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

Mixed Topic Worksheet Grades 6/7: Day 096

Grades 6/7Calculator

  1. Question 1. The table shows the lengths, in metres, of 20 bamboo canes. Work out an estimate for the mean length. Give your answer in centimetres.

    Show worked answerHide worked answer
    1. M1: 1.5 × 3 + 2.5 × 8 + 3.5 × 7 + 4.5 × 2
    2. M1: divides the total of the products by 20
    3. A1: 2.9 metres
    4. A1: 290 cm
    Answer: 290 cm
    Mean, Mode & Median from a Grouped Frequency Table
    Length, h (metres)Frequency1 < h ≤ 232 < h ≤ 383 < h ≤ 474 < h ≤ 52
    [4 marks]

  2. Question 2. An enlargement has scale factor -2 and centre (1, 1).
    It maps the point P onto the point (7, -3).
    Work out the coordinates of P.

    Show worked answerHide worked answer
    1. M1: the image is 7 - 1 = 6 right and -3 - 1 = -4 from the centre, so P is 6 ÷ (-2) and -4 ÷ (-2) from the centre
    2. A1: P = (-2, 3)
    Answer: (-2, 3)
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. √k × √3 = 6
    Work out the value of k.

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    1. M1: 3k = 36
    2. A1: 12
    Answer: 12
    Rational & Irrational Numbers
    [2 marks]

  4. Question 4. Leah expands (x + 2)(x - 3)(x + 4). Her working:
    (x + 2)(x - 3) = x² - x + 6
    (x² - x + 6)(x + 4) = x³ + 3x² + 2x + 24
    Her answer is wrong. Work out the correct expansion and describe her mistake.

    Show worked answerHide worked answer
    1. M1: 2 × (-3) = -6
    2. M1: (x² - x - 6)(x + 4) = x³ + 4x² - x² - 4x - 6x - 24
    3. A1: x³ + 3x² - 10x - 24
    Answer: The product of 2 and -3 is -6, not +6. The correct expansion is x³ + 3x² - 10x - 24.
    Expanding Triple Brackets
    [3 marks]

  5. Question 5. Triangle ABC has
    AB = 7 cm, AC = 11 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 7² + 11² - 2 × 7 × 11 × cos 48^°
    2. M1: BC² = 66.95ldots
    3. M1: BC = √66.95ldots
    4. A1: 8.2 cm
    Answer: 8.2 cm
    Combining the Cosine Rule with Other Rules
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 096

Grades 6/7Calculator

  1. Question 1. The table shows the lengths, in metres, of 20 bamboo canes. Work out an estimate for the mean length. Give your answer in centimetres.

    [4 marks]
    Length, h (metres)Frequency1 < h ≤ 232 < h ≤ 383 < h ≤ 474 < h ≤ 52
    Show worked answerHide worked answer
    1. M1: 1.5 × 3 + 2.5 × 8 + 3.5 × 7 + 4.5 × 2
    2. M1: divides the total of the products by 20
    3. A1: 2.9 metres
    4. A1: 290 cm
    Answer: 290 cm
    Mean, Mode & Median from a Grouped Frequency Table

  2. Question 2. An enlargement has scale factor -2 and centre (1, 1).
    It maps the point P onto the point (7, -3).
    Work out the coordinates of P.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: the image is 7 - 1 = 6 right and -3 - 1 = -4 from the centre, so P is 6 ÷ (-2) and -4 ÷ (-2) from the centre
    2. A1: P = (-2, 3)
    Answer: (-2, 3)
    Enlargements with Negative Integer Scale Factors

  3. Question 3. √k × √3 = 6
    Work out the value of k.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 3k = 36
    2. A1: 12
    Answer: 12
    Rational & Irrational Numbers

  4. Question 4. Leah expands (x + 2)(x - 3)(x + 4). Her working:
    (x + 2)(x - 3) = x² - x + 6
    (x² - x + 6)(x + 4) = x³ + 3x² + 2x + 24
    Her answer is wrong. Work out the correct expansion and describe her mistake.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2 × (-3) = -6
    2. M1: (x² - x - 6)(x + 4) = x³ + 4x² - x² - 4x - 6x - 24
    3. A1: x³ + 3x² - 10x - 24
    Answer: The product of 2 and -3 is -6, not +6. The correct expansion is x³ + 3x² - 10x - 24.
    Expanding Triple Brackets

  5. Question 5. Triangle ABC has
    AB = 7 cm, AC = 11 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer to 1 decimal place.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: BC² = 7² + 11² - 2 × 7 × 11 × cos 48^°
    2. M1: BC² = 66.95ldots
    3. M1: BC = √66.95ldots
    4. A1: 8.2 cm
    Answer: 8.2 cm
    Combining the Cosine Rule with Other Rules
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 096

Grades 6/7Calculator

  1. Question 1. The table shows the lengths, in metres, of 20 bamboo canes. Work out an estimate for the mean length. Give your answer in centimetres.

    Show worked answerHide worked answer
    1. M1: 1.5 × 3 + 2.5 × 8 + 3.5 × 7 + 4.5 × 2
    2. M1: divides the total of the products by 20
    3. A1: 2.9 metres
    4. A1: 290 cm
    Answer: 290 cm
    Mean, Mode & Median from a Grouped Frequency Table
    Length, h (metres)Frequency1 < h ≤ 232 < h ≤ 383 < h ≤ 474 < h ≤ 52
    [4 marks]

  2. Question 2. An enlargement has scale factor -2 and centre (1, 1).
    It maps the point P onto the point (7, -3).
    Work out the coordinates of P.

    Show worked answerHide worked answer
    1. M1: the image is 7 - 1 = 6 right and -3 - 1 = -4 from the centre, so P is 6 ÷ (-2) and -4 ÷ (-2) from the centre
    2. A1: P = (-2, 3)
    Answer: (-2, 3)
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. √k × √3 = 6
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: 3k = 36
    2. A1: 12
    Answer: 12
    Rational & Irrational Numbers
    [2 marks]

  4. Question 4. Leah expands (x + 2)(x - 3)(x + 4). Her working:
    (x + 2)(x - 3) = x² - x + 6
    (x² - x + 6)(x + 4) = x³ + 3x² + 2x + 24
    Her answer is wrong. Work out the correct expansion and describe her mistake.

    Show worked answerHide worked answer
    1. M1: 2 × (-3) = -6
    2. M1: (x² - x - 6)(x + 4) = x³ + 4x² - x² - 4x - 6x - 24
    3. A1: x³ + 3x² - 10x - 24
    Answer: The product of 2 and -3 is -6, not +6. The correct expansion is x³ + 3x² - 10x - 24.
    Expanding Triple Brackets
    [3 marks]

  5. Question 5. Triangle ABC has
    AB = 7 cm, AC = 11 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 7² + 11² - 2 × 7 × 11 × cos 48^°
    2. M1: BC² = 66.95ldots
    3. M1: BC = √66.95ldots
    4. A1: 8.2 cm
    Answer: 8.2 cm
    Combining the Cosine Rule with Other Rules
    [4 marks]