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

Mixed Topic Worksheet Grades 6/7: Day 008

Grades 6/7Calculator

  1. Question 1. x : y = 2 : 5 and x + y = 63
    Work out the value of x and the value of y.

    Show worked answerHide worked answer
    1. M1: y = dfrac5x2 or 5x = 2y
    2. M1: x + dfrac5x2 = 63, so dfrac7x2 = 63
    3. A1: x = 18 and y = 45
    Answer: x = 18, y = 45
    Expressing Ratios as Linear Equations
    [3 marks]

  2. Question 2. The diagram shows triangle WXY. Work out the exact area of triangle WXY. Give your answer in the form a√3 cm² where a is an integer.

    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 60^° with sin 60^° = frac√32
    2. A1: 21√3
    Answer: 21√3 cm²
    Area of Triangles Using ½ab sin C
    12 cm7 cm60°WXYNot drawn accurately
    [2 marks]

  3. Question 3. Ticket prices in £ at two theatres. A: minimum 15.50, lower quartile 20, median 28.50, upper quartile 38.50, maximum 60.50. B: minimum 18.25, lower quartile 25, median 30, upper quartile 35, maximum 50.75. Compare the prices using the median and the range.

    Show worked answerHide worked answer
    1. M1: medians: A £28.50, B £30
    2. M1: ranges: A 60.50 - 15.50 = 45, B 50.75 - 18.25 = 32.50
    3. A1: B has the higher median; A's prices vary more
    Answer: B has the higher median (£30 > £28.50). A has the larger range (£45 > £32.50), so A's prices vary more.
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. n is an integer.
    Prove that (n + 3)² - 6n - 9 is a square number.

    Show worked answerHide worked answer
    1. M1: n² + 6n + 9 - 6n - 9
    2. C1: n², which is the square of the integer n
    Answer: n²
    Proof with Square Numbers
    [2 marks]

  5. Question 5. B is 8 km from A on a bearing of 060^°.
    C is on a bearing of 125^° from A.
    C is on a bearing of 170^° from B.
    Work out the distance AC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: angle ABC = (60^° + 180^°) - 170^°
    2. M1: angle ACB = 180^° - 65^° - 70^°
    3. M1: dfracACsin 70^° = dfrac8sin 45^°
    4. A1: 10.6
    Answer: 10.6
    Combining the Sine Rule with Other Rules
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 008

Grades 6/7Calculator

  1. Question 1. x : y = 2 : 5 and x + y = 63
    Work out the value of x and the value of y.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = dfrac5x2 or 5x = 2y
    2. M1: x + dfrac5x2 = 63, so dfrac7x2 = 63
    3. A1: x = 18 and y = 45
    Answer: x = 18, y = 45
    Expressing Ratios as Linear Equations

  2. Question 2. The diagram shows triangle WXY. Work out the exact area of triangle WXY. Give your answer in the form a√3 cm² where a is an integer.

    [2 marks]
    12 cm7 cm60°WXYNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 60^° with sin 60^° = frac√32
    2. A1: 21√3
    Answer: 21√3 cm²
    Area of Triangles Using ½ab sin C

  3. Question 3. Ticket prices in £ at two theatres. A: minimum 15.50, lower quartile 20, median 28.50, upper quartile 38.50, maximum 60.50. B: minimum 18.25, lower quartile 25, median 30, upper quartile 35, maximum 50.75. Compare the prices using the median and the range.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: medians: A £28.50, B £30
    2. M1: ranges: A 60.50 - 15.50 = 45, B 50.75 - 18.25 = 32.50
    3. A1: B has the higher median; A's prices vary more
    Answer: B has the higher median (£30 > £28.50). A has the larger range (£45 > £32.50), so A's prices vary more.
    Comparing Data Using Box Plots

  4. Question 4. n is an integer.
    Prove that (n + 3)² - 6n - 9 is a square number.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: n² + 6n + 9 - 6n - 9
    2. C1: n², which is the square of the integer n
    Answer: n²
    Proof with Square Numbers

  5. Question 5. B is 8 km from A on a bearing of 060^°.
    C is on a bearing of 125^° from A.
    C is on a bearing of 170^° from B.
    Work out the distance AC.
    Give your answer to 1 decimal place.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: angle ABC = (60^° + 180^°) - 170^°
    2. M1: angle ACB = 180^° - 65^° - 70^°
    3. M1: dfracACsin 70^° = dfrac8sin 45^°
    4. A1: 10.6
    Answer: 10.6
    Combining the Sine Rule with Other Rules
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 008

Grades 6/7Calculator

  1. Question 1. x : y = 2 : 5 and x + y = 63
    Work out the value of x and the value of y.

    Show worked answerHide worked answer
    1. M1: y = dfrac5x2 or 5x = 2y
    2. M1: x + dfrac5x2 = 63, so dfrac7x2 = 63
    3. A1: x = 18 and y = 45
    Answer: x = 18, y = 45
    Expressing Ratios as Linear Equations
    [3 marks]

  2. Question 2. The diagram shows triangle WXY. Work out the exact area of triangle WXY. Give your answer in the form a√3 cm² where a is an integer.

    Show worked answerHide worked answer
    1. M1: 1/2 × 12 × 7 × sin 60^° with sin 60^° = frac√32
    2. A1: 21√3
    Answer: 21√3 cm²
    Area of Triangles Using ½ab sin C
    12 cm7 cm60°WXYNot drawn accurately
    [2 marks]

  3. Question 3. Ticket prices in £ at two theatres. A: minimum 15.50, lower quartile 20, median 28.50, upper quartile 38.50, maximum 60.50. B: minimum 18.25, lower quartile 25, median 30, upper quartile 35, maximum 50.75. Compare the prices using the median and the range.

    Show worked answerHide worked answer
    1. M1: medians: A £28.50, B £30
    2. M1: ranges: A 60.50 - 15.50 = 45, B 50.75 - 18.25 = 32.50
    3. A1: B has the higher median; A's prices vary more
    Answer: B has the higher median (£30 > £28.50). A has the larger range (£45 > £32.50), so A's prices vary more.
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. n is an integer.
    Prove that (n + 3)² - 6n - 9 is a square number.

    Show worked answerHide worked answer
    1. M1: n² + 6n + 9 - 6n - 9
    2. C1: n², which is the square of the integer n
    Answer: n²
    Proof with Square Numbers
    [2 marks]

  5. Question 5. B is 8 km from A on a bearing of 060^°.
    C is on a bearing of 125^° from A.
    C is on a bearing of 170^° from B.
    Work out the distance AC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: angle ABC = (60^° + 180^°) - 170^°
    2. M1: angle ACB = 180^° - 65^° - 70^°
    3. M1: dfracACsin 70^° = dfrac8sin 45^°
    4. A1: 10.6
    Answer: 10.6
    Combining the Sine Rule with Other Rules
    [4 marks]