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

Mixed Topic Worksheet Grades 6/7: Day 066

Grades 6/7Calculator

  1. Question 1. x : y = 3 : 4
    x + y = 56

    Kim says that y = 36

    Is Kim correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 3 + 4 = 7 parts, so 56 ÷ 7 = 8
    2. M1: 4 × 8 = 32
    3. A1: No, with y = 32
    Answer: No. 56 ÷ 7 = 8 so y = 4 × 8 = 32
    Expressing Ratios as Linear Equations
    [3 marks]

  2. Question 2. Make x the subject of y = dfrac3x + 25

    Show worked answerHide worked answer
    1. M1: 5y = 3x + 2
    2. A1: x = dfrac5y - 23
    Answer: x = dfrac5y - 23
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. The area of triangle ABC is 36 cm².
    Work out the length of AC.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9.5 × x × sin 62^° = 36
    2. M1: x = 72/9.5 × sin 62^°
    3. A1: 8.6
    Answer: 8.6 cm
    Area of Triangles Using ½ab sin C
    9.5 cmx62°ABC
    [3 marks]

  4. Question 4. The number of bacteria in a dish is N = 200 × 2t, where t is the time in hours.
    (a) Describe how the number of bacteria changes each hour. [1]
    (b) Work out N when t = 3. [1]

    Show worked answerHide worked answer
    1. B1: (a) it doubles every hour
    2. B1: (b) 200 × 8 = 1600
    Answer: (a) Doubles every hour; (b) 1600
    Sketching Exponential Graphs
    [2 marks]

  5. Question 5. In triangle PQR
    PQ = 9 cm, QR = 7 cm and angle PRQ = 52^°
    Work out the size of angle QPR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracsin QPR7 = dfracsin 52^°9
    2. M1: sin QPR = 0.6128ldots
    3. A1: 37.8^°
    Answer: 37.8^°
    Finding Angles Using the Sine Rule
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 066

Grades 6/7Calculator

  1. Question 1. x : y = 3 : 4
    x + y = 56

    Kim says that y = 36

    Is Kim correct?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3 + 4 = 7 parts, so 56 ÷ 7 = 8
    2. M1: 4 × 8 = 32
    3. A1: No, with y = 32
    Answer: No. 56 ÷ 7 = 8 so y = 4 × 8 = 32
    Expressing Ratios as Linear Equations

  2. Question 2. Make x the subject of y = dfrac3x + 25

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5y = 3x + 2
    2. A1: x = dfrac5y - 23
    Answer: x = dfrac5y - 23
    Rearranging Harder Equations

  3. Question 3. The area of triangle ABC is 36 cm².
    Work out the length of AC.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    [3 marks]
    9.5 cmx62°ABC
    Show worked answerHide worked answer
    1. M1: 1/2 × 9.5 × x × sin 62^° = 36
    2. M1: x = 72/9.5 × sin 62^°
    3. A1: 8.6
    Answer: 8.6 cm
    Area of Triangles Using ½ab sin C

  4. Question 4. The number of bacteria in a dish is N = 200 × 2t, where t is the time in hours.
    (a) Describe how the number of bacteria changes each hour. [1]
    (b) Work out N when t = 3. [1]

    [2 marks]
    Show worked answerHide worked answer
    1. B1: (a) it doubles every hour
    2. B1: (b) 200 × 8 = 1600
    Answer: (a) Doubles every hour; (b) 1600
    Sketching Exponential Graphs

  5. Question 5. In triangle PQR
    PQ = 9 cm, QR = 7 cm and angle PRQ = 52^°
    Work out the size of angle QPR.
    Give your answer to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfracsin QPR7 = dfracsin 52^°9
    2. M1: sin QPR = 0.6128ldots
    3. A1: 37.8^°
    Answer: 37.8^°
    Finding Angles Using the Sine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 066

Grades 6/7Calculator

  1. Question 1. x : y = 3 : 4
    x + y = 56

    Kim says that y = 36

    Is Kim correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: 3 + 4 = 7 parts, so 56 ÷ 7 = 8
    2. M1: 4 × 8 = 32
    3. A1: No, with y = 32
    Answer: No. 56 ÷ 7 = 8 so y = 4 × 8 = 32
    Expressing Ratios as Linear Equations
    [3 marks]

  2. Question 2. Make x the subject of y = dfrac3x + 25

    Show worked answerHide worked answer
    1. M1: 5y = 3x + 2
    2. A1: x = dfrac5y - 23
    Answer: x = dfrac5y - 23
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. The area of triangle ABC is 36 cm².
    Work out the length of AC.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9.5 × x × sin 62^° = 36
    2. M1: x = 72/9.5 × sin 62^°
    3. A1: 8.6
    Answer: 8.6 cm
    Area of Triangles Using ½ab sin C
    9.5 cmx62°ABC
    [3 marks]

  4. Question 4. The number of bacteria in a dish is N = 200 × 2t, where t is the time in hours.
    (a) Describe how the number of bacteria changes each hour. [1]
    (b) Work out N when t = 3. [1]

    Show worked answerHide worked answer
    1. B1: (a) it doubles every hour
    2. B1: (b) 200 × 8 = 1600
    Answer: (a) Doubles every hour; (b) 1600
    Sketching Exponential Graphs
    [2 marks]

  5. Question 5. In triangle PQR
    PQ = 9 cm, QR = 7 cm and angle PRQ = 52^°
    Work out the size of angle QPR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: dfracsin QPR7 = dfracsin 52^°9
    2. M1: sin QPR = 0.6128ldots
    3. A1: 37.8^°
    Answer: 37.8^°
    Finding Angles Using the Sine Rule
    [3 marks]