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

Mixed Topic Worksheet Grades 6/7: Day 047

Grades 6/7Non-calculator

  1. Question 1. 4sin x = 2√2
    x is an acute angle.
    Work out the value of x.

    Show worked answerHide worked answer
    1. M1: sin x = dfrac2√24
    2. M1: sin x = dfrac√22
    3. A1: 45
    Answer: 45
    Hand Method for Exact Trig Values
    [3 marks]

  2. Question 2. Asha works out an estimate for the cube root of 60
    Her working is 60 ÷ 3 = 20
    Asha says that an estimate for the cube root of 60 is 20
    Is Asha correct? You must give a reason.

    Show worked answerHide worked answer
    1. M1: 3³ = 27 and 4³ = 64
    2. M1: 20³ = 8000, which is far more than 60
    3. C1: an estimate is 4, so Asha is not correct
    Answer: No
    Estimating Roots
    [3 marks]

  3. Question 3. Cylinder A and cylinder B are mathematically similar.
    The surface area of A is 64 cm².
    The surface area of B is 100 cm².
    The height of A is 8 cm.
    Work out the height of B.

    Show worked answerHide worked answer
    1. M1: area scale factor = 100 ÷ 64
    2. M1: length scale factor = √100/64 = 5/4
    3. A1: 8 × 5/4 = 10 cm
    Answer: 10 cm
    Similar Areas & Volumes
    [3 marks]

  4. Question 4. Kai and Zoe find the coefficient of x² in the expansion of (x + 2)(x - 3)(x + 6). Kai says 5. Zoe says 11. Who is correct? Give a reason.

    Show worked answerHide worked answer
    1. M1: 2 + (-3) + 6 = 5
    2. A1: Kai, because x² comes from one constant and two letters in each product
    Answer: Kai is correct. The coefficient of x² is the sum of the three constants, 2 + (-3) + 6.
    Expanding Triple Brackets
    [2 marks]

  5. Question 5. Line mathbfL_1 has equation y = kx - 4
    Line mathbfL_2 has equation 3y + 5x = 21
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: mathbfL_2 has gradient -dfrac53, so k × ≤ft(-dfrac53) = -1
    2. A1: k = dfrac35
    Answer: k = dfrac35
    Properties of Perpendicular Lines
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 047

Grades 6/7Non-calculator

  1. Question 1. 4sin x = 2√2
    x is an acute angle.
    Work out the value of x.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: sin x = dfrac2√24
    2. M1: sin x = dfrac√22
    3. A1: 45
    Answer: 45
    Hand Method for Exact Trig Values

  2. Question 2. Asha works out an estimate for the cube root of 60
    Her working is 60 ÷ 3 = 20
    Asha says that an estimate for the cube root of 60 is 20
    Is Asha correct? You must give a reason.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3³ = 27 and 4³ = 64
    2. M1: 20³ = 8000, which is far more than 60
    3. C1: an estimate is 4, so Asha is not correct
    Answer: No
    Estimating Roots

  3. Question 3. Cylinder A and cylinder B are mathematically similar.
    The surface area of A is 64 cm².
    The surface area of B is 100 cm².
    The height of A is 8 cm.
    Work out the height of B.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: area scale factor = 100 ÷ 64
    2. M1: length scale factor = √100/64 = 5/4
    3. A1: 8 × 5/4 = 10 cm
    Answer: 10 cm
    Similar Areas & Volumes

  4. Question 4. Kai and Zoe find the coefficient of x² in the expansion of (x + 2)(x - 3)(x + 6). Kai says 5. Zoe says 11. Who is correct? Give a reason.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 2 + (-3) + 6 = 5
    2. A1: Kai, because x² comes from one constant and two letters in each product
    Answer: Kai is correct. The coefficient of x² is the sum of the three constants, 2 + (-3) + 6.
    Expanding Triple Brackets

  5. Question 5. Line mathbfL_1 has equation y = kx - 4
    Line mathbfL_2 has equation 3y + 5x = 21
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: mathbfL_2 has gradient -dfrac53, so k × ≤ft(-dfrac53) = -1
    2. A1: k = dfrac35
    Answer: k = dfrac35
    Properties of Perpendicular Lines
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 047

Grades 6/7Non-calculator

  1. Question 1. 4sin x = 2√2
    x is an acute angle.
    Work out the value of x.

    Show worked answerHide worked answer
    1. M1: sin x = dfrac2√24
    2. M1: sin x = dfrac√22
    3. A1: 45
    Answer: 45
    Hand Method for Exact Trig Values
    [3 marks]

  2. Question 2. Asha works out an estimate for the cube root of 60
    Her working is 60 ÷ 3 = 20
    Asha says that an estimate for the cube root of 60 is 20
    Is Asha correct? You must give a reason.

    Show worked answerHide worked answer
    1. M1: 3³ = 27 and 4³ = 64
    2. M1: 20³ = 8000, which is far more than 60
    3. C1: an estimate is 4, so Asha is not correct
    Answer: No
    Estimating Roots
    [3 marks]

  3. Question 3. Cylinder A and cylinder B are mathematically similar.
    The surface area of A is 64 cm².
    The surface area of B is 100 cm².
    The height of A is 8 cm.
    Work out the height of B.

    Show worked answerHide worked answer
    1. M1: area scale factor = 100 ÷ 64
    2. M1: length scale factor = √100/64 = 5/4
    3. A1: 8 × 5/4 = 10 cm
    Answer: 10 cm
    Similar Areas & Volumes
    [3 marks]

  4. Question 4. Kai and Zoe find the coefficient of x² in the expansion of (x + 2)(x - 3)(x + 6). Kai says 5. Zoe says 11. Who is correct? Give a reason.

    Show worked answerHide worked answer
    1. M1: 2 + (-3) + 6 = 5
    2. A1: Kai, because x² comes from one constant and two letters in each product
    Answer: Kai is correct. The coefficient of x² is the sum of the three constants, 2 + (-3) + 6.
    Expanding Triple Brackets
    [2 marks]

  5. Question 5. Line mathbfL_1 has equation y = kx - 4
    Line mathbfL_2 has equation 3y + 5x = 21
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: mathbfL_2 has gradient -dfrac53, so k × ≤ft(-dfrac53) = -1
    2. A1: k = dfrac35
    Answer: k = dfrac35
    Properties of Perpendicular Lines
    [2 marks]