Maths

• What is the first step in handling fractional negative indices?

  Flip the base for negative indices
• What does the number on the bottom of a fractional negative index represent?

  It represents the root
• What does the number on the top of a fractional negative index represent?

  It represents a normal power
• How do you simplify $\frac{1}{8^{-2/3}}$?


  $\frac{1}{8^{-2/3}} =$$\frac{1}{\frac{1}{4}} =$$\frac{1}{4}$
• What is the cube root of 8?

  2
• What is the final answer for $(\frac{1}{8})^{2}$?


  $\frac{1}{4}$
• What does the term "bounds" refer to in mathematics?

  It refers to the limits of accuracy
• What is the upper bound for a number correct to two decimal places?

  Add 0.005 to the number
• What is the lower bound for a number correct to one decimal place?

  Subtract 0.05 from the number
• How do you find the upper bound of a fraction?

  Upper bound of numerator divided by lower bound of denominator
• What is the result of $\frac{8.245}{3.45}$ rounded to three decimal places?


  1. 390
• How do you round numbers when considering bounds?

  Round according to the closest significant figure
• What is the method for converting recurring decimals to fractions?

  Multiply by 10 or 100 based on recurrence
• What does the dot above a number in a decimal indicate?

  It indicates a recurring decimal
• How do you eliminate recurring decimals when converting to fractions?

  Subtract the equations after multiplying
• What is the simplified form of $\frac{54}{99}$?


  $\frac{6}{11}$
• How do you convert $0.23\overline{3}$ to a fraction?


  $\frac{7}{30}$
• What is the formula for compound interest?

  A = P(1 + r)^n
• How do you calculate the amount after the first year of compound interest?

  Multiply by $1 +$$r$
• How do you find the unknown percentage in compound interest?

  Rearrange the formula and solve
• What is the final amount after three years if the initial investment is £2500?

  £2705.36
• What is the significance of the decimal in the percentage result?

  It indicates the actual percentage increase
• How do you rationalize a fraction with a surd in the denominator?

  Multiply by the conjugate of the denominator
• What happens when you multiply a surd by itself?

  It becomes a whole number
• What is the final form of $(3 + \sqrt{5})^2$?


  $14 +$$6\sqrt{5}$
• What is the process for rationalizing $\frac{1}{2 + \sqrt{3}}$?


  Multiply by $2 - \sqrt{3}$
• What is the result of rationalizing $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$?


  It simplifies to a rational number
• What are the key steps in simplifying surds?

  • Identify like terms
  • Multiply and combine
  • Rationalize if necessary
  • Simplify to simplest form
• What is the purpose of multiplying the top by \(2 - \sqrt{3}\)?

  To create an equivalent fraction
• What do you multiply both parts by first in the expression?

  5
• What is the result of \(5 \times 2\)?

  10
• What is the result of \(5 \times -\sqrt{3}\)?

  • 5\sqrt{3}
• What does \(2\sqrt{3} \times 2\) equal?


  4\sqrt{3}
• What is the result of \(2\sqrt{3} \times -\sqrt{3}\)?


  • 2
• What is \(2 \times \sqrt{9}\)?

  6
• Why does the fraction simplify in the denominator?

  Because \(4 - 3 = 1\)
• What is the simplified result of the top expression \(10 - 6 - \sqrt{3}\)?

  4 - \sqrt{3}
• What happens when you divide by 1 in a fraction?

  The fraction disappears
• What is the result of multiplying \(3.2\) by \(4\)?

  12.8
• What is the power when multiplying \(10^3\) and \(10^4\)?

  10^7