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

Mixed Topic Worksheet Grades 6/7: Day 003

Grades 6/7Non-calculator

  1. Question 1. Solve 2x - 3 < 9

    Show worked answerHide worked answer
    1. M1: add 3 to both sides, 2x < 9 + 3
    2. A1: x < 6
    Answer: x < 6
    Solving Single Inequalities
    [2 marks]

  2. Question 2. Make x the subject of y = 2x² + 7
    x is positive.

    Show worked answerHide worked answer
    1. M1: subtracts 7 from both sides, giving y - 7 = 2x²
    2. M1: divides by 2, giving x² = dfracy - 72
    3. A1: takes the square root, giving x = sqrtdfracy - 72
    Answer: x = sqrtdfracy - 72
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. An estimate of the number of newts in a pond is 400.
    The estimate was found by marking 50 newts in the first catch.
    In the second catch there were 32 newts, some of which were marked.
    Work out how many newts in the second catch were marked.

    Show worked answerHide worked answer
    1. M1: 400 = 50 × 32 ÷ c
    2. M1: c = 50 × 32 ÷ 400
    3. A1: 4
    Answer: 4
    Capture-Recapture
    [3 marks]

  4. Question 4. p is inversely proportional to the square root of q.
    p = 6 when q = 25.
    Find the value of p when q = 36.

    Show worked answerHide worked answer
    1. M1: 6 = k ÷ √25
    2. M1: p = 30 ÷ √36
    3. A1: 5
    Answer: 5
    Algebraic Inverse Proportion
    [3 marks]

  5. Question 5. The graph shows a runner's distance from the start against time. The tangent to the curve at 4 seconds passes through (2, 0) and (6, 16). Work out the speed of the runner at 4 seconds.

    Show worked answerHide worked answer
    1. M1: (16 − 0) ÷ (6 − 2)
    2. A1: 4
    Answer: 4
    Instantaneous Gradients of Lines
    Time (seconds)Distance (metres)0816243202468
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 003

Grades 6/7Non-calculator

  1. Question 1. Solve 2x - 3 < 9

    [2 marks]
    Show worked answerHide worked answer
    1. M1: add 3 to both sides, 2x < 9 + 3
    2. A1: x < 6
    Answer: x < 6
    Solving Single Inequalities

  2. Question 2. Make x the subject of y = 2x² + 7
    x is positive.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: subtracts 7 from both sides, giving y - 7 = 2x²
    2. M1: divides by 2, giving x² = dfracy - 72
    3. A1: takes the square root, giving x = sqrtdfracy - 72
    Answer: x = sqrtdfracy - 72
    Rearranging Harder Equations

  3. Question 3. An estimate of the number of newts in a pond is 400.
    The estimate was found by marking 50 newts in the first catch.
    In the second catch there were 32 newts, some of which were marked.
    Work out how many newts in the second catch were marked.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 400 = 50 × 32 ÷ c
    2. M1: c = 50 × 32 ÷ 400
    3. A1: 4
    Answer: 4
    Capture-Recapture

  4. Question 4. p is inversely proportional to the square root of q.
    p = 6 when q = 25.
    Find the value of p when q = 36.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 6 = k ÷ √25
    2. M1: p = 30 ÷ √36
    3. A1: 5
    Answer: 5
    Algebraic Inverse Proportion

  5. Question 5. The graph shows a runner's distance from the start against time. The tangent to the curve at 4 seconds passes through (2, 0) and (6, 16). Work out the speed of the runner at 4 seconds.

    [2 marks]
    Time (seconds)Distance (metres)0816243202468
    Show worked answerHide worked answer
    1. M1: (16 − 0) ÷ (6 − 2)
    2. A1: 4
    Answer: 4
    Instantaneous Gradients of Lines
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 003

Grades 6/7Non-calculator

  1. Question 1. Solve 2x - 3 < 9

    Show worked answerHide worked answer
    1. M1: add 3 to both sides, 2x < 9 + 3
    2. A1: x < 6
    Answer: x < 6
    Solving Single Inequalities
    [2 marks]

  2. Question 2. Make x the subject of y = 2x² + 7
    x is positive.

    Show worked answerHide worked answer
    1. M1: subtracts 7 from both sides, giving y - 7 = 2x²
    2. M1: divides by 2, giving x² = dfracy - 72
    3. A1: takes the square root, giving x = sqrtdfracy - 72
    Answer: x = sqrtdfracy - 72
    Rearranging Harder Equations
    [3 marks]

  3. Question 3. An estimate of the number of newts in a pond is 400.
    The estimate was found by marking 50 newts in the first catch.
    In the second catch there were 32 newts, some of which were marked.
    Work out how many newts in the second catch were marked.

    Show worked answerHide worked answer
    1. M1: 400 = 50 × 32 ÷ c
    2. M1: c = 50 × 32 ÷ 400
    3. A1: 4
    Answer: 4
    Capture-Recapture
    [3 marks]

  4. Question 4. p is inversely proportional to the square root of q.
    p = 6 when q = 25.
    Find the value of p when q = 36.

    Show worked answerHide worked answer
    1. M1: 6 = k ÷ √25
    2. M1: p = 30 ÷ √36
    3. A1: 5
    Answer: 5
    Algebraic Inverse Proportion
    [3 marks]

  5. Question 5. The graph shows a runner's distance from the start against time. The tangent to the curve at 4 seconds passes through (2, 0) and (6, 16). Work out the speed of the runner at 4 seconds.

    Show worked answerHide worked answer
    1. M1: (16 − 0) ÷ (6 − 2)
    2. A1: 4
    Answer: 4
    Instantaneous Gradients of Lines
    Time (seconds)Distance (metres)0816243202468
    [2 marks]