📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 094

Grades 8/9Calculator

  1. Question 1. Simplify √245 - √80. Give your answer in the form a√b.

    Show worked answerHide worked answer
    1. M1: √245 = 7√5 and √80 = 4√5
    2. A1: 3√5
    Answer: 3√5
    Simplifying Surds
    [2 marks]

  2. Question 2. y is directly proportional to the square of x and inversely proportional to z.
    y = 18 when x = 3 and z = 2.
    Find the value of z when y = 48 and x = 6.

    Show worked answerHide worked answer
    1. M1: 18 = k × 3² ÷ 2
    2. M1: 48 = 4 × 6² ÷ z
    3. A1: 3
    Answer: 3
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. Simplify fully dfracx²+3xx-2÷dfracx+3x²-4

    Show worked answerHide worked answer
    1. M1: dfracx²+3xx-2×dfracx²-4x+3
    2. M1: x(x+3) and (x-2)(x+2)
    3. M1: cancels (x-2) and (x+3)
    4. A1: x(x+2)
    Answer: x(x+2)
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  4. Question 4. A runner travels 360 m, correct to the nearest 10 m.
    The time taken is 20.1 seconds, correct to 1 decimal place.
    Show clearly that the average speed is 18 metres per second, correct to 2 significant figures.

    Show worked answerHide worked answer
    1. M1: 360 + 5 and 20.1 - 0.05
    2. M1: 365 ÷ 20.05
    3. M1: 355 ÷ 20.15
    4. C1: 18.2... and 17.6... both round to 18 to 2 significant figures
    Answer: Upper bound of speed = 365 ÷ 20.05 = 18.2... and lower bound = 355 ÷ 20.15 = 17.6...; both round to 18.
    Combining Upper & Lower Bounds
    [4 marks]

  5. Question 5. Solve x²+3x-70 ≤ 0

    Show worked answerHide worked answer
    1. M1: (x + 10)(x - 7) ≤ 0
    2. A1: -10 ≤ x ≤ 7
    Answer: -10 ≤ x ≤ 7
    Solving Quadratic Inequalities
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 094

Grades 8/9Calculator

  1. Question 1. Simplify √245 - √80. Give your answer in the form a√b.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √245 = 7√5 and √80 = 4√5
    2. A1: 3√5
    Answer: 3√5
    Simplifying Surds

  2. Question 2. y is directly proportional to the square of x and inversely proportional to z.
    y = 18 when x = 3 and z = 2.
    Find the value of z when y = 48 and x = 6.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 18 = k × 3² ÷ 2
    2. M1: 48 = 4 × 6² ÷ z
    3. A1: 3
    Answer: 3
    Direct & Inverse Proportion with Functions

  3. Question 3. Simplify fully dfracx²+3xx-2÷dfracx+3x²-4

    [4 marks]
    Show worked answerHide worked answer
    1. M1: dfracx²+3xx-2×dfracx²-4x+3
    2. M1: x(x+3) and (x-2)(x+2)
    3. M1: cancels (x-2) and (x+3)
    4. A1: x(x+2)
    Answer: x(x+2)
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. A runner travels 360 m, correct to the nearest 10 m.
    The time taken is 20.1 seconds, correct to 1 decimal place.
    Show clearly that the average speed is 18 metres per second, correct to 2 significant figures.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 360 + 5 and 20.1 - 0.05
    2. M1: 365 ÷ 20.05
    3. M1: 355 ÷ 20.15
    4. C1: 18.2... and 17.6... both round to 18 to 2 significant figures
    Answer: Upper bound of speed = 365 ÷ 20.05 = 18.2... and lower bound = 355 ÷ 20.15 = 17.6...; both round to 18.
    Combining Upper & Lower Bounds

  5. Question 5. Solve x²+3x-70 ≤ 0

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (x + 10)(x - 7) ≤ 0
    2. A1: -10 ≤ x ≤ 7
    Answer: -10 ≤ x ≤ 7
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 094

Grades 8/9Calculator

  1. Question 1. Simplify √245 - √80. Give your answer in the form a√b.

    Show worked answerHide worked answer
    1. M1: √245 = 7√5 and √80 = 4√5
    2. A1: 3√5
    Answer: 3√5
    Simplifying Surds
    [2 marks]

  2. Question 2. y is directly proportional to the square of x and inversely proportional to z.
    y = 18 when x = 3 and z = 2.
    Find the value of z when y = 48 and x = 6.

    Show worked answerHide worked answer
    1. M1: 18 = k × 3² ÷ 2
    2. M1: 48 = 4 × 6² ÷ z
    3. A1: 3
    Answer: 3
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. Simplify fully dfracx²+3xx-2÷dfracx+3x²-4

    Show worked answerHide worked answer
    1. M1: dfracx²+3xx-2×dfracx²-4x+3
    2. M1: x(x+3) and (x-2)(x+2)
    3. M1: cancels (x-2) and (x+3)
    4. A1: x(x+2)
    Answer: x(x+2)
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  4. Question 4. A runner travels 360 m, correct to the nearest 10 m.
    The time taken is 20.1 seconds, correct to 1 decimal place.
    Show clearly that the average speed is 18 metres per second, correct to 2 significant figures.

    Show worked answerHide worked answer
    1. M1: 360 + 5 and 20.1 - 0.05
    2. M1: 365 ÷ 20.05
    3. M1: 355 ÷ 20.15
    4. C1: 18.2... and 17.6... both round to 18 to 2 significant figures
    Answer: Upper bound of speed = 365 ÷ 20.05 = 18.2... and lower bound = 355 ÷ 20.15 = 17.6...; both round to 18.
    Combining Upper & Lower Bounds
    [4 marks]

  5. Question 5. Solve x²+3x-70 ≤ 0

    Show worked answerHide worked answer
    1. M1: (x + 10)(x - 7) ≤ 0
    2. A1: -10 ≤ x ≤ 7
    Answer: -10 ≤ x ≤ 7
    Solving Quadratic Inequalities
    [2 marks]