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

Mixed Topic Worksheet Grades 6/7: Day 071

Grades 6/7Non-calculator

  1. Question 1. ABC is an equilateral triangle. North lines are shown at A and at B.
    The bearing of B from A is 035^°.
    Work out the bearing of C from B.

    Show worked answerHide worked answer
    1. M1: 35 + 180 = 215
    2. M1: 215 - 60
    3. A1: 155^°
    Answer: 155^°
    Problem Solving with Bearings
    NN035°ABCNot drawn accurately
    [3 marks]

  2. Question 2. Class X: minimum 12, lower quartile 20, median 25, upper quartile 32, maximum 45. Work out the interquartile range.

    Show worked answerHide worked answer
    1. M1: 32 - 20
    2. A1: 12
    Answer: 12
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. k is an integer greater than 1. √27 × √k is a rational number. Work out the smallest possible value of k.

    Show worked answerHide worked answer
    1. M1: √27k is rational when 27k is a square number
    2. M1: tests k = 2 (54) and k = 3 (81 = 9²)
    3. A1: 3
    Answer: 3
    Rational & Irrational Numbers
    [3 marks]

  4. Question 4. Line mathbfL_1 has equation 4y + 3x = 36
    Line mathbfL_2 has equation 9y + kx = 26
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: gradient of mathbfL_1 is -dfrac34, gradient of mathbfL_2 is -dfrack9, and -dfrac34 × -dfrack9 = -1
    2. A1: k = -12
    Answer: k = -12
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. Prove algebraically that the sum of three consecutive odd numbers is a multiple of 3.

    Show worked answerHide worked answer
    1. M1: (2n + 1) + (2n + 3) + (2n + 5)
    2. A1: 6n + 9
    3. C1: 3(2n + 3), which is a multiple of 3
    Answer: 3(2n + 3)
    Proof with Odd Numbers
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 071

Grades 6/7Non-calculator

  1. Question 1. ABC is an equilateral triangle. North lines are shown at A and at B.
    The bearing of B from A is 035^°.
    Work out the bearing of C from B.

    [3 marks]
    NN035°ABCNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 35 + 180 = 215
    2. M1: 215 - 60
    3. A1: 155^°
    Answer: 155^°
    Problem Solving with Bearings

  2. Question 2. Class X: minimum 12, lower quartile 20, median 25, upper quartile 32, maximum 45. Work out the interquartile range.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 32 - 20
    2. A1: 12
    Answer: 12
    Comparing Data Using Box Plots

  3. Question 3. k is an integer greater than 1. √27 × √k is a rational number. Work out the smallest possible value of k.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √27k is rational when 27k is a square number
    2. M1: tests k = 2 (54) and k = 3 (81 = 9²)
    3. A1: 3
    Answer: 3
    Rational & Irrational Numbers

  4. Question 4. Line mathbfL_1 has equation 4y + 3x = 36
    Line mathbfL_2 has equation 9y + kx = 26
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: gradient of mathbfL_1 is -dfrac34, gradient of mathbfL_2 is -dfrack9, and -dfrac34 × -dfrack9 = -1
    2. A1: k = -12
    Answer: k = -12
    Properties of Perpendicular Lines

  5. Question 5. Prove algebraically that the sum of three consecutive odd numbers is a multiple of 3.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2n + 1) + (2n + 3) + (2n + 5)
    2. A1: 6n + 9
    3. C1: 3(2n + 3), which is a multiple of 3
    Answer: 3(2n + 3)
    Proof with Odd Numbers
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 071

Grades 6/7Non-calculator

  1. Question 1. ABC is an equilateral triangle. North lines are shown at A and at B.
    The bearing of B from A is 035^°.
    Work out the bearing of C from B.

    Show worked answerHide worked answer
    1. M1: 35 + 180 = 215
    2. M1: 215 - 60
    3. A1: 155^°
    Answer: 155^°
    Problem Solving with Bearings
    NN035°ABCNot drawn accurately
    [3 marks]

  2. Question 2. Class X: minimum 12, lower quartile 20, median 25, upper quartile 32, maximum 45. Work out the interquartile range.

    Show worked answerHide worked answer
    1. M1: 32 - 20
    2. A1: 12
    Answer: 12
    Comparing Data Using Box Plots
    [2 marks]

  3. Question 3. k is an integer greater than 1. √27 × √k is a rational number. Work out the smallest possible value of k.

    Show worked answerHide worked answer
    1. M1: √27k is rational when 27k is a square number
    2. M1: tests k = 2 (54) and k = 3 (81 = 9²)
    3. A1: 3
    Answer: 3
    Rational & Irrational Numbers
    [3 marks]

  4. Question 4. Line mathbfL_1 has equation 4y + 3x = 36
    Line mathbfL_2 has equation 9y + kx = 26
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: gradient of mathbfL_1 is -dfrac34, gradient of mathbfL_2 is -dfrack9, and -dfrac34 × -dfrack9 = -1
    2. A1: k = -12
    Answer: k = -12
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. Prove algebraically that the sum of three consecutive odd numbers is a multiple of 3.

    Show worked answerHide worked answer
    1. M1: (2n + 1) + (2n + 3) + (2n + 5)
    2. A1: 6n + 9
    3. C1: 3(2n + 3), which is a multiple of 3
    Answer: 3(2n + 3)
    Proof with Odd Numbers
    [3 marks]