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

Mixed Topic Worksheet Grades 6/7: Day 049

Grades 6/7Non-calculator

  1. Question 1. xi = 1, 2, 3, ldots, 15
    A = x : x is an odd number
    List the elements of A'

    Show worked answerHide worked answer
    1. M1: removes 1, 3, 5, ..., 15 from the universal set
    2. A1: [2, 4, 6, 8, 10, 12, 14]
    Answer: 2, 4, 6, 8, 10, 12, 14
    Fundamentals of Set Notation
    [2 marks]

  2. Question 2. Make x the subject of y = 3 - 2x

    Show worked answerHide worked answer
    1. M1: subtracts 3 and has y - 3 = -2x, or adds 2x and subtracts y, giving 2x = 3 - y
    2. A1: x = dfrac3 - y2
    Answer: x = dfrac3 - y2
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. An estimate of the number of animals on an island is 1200.
    It is found by marking animals in a first catch and then taking a second catch.
    1 in every 8 of the animals in the second catch are marked.
    Work out the number of animals marked in the first catch.

    Show worked answerHide worked answer
    1. M1: a ÷ 1200 = 1 ÷ 8
    2. M1: 1200 ÷ 8
    3. A1: 150
    Answer: 150
    Capture-Recapture
    [3 marks]

  4. Question 4. Which is greater, dfrac12√6 or 3√3? Rationalise the denominator and show your working.

    Show worked answerHide worked answer
    1. M1: dfrac12√6 = dfrac12√66 = 2√6
    2. M1: 2√6 = √24 and 3√3 = √27
    3. A1: 3√3 is greater
    Answer: 3√3 is greater
    Rationalising Denominators of the Form √a
    [3 marks]

  5. Question 5. The graph of y = x² + bx + c has its turning point at (2, -9).
    Work out the coordinates of the points where the graph crosses the x-axis.

    Show worked answerHide worked answer
    1. M1: y = (x - 2)² - 9
    2. M1: (x - 2)² = 9
    3. A1: x - 2 = 3 or x - 2 = -3
    4. A1: (-1, 0) and (5, 0)
    Answer: (-1, 0) and (5, 0)
    Full Process for Sketching Quadratics
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 049

Grades 6/7Non-calculator

  1. Question 1. xi = 1, 2, 3, ldots, 15
    A = x : x is an odd number
    List the elements of A'

    [2 marks]
    Show worked answerHide worked answer
    1. M1: removes 1, 3, 5, ..., 15 from the universal set
    2. A1: [2, 4, 6, 8, 10, 12, 14]
    Answer: 2, 4, 6, 8, 10, 12, 14
    Fundamentals of Set Notation

  2. Question 2. Make x the subject of y = 3 - 2x

    [2 marks]
    Show worked answerHide worked answer
    1. M1: subtracts 3 and has y - 3 = -2x, or adds 2x and subtracts y, giving 2x = 3 - y
    2. A1: x = dfrac3 - y2
    Answer: x = dfrac3 - y2
    Rearranging Harder Equations

  3. Question 3. An estimate of the number of animals on an island is 1200.
    It is found by marking animals in a first catch and then taking a second catch.
    1 in every 8 of the animals in the second catch are marked.
    Work out the number of animals marked in the first catch.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: a ÷ 1200 = 1 ÷ 8
    2. M1: 1200 ÷ 8
    3. A1: 150
    Answer: 150
    Capture-Recapture

  4. Question 4. Which is greater, dfrac12√6 or 3√3? Rationalise the denominator and show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac12√6 = dfrac12√66 = 2√6
    2. M1: 2√6 = √24 and 3√3 = √27
    3. A1: 3√3 is greater
    Answer: 3√3 is greater
    Rationalising Denominators of the Form √a

  5. Question 5. The graph of y = x² + bx + c has its turning point at (2, -9).
    Work out the coordinates of the points where the graph crosses the x-axis.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: y = (x - 2)² - 9
    2. M1: (x - 2)² = 9
    3. A1: x - 2 = 3 or x - 2 = -3
    4. A1: (-1, 0) and (5, 0)
    Answer: (-1, 0) and (5, 0)
    Full Process for Sketching Quadratics
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 049

Grades 6/7Non-calculator

  1. Question 1. xi = 1, 2, 3, ldots, 15
    A = x : x is an odd number
    List the elements of A'

    Show worked answerHide worked answer
    1. M1: removes 1, 3, 5, ..., 15 from the universal set
    2. A1: [2, 4, 6, 8, 10, 12, 14]
    Answer: 2, 4, 6, 8, 10, 12, 14
    Fundamentals of Set Notation
    [2 marks]

  2. Question 2. Make x the subject of y = 3 - 2x

    Show worked answerHide worked answer
    1. M1: subtracts 3 and has y - 3 = -2x, or adds 2x and subtracts y, giving 2x = 3 - y
    2. A1: x = dfrac3 - y2
    Answer: x = dfrac3 - y2
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. An estimate of the number of animals on an island is 1200.
    It is found by marking animals in a first catch and then taking a second catch.
    1 in every 8 of the animals in the second catch are marked.
    Work out the number of animals marked in the first catch.

    Show worked answerHide worked answer
    1. M1: a ÷ 1200 = 1 ÷ 8
    2. M1: 1200 ÷ 8
    3. A1: 150
    Answer: 150
    Capture-Recapture
    [3 marks]

  4. Question 4. Which is greater, dfrac12√6 or 3√3? Rationalise the denominator and show your working.

    Show worked answerHide worked answer
    1. M1: dfrac12√6 = dfrac12√66 = 2√6
    2. M1: 2√6 = √24 and 3√3 = √27
    3. A1: 3√3 is greater
    Answer: 3√3 is greater
    Rationalising Denominators of the Form √a
    [3 marks]

  5. Question 5. The graph of y = x² + bx + c has its turning point at (2, -9).
    Work out the coordinates of the points where the graph crosses the x-axis.

    Show worked answerHide worked answer
    1. M1: y = (x - 2)² - 9
    2. M1: (x - 2)² = 9
    3. A1: x - 2 = 3 or x - 2 = -3
    4. A1: (-1, 0) and (5, 0)
    Answer: (-1, 0) and (5, 0)
    Full Process for Sketching Quadratics
    [4 marks]