GCSE Edexcel – Maths EXAM WITH CORRECT ANSWERS A+

GCSE Edexcel – Maths EXAM WITH CORRECT ANSWERS A+ Finding the LCM of two numbers when you have the prime factors - CORRECT ANSWERS - 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 - CORRECT ANSWERS - List all the prime factors that appear in both numbers - Multiply these together Multiplying fractions - CORRECT ANSWERS Multiply the top and bottom separately Dividing fractions - CORRECT ANSWERS Turn the second fraction upside down then multiply Rule for terminating and recurring decimals - CORRECT ANSWERS If the denominator has prime factors of only 2 or 5, it is a terminal decimal Turning a recurring decimal into a fraction - CORRECT ANSWERS - 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... - CORRECT ANSWERS - 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 - CORRECT ANSWERS - 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 - CORRECT ANSWERS The first number which isn't a zero. This is rounded. Rules for calculating with significant digits - CORRECT ANSWERS Estimating square roots - CORRECT ANSWERS - 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 - CORRECT ANSWERS 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 - CORRECT ANSWERS - Convert both numbers to standard form - Separate the power of ten and the other number - Do each calculation separately Adding and subtracting standard form - CORRECT ANSWERS - 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 - CORRECT ANSWERS 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 - CORRECT ANSWERS 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 - CORRECT ANSWERS 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 - CORRECT ANSWERS a²-b²=(a+b)(a-b) Simplifying surds - CORRECT ANSWERS 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 - CORRECT ANSWERS 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 - CORRECT ANSWERS - Multiply by the lowest common multiple of both numbers - Simplify Quadratic formula - CORRECT ANSWERS Completing the square - CORRECT ANSWERS - 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