GCSE EDEXCEL – MATHS EXAM QUESTIONS AND ANSWERS WITH COMPLETE SOLUTIONS VERIFIED LATEST UPDATE

GCSE EDEXCEL – MATHS EXAM QUESTIONS AND ANSWERS WITH COMPLETE SOLUTIONS VERIFIED LATEST UPDATE Practice questions for this set Terms in this set (139) 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 to get the LCM 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