Chapter1

• What topics are covered in unit one of the higher maths GCSE course?

  Multiples, factors, prime factorization, thirds, indices
• How are multiples of a number defined?

  They are the results of multiplying the number.
• What are the first five multiples of eight?

  8, 16, 24, 32, 40
• What are factors of a number?

  Numbers that fit into it an exact number of times.
• What are the factors of eight?

  1, 2, 4, 8
• What defines a prime number?

  It has exactly two factors: one and itself.
• What is the first prime number?

  2
• Which prime numbers are in the 20s?

  23 and 29
• How are square numbers defined?

  Numbers multiplied by themselves.
• What is the square of 3?

  9
• What are cube numbers?

  Numbers multiplied by themselves twice.
• What is 2 cubed?

  8
• What is 3 cubed?

  27
• What does BIDMAS stand for?

  Brackets, Indices, Divide, Multiply, Add, Subtract
• How should you handle addition and subtraction in BIDMAS?

  Work from left to right.
• What is the result of 5 - 3 + 7?

  9
• What is the result of cubing -2?

  -8
• What is the result of 24 - 8 / -8?

  25
• How do you find the prime factorization of a number?

  Use a factor tree to break it down.
• What is the prime factorization of 108?

  2^2 * 3^3
• What is the highest common factor (HCF)?

  Largest number that divides both numbers.
• What is the HCF of 108 and 72?

  36
• What is the lowest common multiple (LCM)?

  Smallest number that is a multiple of both.
• What is the LCM of 108 and 72?

  216
• What happens when you simplify a power of a power?

  You multiply the powers together.
• What is g to the power of -4 cubed?

  g to the power of -12
• How do you multiply powers with the same base?

  Add the exponents together.
• What is the result of 17 * 3?

  51
• What is the result of adding two negative exponents?

  It results in a more negative exponent.
• What is the result of 2 cubed * 2 - 6?

  2
• What is the result of multiplying $x^3$ by $x^1$?


  $x^4$
• Why do we add the powers when multiplying $x^3$ and $x^1$?


  Because we are multiplying the same base
• What is the result of multiplying $y^{-2}$ by $y^{-2}$?


  $y^{-4}$
• What does adding two negative powers result in?

  A more negative power
• What is the result of $2^3 \cdot 2^{-6}$?


  $2^{-3}$
• What happens to the powers when dividing bases?

  We subtract the powers
• What is $2^{-3}$ when simplified?


  $\frac{1}{2^3}$
• What does a negative power indicate about a base number?

  It indicates the reciprocal of the base
• What is $36^{\frac{1}{2}}$?


  6
• What does $1.43 \times 10^5$ represent in ordinary numbers?


  143,000