math

• What is factorising in mathematics?

  Breaking something into its factors
• How would you factorise the number 55?

  5 times 11 or 1 times 55
• What are the factors of the algebraic term 3x?

  3 and x
• What is the highest common factor in the expression 3x + 15?


  3
• How do you factorise the expression 3x + 15?

  • Identify the highest common factor: 3
  • Factor out 3: 3(x + 5)
• Why is factorising useful in algebra?

  It simplifies expressions and helps with fractions
• What is the highest common factor of 6ab and a²b?

  ab
• How do you factorise the expression 6ab - a²b?

  • Identify the highest common factor: ab
  • Factor out ab: ab(6 - a)
• How can you verify your factorisation is correct?

  Expand it back to the original expression
• What is the common factor in the expression pqr?


  q
• How do you factorise the expression pqr + qrt - sw?

  • Identify the common factor: q
  • Factor out q: q(pr + rt - s)
• What is the highest common factor of 25p² and 10p?

  5p
• How do you factorise the expression 25p² - 10p?

  • Identify the highest common factor: 5p
  • Factor out 5p: 5p(5p - 2)
• What is the highest common factor of 6p⁴ and 12p?

  6p
• How do you factorise the expression 6p⁴ - 12p?

  • Identify the highest common factor: 6p
  • Factor out 6p: 6p(p³ - 2)
• What does p⁴ represent in terms of multiplication?

  p times p times p times p
• What should you do if you encounter higher indices while factorising?

  Break them down into their base factors
• What are the steps to factorise an algebraic expression?

  1. Identify the highest common factor
  2. Factor it out from each term
  3. Write the remaining expression in brackets
  4. Verify by expanding back to original
• What is the first term of the sequence mentioned?

  5
• What is the pattern in the sequence 5, 9, 13, 17, 21?

  It increases by 4 each time
• What is the term-to-term rule for the sequence 5, 9, 13, 17, 21?

  Plus four every time
• How is the sequence related to the four times table?

  It is four times table plus one
• What is the nth term formula for the sequence 5, 9, 13, 17, 21?

  4n + 1
• What is the first term of the second sequence mentioned?

  1
• What is the pattern in the sequence 1, 9, 17, 25, 33?

  It increases by 8 each time
• What is the term-to-term rule for the sequence 1, 9, 17, 25, 33?

  Plus eight every time
• How is the sequence related to the eight times table?

  It is eight times table minus seven
• What is the nth term formula for the sequence 1, 9, 17, 25, 33?

  8n - 7
• What is the first term of the third sequence mentioned?

  27
• What is the pattern in the sequence that decreases every time?

  It decreases by 2 each time
• What is the term-to-term rule for the sequence decreasing by 2?

  Minus two every time
• How is the sequence related to the minus two times table?

  It is minus two times table plus 27
• What is the nth term formula for the sequence decreasing by 2?

  -2n + 27
• What is the first term of the sequence going up in sixes?

  6
• What is the term-to-term rule for the sequence going up in sixes?

  It is just 6n
• What is the first term of the sequence going up in fives?

  5
• What do we need to do to the five times table to get the sequence?

  Take off three every time
• What is the nth term formula for the sequence going up in fives?

  5n - 3
• What is the first term of the sequence going up in fours?

  4
• What do we need to do to the four times table to get the sequence?

  Add five every time