way round. Removing fractions when they (the fractions) appear on both sides of an equation - - Multiply by the lowest common multiple of both numbers - Simplify Quadratic formula - Completing the square - - Write out in the form ax²+bx+c - Write out the first bracket in the form (x + b/2)² - Multiply out the brackets and add or subtract to make the number outside the bracket match the original Completing the square when 'a' isn't one - - Factorise with the 'a' value outside the brackets - Write out in the form a(x+b/2) - Add or subtract the remaining number Facts about completing the square - For a positive quadratic, - The number outside the bracket is the y value of a graph - The number inside the bracket is the x value multiplied by -1 Adding and subtracting algebraic fractions - - Make both denominators equal by multiplying the numerators by the other denominator - Simplify Finding the nth term of quadratic sequence - - Find the difference between the difference in each term (this can be called a second difference) - Divide the second difference by two to get the coefficient of the n² term - Take away the n² term from the original sequence to get a linear sequence, which can be easily worked out Algebra with inequalities exception - Whenever you *multiply* or *divide* by a negative number, *flip the inequality* sign round Inequalities on number lines - - Open circles for or - Closed circles for ≤ or ≥ Quadratic inequalities general rule - - If x² a² then x a or x -a - If x² a² then -a x a (this is because with a square root the number can be positive or negative, and the negative would mean flipping the sign)