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

Mixed Topic Worksheet Grades 6/7: Day 034

Grades 6/7Calculator

  1. Question 1. Here is a right-angled triangle TUV.
    Work out the value of x.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin 36° = 5.8/x
    2. M1: x = 5.8 ÷ sin 36°
    3. A1: 9.9
    Answer: 9.9 cm
    Finding Angles Using SOH, CAH, TOA
    5.8 cmx36°TUV
    [3 marks]

  2. Question 2. An extra value of 50 is added to the data 4, 6, 7, 9, 10, 12. Work out the interquartile range before and after, and the range before and after.

    Show worked answerHide worked answer
    1. B1: IQR before: 10 - 6 = 4 and range 12 - 4 = 8
    2. B1: IQR after (4, 6, 7, 9, 10, 12, 50): 12 - 6 = 6 and range 50 - 4 = 46
    Answer: IQR: before 4, after 6; range: before 8, after 46
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. 3(n + 2) + k(n + 9) is a multiple of 7 for all integer values of n.
    k is a positive integer less than 7.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: 3n + 6 + kn + 9k = (3 + k)n + 6 + 9k
    2. M1: 3 + k is a multiple of 7
    3. A1: k = 4
    Answer: k = 4
    Proof with Multiples
    [3 marks]

  4. Question 4. Expand and simplify (2 + √3)(5 - √3)

    Show worked answerHide worked answer
    1. M1: four terms 10 - 2√3 + 5√3 - 3
    2. A1: 7 + 3√3
    Answer: 7 + 3√3
    Expanding Brackets with Surds
    [2 marks]

  5. Question 5. A=x : 3(x-2)<12, x is an integer and B=x : x ≥ -1, x is an integer. Work out n(A cap B).

    Show worked answerHide worked answer
    1. M1: x-2<4, so x<6
    2. M1: A cap B=-1, 0, 1, 2, 3, 4, 5
    3. A1: 7
    Answer: 7
    Sets & Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 034

Grades 6/7Calculator

  1. Question 1. Here is a right-angled triangle TUV.
    Work out the value of x.
    Give your answer to 1 decimal place.

    [3 marks]
    5.8 cmx36°TUV
    Show worked answerHide worked answer
    1. M1: sin 36° = 5.8/x
    2. M1: x = 5.8 ÷ sin 36°
    3. A1: 9.9
    Answer: 9.9 cm
    Finding Angles Using SOH, CAH, TOA

  2. Question 2. An extra value of 50 is added to the data 4, 6, 7, 9, 10, 12. Work out the interquartile range before and after, and the range before and after.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: IQR before: 10 - 6 = 4 and range 12 - 4 = 8
    2. B1: IQR after (4, 6, 7, 9, 10, 12, 50): 12 - 6 = 6 and range 50 - 4 = 46
    Answer: IQR: before 4, after 6; range: before 8, after 46
    Benefits of IQR & Range

  3. Question 3. 3(n + 2) + k(n + 9) is a multiple of 7 for all integer values of n.
    k is a positive integer less than 7.
    Work out the value of k.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3n + 6 + kn + 9k = (3 + k)n + 6 + 9k
    2. M1: 3 + k is a multiple of 7
    3. A1: k = 4
    Answer: k = 4
    Proof with Multiples

  4. Question 4. Expand and simplify (2 + √3)(5 - √3)

    [2 marks]
    Show worked answerHide worked answer
    1. M1: four terms 10 - 2√3 + 5√3 - 3
    2. A1: 7 + 3√3
    Answer: 7 + 3√3
    Expanding Brackets with Surds

  5. Question 5. A=x : 3(x-2)<12, x is an integer and B=x : x ≥ -1, x is an integer. Work out n(A cap B).

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x-2<4, so x<6
    2. M1: A cap B=-1, 0, 1, 2, 3, 4, 5
    3. A1: 7
    Answer: 7
    Sets & Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 034

Grades 6/7Calculator

  1. Question 1. Here is a right-angled triangle TUV.
    Work out the value of x.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin 36° = 5.8/x
    2. M1: x = 5.8 ÷ sin 36°
    3. A1: 9.9
    Answer: 9.9 cm
    Finding Angles Using SOH, CAH, TOA
    5.8 cmx36°TUV
    [3 marks]

  2. Question 2. An extra value of 50 is added to the data 4, 6, 7, 9, 10, 12. Work out the interquartile range before and after, and the range before and after.

    Show worked answerHide worked answer
    1. B1: IQR before: 10 - 6 = 4 and range 12 - 4 = 8
    2. B1: IQR after (4, 6, 7, 9, 10, 12, 50): 12 - 6 = 6 and range 50 - 4 = 46
    Answer: IQR: before 4, after 6; range: before 8, after 46
    Benefits of IQR & Range
    [2 marks]

  3. Question 3. 3(n + 2) + k(n + 9) is a multiple of 7 for all integer values of n.
    k is a positive integer less than 7.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: 3n + 6 + kn + 9k = (3 + k)n + 6 + 9k
    2. M1: 3 + k is a multiple of 7
    3. A1: k = 4
    Answer: k = 4
    Proof with Multiples
    [3 marks]

  4. Question 4. Expand and simplify (2 + √3)(5 - √3)

    Show worked answerHide worked answer
    1. M1: four terms 10 - 2√3 + 5√3 - 3
    2. A1: 7 + 3√3
    Answer: 7 + 3√3
    Expanding Brackets with Surds
    [2 marks]

  5. Question 5. A=x : 3(x-2)<12, x is an integer and B=x : x ≥ -1, x is an integer. Work out n(A cap B).

    Show worked answerHide worked answer
    1. M1: x-2<4, so x<6
    2. M1: A cap B=-1, 0, 1, 2, 3, 4, 5
    3. A1: 7
    Answer: 7
    Sets & Inequalities
    [3 marks]