GCSE maths revision

• When rounding numbers to one significant figure:

  • 6.32 rounds to 6
  • 6.51 rounds to 7
  • 0.503 rounds to 0.5
  • When dividing by 0.5, the result doubles
• To write 280 as a product of prime factors in index form:

  • Prime factor tree: 280 = 2^3 * 5 * 7
• To find the lowest common multiple of 15 and 40:

  • List multiples: 15, 30, 45, 60, 75, 90, 105, 120
  • The lowest common multiple is 120
• To find the highest common factor of 72 and 90:

  • Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
  • Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
  • The highest common factor is 18
• When graphing inequalities on a number line:

  • Use open or closed circles to represent values
  • Use the symbols (<, >, ≤, ≥) to indicate the range
• To calculate monthly payments after a deposit:

  • Calculate the total cost after deposit
  • Divide the remaining cost by the number of installments
• For reverse percentage problems:

  • Identify the percentage given in the question
  • Work backwards to find the original amount
• To calculate simple interest for an investment of £800 at a rate of 1.5% per annum for 2 years:

  • Calculate 1.5% of £800, which is £12 per year
  • Multiply this by 2 years to get a total interest of £24
  • Add this interest back to the initial investment to find the total amount after 2 years: £800 + £24 = £824
• For compound interest on an investment of £150,000 at a rate of 2.4% per annum for 4 years:

  • Calculate the total amount after 4 years using the formula: £150,000 * (1 + 0.024)^4 = £164,926.74
  • To find the interest earned, subtract the initial investment from the total amount: £164,926.74 - £150,000 = £14,926.74
• To calculate depreciation on a car bought for £4,000 that depreciates by 20% each year for 3 years:

  • Calculate the value after each year:
  • Year 1: £4,000 - 20% = £3,200
  • Year 2: £3,200 - 20% = £2,560
  • Year 3: £2,560 - 20% = £2,048
• When multiplying fractions:

  • Multiply the numerators to get the new numerator
  • Multiply the denominators to get the new denominator
  • Simplify the fraction if needed
• When dividing fractions:

  • Keep the first fraction the same
  • Flip the second fraction (take the reciprocal)
  • Multiply the fractions as usual
  • Simplify the fraction if needed
• When adding or subtracting fractions:

  • Find a common denominator
  • Add or subtract the numerators
  • Simplify the fraction if needed
• To convert numbers to standard form:

  • Move the decimal point to create a number between 1 and 10
  • Count the number of places moved to determine the power of 10
  • For negative powers, move the decimal to the left
• When dealing with numbers in powers:

  • When multiplying with the same base, add the exponents
  • When dividing with the same base, subtract the exponents
• When multiplying with the same base numbers, add the powers; when dividing, subtract the powers
• For negative powers, flip the number to its reciprocal; for fractional powers, the number at the bottom of the fraction represents a root
• In combinations, multiply the number of choices for each pick to find the total combinations
• For a three-digit padlock with no repeated digits, multiply the number of choices for each digit to find the total combinations
• For rounded intervals, consider the possible numbers it could have been and add/subtract the rounding error
• For truncated intervals, consider the possible numbers it could have been and the fact that it was just chopped off
• When using a calculator for complex calculations, ensure you are familiar with functions like square root, cube root, sin, cos, tan, and fractions
• In algebra, apply index laws when multiplying/dividing powers with the same base number or when dealing with powers in brackets
• In single-celled organisms, substances can easily enter the cell due to a short distance, while in multicellular organisms, the distance is larger due to a higher surface area to volume ratio
• Multicellular organisms require specialised exchange surfaces for efficient gas exchange of carbon dioxide and oxygen due to their higher surface area to volume ratio
• Expanding brackets:

  • Multiply everything inside the bracket by B
  • B times 3B equals 3B^2
  • 1 times 3 is 3
  • B times B is B^2
  • 1B times 7 is 7B
• Expanding and simplifying brackets:

  • 3y times 5 equals 15y
  • 3y times 2y equals 6y^2
  • Copy the symbol as a negative
• Expanding and simplifying brackets:

  • 3 times 5 equals 15
  • 3 times 4 equals 12
  • 15x plus 12
• Factorizing:

  • Take out a factor by finding a number that goes into both terms
  • Divide both terms by the factor to simplify
• Factorizing fully:

  • Identify the highest common factor of both terms
  • Divide both terms by the factor, ensuring all terms are accounted for
• Factorizing quadratic expressions:

  • Find a pair of numbers that multiply to the constant term and add up to the coefficient of the middle term
  • Write the expression as a product of two binomials
• Solving equations:

  • Reverse the operations to isolate the variable
  • Perform the same operation on both sides of the equation
• Making a variable the subject of a formula:

  • Rearrange the formula to express the desired variable on one side
  • Perform inverse operations to isolate the variable
• To solve the equation 3y - 5 = x, where 3y equals x + 5:

  • Multiply both sides by 3 to remove the fraction and unlock what's on top
  • Resulting in 3y - 5 = x
• To find the value of a in the equation a = 5B + 2C, where B = 3 and C = -2:

  • Substitute B = 3 and C = -2 into the equation
  • Calculate 5 * 3 + 2 * (-2) = 15 - 4 = 11
  • Therefore, a = 11
• When solving simultaneous equations:

  • Make the coefficients of one of the variables the same in both equations
  • Add or subtract the equations to eliminate that variable
• In the word problem involving calculators and books:

  • Create equations based on the given information
  • Solve the equations by making the coefficients of one variable the same
• For the age problem involving Adam, Brian, and Chris:

  • Assign variables for each person's age based on the given relationships
  • Write an equation based on the sum of their ages being 92
  • Solve the equation to find the ages of each person
• In the problem comparing the perimeters of a quadrilateral and a triangle:

  • Express the perimeters of each shape in terms of X
  • Set the expressions for the perimeters equal to each other to find X
• To solve the equation 8x - 4 = 2(4x + 18):

  • Start by simplifying the equation: 8x - 4 = 8x + 36
  • Subtract 8x from both sides: -4 = 36
  • This equation has no solution