maths

• This video covers everything you need to get a grade six to nine in maths
• To get a grade five, you need a solid understanding of all topics
• Fractional negative indices


  Negative does the reciprocal, bottom is the root, top is the normal power
• Calculating fractional negative indices

  1. Flip the number

  2. Do the root

  3. Do the power
• The cube root of 1 is 1 and the cube root of 8 is 2
• 1/8 squared is 1/4
• Error intervals


  Used to determine upper and lower bounds
• Finding error intervals


  1. Write upper bound

  2. Write lower bound
• Upper bound of s is 8.245 and lower bound of t is 3.45
• Finding upper bound of a fraction

  Upper bound divided by lower bound
• Recurring decimals as fractions


  Use algebra to convert recurring decimals to fractions
• Converting recurring decimals


  1. Multiply by 100 for two recurring decimals

  2. Multiply by 10 for one recurring decimal

  3. Subtract to eliminate recurring decimals

  4. Divide to simplify
• Calculating compound interest


  1. Calculate first year amount

  2. Use reverse compound interest for subsequent years
• James invests £2,500 for three years at 3% per annum compound interest
• After the first year, James has £2,575
• To find x, rearrange the compound interest formula
• Surd


  A root that cannot be simplified to remove the root
• Expanding a surd


  1. Use double brackets

  2. Multiply out terms

  3. Combine like terms
• 3 + √5 squared equals 14 + 6√5
• Rationalizing a fraction with a surd

  1. Multiply by the conjugate

  2. Simplify the result
• To rationalize 2 + √3, multiply by 2 - √3
• When creating an equivalent fraction, you can multiply the top by 2 minus root 3
• Multiplying fractions


  1. Multiply top by 5

  2. Multiply top by 2 root 3

  3. Multiply bottom by first two

  4. Multiply bottom by last two
• 5 times 2 gives us 10
• 5 times negative root 3 gives us negative 5 root 3
• 2 root 3 times 2 is positive 4 root 3
• 2 root 3 times negative root 3 gives you 2
• 2 lots of root 9 is 2 times 3 which is 6
• 1 positive 1 is negative gives us negative 6
• The bottom is to eliminate the thirds in the middle
• Two times two is four
• Root three times root three is three
• 4 minus 3 is 1
• On the top we have 6 and 10 which gives us 10 minus 6 which is 4
• Negative five root three add four root three gives us negative one root three
• When dividing by one, we can get rid of the fraction
• The result is 4 minus root three
• Sirds can only be collected together when the number underneath the third is the same
• Standard forms involve multiplication and division
• Multiplying in standard form


  1. Multiply 3.2 by 4

  2. Hop the decimal back in

  3. Add powers