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

Mixed Topic Worksheet Grades 6/7: Day 092

Grades 6/7Calculator

  1. Question 1. Tom says that the points (5, 7) and (-5, 7) both lie on the graph of y = dfrac35x
    Is Tom correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 35 ÷ (-5) = -7
    2. A1: not 7, so Tom is not correct
    Answer: No: only (5, 7) is on the graph
    Sketching Reciprocal Graphs
    [2 marks]

  2. Question 2. An enlargement has centre (2, 1).
    It maps the point (3, 2) onto the point (0, -1).
    Work out the scale factor of the enlargement.

    Show worked answerHide worked answer
    1. M1: (3, 2) is 1 right and 1 up from the centre and (0, -1) is 2 left and 2 down from the centre
    2. A1: scale factor -2
    Answer: -2
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. The diagram shows triangle GHJ. Work out the area of triangle GHJ. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 7.4 × 10.2 × sin 58^°
    2. A1: 32.0
    Answer: 32.0
    Area of Triangles Using ½ab sin C
    7.4 cm10.2 cm58°GHJNot drawn accurately
    [2 marks]

  4. Question 4. In triangle ABC, AB = 7.3 cm, AC = 5.8 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 7.3² + 5.8² - 2 × 7.3 × 5.8 × cos 48^°
    2. M1: BC² = 30.27ldots
    3. A1: 5.5 cm
    Answer: 5.5 cm
    Fundamentals of the Cosine Rule
    [3 marks]

  5. Question 5. x_n+1 = dfracx_n² + 1112
    x_0 = 3
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    Show worked answerHide worked answer
    1. M1: x_1 = dfrac3² + 1112
    2. A1: x_1 = 1.667 and x_2 = 1.148
    3. A1: x_3 = 1.027
    Answer: x_1 = 1.667, x_2 = 1.148, x_3 = 1.027
    Iteration Equations
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 092

Grades 6/7Calculator

  1. Question 1. Tom says that the points (5, 7) and (-5, 7) both lie on the graph of y = dfrac35x
    Is Tom correct? You must show your working.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 35 ÷ (-5) = -7
    2. A1: not 7, so Tom is not correct
    Answer: No: only (5, 7) is on the graph
    Sketching Reciprocal Graphs

  2. Question 2. An enlargement has centre (2, 1).
    It maps the point (3, 2) onto the point (0, -1).
    Work out the scale factor of the enlargement.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (3, 2) is 1 right and 1 up from the centre and (0, -1) is 2 left and 2 down from the centre
    2. A1: scale factor -2
    Answer: -2
    Enlargements with Negative Integer Scale Factors

  3. Question 3. The diagram shows triangle GHJ. Work out the area of triangle GHJ. Give your answer to 1 decimal place.

    [2 marks]
    7.4 cm10.2 cm58°GHJNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × 7.4 × 10.2 × sin 58^°
    2. A1: 32.0
    Answer: 32.0
    Area of Triangles Using ½ab sin C

  4. Question 4. In triangle ABC, AB = 7.3 cm, AC = 5.8 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer correct to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: BC² = 7.3² + 5.8² - 2 × 7.3 × 5.8 × cos 48^°
    2. M1: BC² = 30.27ldots
    3. A1: 5.5 cm
    Answer: 5.5 cm
    Fundamentals of the Cosine Rule

  5. Question 5. x_n+1 = dfracx_n² + 1112
    x_0 = 3
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x_1 = dfrac3² + 1112
    2. A1: x_1 = 1.667 and x_2 = 1.148
    3. A1: x_3 = 1.027
    Answer: x_1 = 1.667, x_2 = 1.148, x_3 = 1.027
    Iteration Equations
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 092

Grades 6/7Calculator

  1. Question 1. Tom says that the points (5, 7) and (-5, 7) both lie on the graph of y = dfrac35x
    Is Tom correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 35 ÷ (-5) = -7
    2. A1: not 7, so Tom is not correct
    Answer: No: only (5, 7) is on the graph
    Sketching Reciprocal Graphs
    [2 marks]

  2. Question 2. An enlargement has centre (2, 1).
    It maps the point (3, 2) onto the point (0, -1).
    Work out the scale factor of the enlargement.

    Show worked answerHide worked answer
    1. M1: (3, 2) is 1 right and 1 up from the centre and (0, -1) is 2 left and 2 down from the centre
    2. A1: scale factor -2
    Answer: -2
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. The diagram shows triangle GHJ. Work out the area of triangle GHJ. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 7.4 × 10.2 × sin 58^°
    2. A1: 32.0
    Answer: 32.0
    Area of Triangles Using ½ab sin C
    7.4 cm10.2 cm58°GHJNot drawn accurately
    [2 marks]

  4. Question 4. In triangle ABC, AB = 7.3 cm, AC = 5.8 cm and angle BAC = 48^°
    Work out the length of BC.
    Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 7.3² + 5.8² - 2 × 7.3 × 5.8 × cos 48^°
    2. M1: BC² = 30.27ldots
    3. A1: 5.5 cm
    Answer: 5.5 cm
    Fundamentals of the Cosine Rule
    [3 marks]

  5. Question 5. x_n+1 = dfracx_n² + 1112
    x_0 = 3
    Work out x_1, x_2 and x_3
    Give your answers correct to 3 decimal places.

    Show worked answerHide worked answer
    1. M1: x_1 = dfrac3² + 1112
    2. A1: x_1 = 1.667 and x_2 = 1.148
    3. A1: x_3 = 1.027
    Answer: x_1 = 1.667, x_2 = 1.148, x_3 = 1.027
    Iteration Equations
    [3 marks]