paper 3 calc

• What does the term "truncated" mean in the context of the video?

  Chopped off without rounding
• What is the upper bound for the number 6.4 rounded to one decimal place?

  Less than 6.45
• What is the lower bound for the number 6.4 rounded to one decimal place?

  Equal to 6.35
• How do you find the lower bound when a number is rounded?

  Subtract 0.05 from the rounded number
• What is the difference between rounding and truncating a number?

  Rounding adjusts the number, truncating does not
• What is the first step in using a calculator for complex calculations?

  Identify the required functions on the calculator
• How do you calculate the cube root on most calculators?

  Press shift and then the square root button
• What should you do before rounding your calculator's answer?

  Write down all displayed digits
• How do you round the number 0.585593423233 to one decimal place?

  Round to 0.6
• How do you round the number 0.585593423233 to two decimal places?

  Round to 0.59
• What happens to powers when multiplying with the same base?

  Powers are added together
• What happens to powers when dividing with the same base?

  Powers are subtracted
• What is the result of $x^2 / x^1$?


  $x^1$
• What is $(x^2)^3$?


  $x^6$
• What is the result of $30x^2y^3 / 6xy^2$?


  5xy
• What is $2^3$?


  $8$
• What is the result of $3b(3b + 7)$?


  $9b^2 +$$21b$
• What is the result of $3y(5 - 4y)$?


  $15y - 12y^2$
• What is the final simplified result of $3(5x + 4) - 2(3x - 2)$?


  $9x +$$16$
• What is the result of $(x - 5)(x + 3)$?


  $x^2 - 2x - 15$
• What is the result of $2x(3x - 4) - 3(3x + 2)$?


  $6x^2 - 17x - 6$
• What is the process of factorizing an expression?

  Taking out common factors and putting in brackets
• What are the key index laws?

  • Multiplying powers: add exponents
  • Dividing powers: subtract exponents
  • Powers in brackets: multiply exponents
• What are the steps for expanding brackets?

  1. Multiply each term inside the bracket by the term outside
  2. Combine like terms
• What is the process for expanding and simplifying double brackets?

  1. Multiply each term in the first bracket by each term in the second bracket
  2. Combine like terms
• What is the process for factorizing fully?

  1. Identify common factors
  2. Factor out the common factors
  3. Write the remaining expression in brackets
• What is the importance of writing down all digits from a calculator?

  • Ensures accuracy before rounding
  • Prevents loss of significant figures
• What is the result of simplifying $-9x +$$12$?


  $-17x +$$12$
• What factor can be taken out from $3x +$$15$?


  3
• How do you factor $3x +$$15$?


  By taking out 3, resulting in $3(x + 5)$
• What is the process for fully factorizing $35x +$$21x^2$?


  • Identify common factors: 7 and x
  • Factor out: $7x(5 + 3x)$
• What is the highest common factor of $35$ and $21$?


  7
• How do you factor $35x +$$21x^2$ completely?


  $7x(5 + 3x)$
• What is the form of the answer when factorizing a quadratic?

  It will be in double brackets
• What pairs of numbers multiply to make $12$?


  1 and 12, 2 and 6, 3 and 4
• Which pair of numbers adds up to $7$ and multiplies to $12$?


  3 and 4
• What is the factorization of $x^2 +$$7x +$$12$?


  $(x + 3)(x + 4)$
• How do you factor $28x^2 - 3x - 28$?


  $(x + 4)(x - 7)$
• What pairs of numbers multiply to make $28$?


  1 and 28, 2 and 14, 4 and 7
• How do you solve the equation $3x +$$5 =$$26$?


  Subtract 5, then divide by 3