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

Mixed Topic Worksheet Grades 6/7: Day 091

Grades 6/7Non-calculator

  1. Question 1. A rod is 12 cm long, correct to the nearest cm.
    Sam says the rod could be exactly 12.5 cm long.
    Is Sam correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 12 + 0.5 = 12.5 as the upper bound
    2. C1: No, 12.5 is not included
    Answer: No: the interval is 11.5 ≤ x < 12.5, and 12.5 is not less than 12.5 (it would round to 13).
    Finding Bounds & Error Intervals
    [2 marks]

  2. Question 2. A translation has vector beginpmatrix 3 -2 endpmatrix.
    Write down the number of invariant points of this translation.

    Show worked answerHide worked answer
    1. B1: 0
    Answer: 0
    Invariant Points
    [1 mark]

  3. Question 3. n is an integer.
    Prove that (2n + 3)² - (2n - 1)² is a multiple of 8.

    Show worked answerHide worked answer
    1. M1: (2n + 3)² = 4n² + 12n + 9
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 4n² + 12n + 9 - (4n² - 4n + 1) = 16n + 8
    4. C1: 8(2n + 1), which is a multiple of 8
    Answer: 8(2n + 1), a multiple of 8
    Proof with Multiples
    [4 marks]

  4. Question 4. Line mathbfL_1 has equation 3y = -5x + 12
    Line mathbfL_2 has equation 5y - 3x = 40
    Show that mathbfL_1 and mathbfL_2 are perpendicular.

    Show worked answerHide worked answer
    1. M1: mathbfL_1 rearranged to y = -dfrac53x + 4; mathbfL_2 rearranged to y = dfrac35x + 8
    2. C1: -dfrac53 × dfrac35 = -1, so the lines are perpendicular
    Answer: gradients -dfrac53 and dfrac35, product -1
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. A = x : 2x - 3 ; > ; 5
    B = x : x + 6 ; > ; 8
    Zoe says that A subset B
    Is Zoe correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 2x > 8 so x > 4
    2. M1: x > 2 for B
    3. C1: every number greater than 4 is greater than 2 so A is a subset of B
    Answer: Yes, A = x : x > 4 and B = x : x > 2, and every x > 4 is greater than 2
    Sets & Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 091

Grades 6/7Non-calculator

  1. Question 1. A rod is 12 cm long, correct to the nearest cm.
    Sam says the rod could be exactly 12.5 cm long.
    Is Sam correct?
    Give a reason for your answer.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 12 + 0.5 = 12.5 as the upper bound
    2. C1: No, 12.5 is not included
    Answer: No: the interval is 11.5 ≤ x < 12.5, and 12.5 is not less than 12.5 (it would round to 13).
    Finding Bounds & Error Intervals

  2. Question 2. A translation has vector beginpmatrix 3 -2 endpmatrix.
    Write down the number of invariant points of this translation.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: 0
    Answer: 0
    Invariant Points

  3. Question 3. n is an integer.
    Prove that (2n + 3)² - (2n - 1)² is a multiple of 8.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (2n + 3)² = 4n² + 12n + 9
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 4n² + 12n + 9 - (4n² - 4n + 1) = 16n + 8
    4. C1: 8(2n + 1), which is a multiple of 8
    Answer: 8(2n + 1), a multiple of 8
    Proof with Multiples

  4. Question 4. Line mathbfL_1 has equation 3y = -5x + 12
    Line mathbfL_2 has equation 5y - 3x = 40
    Show that mathbfL_1 and mathbfL_2 are perpendicular.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: mathbfL_1 rearranged to y = -dfrac53x + 4; mathbfL_2 rearranged to y = dfrac35x + 8
    2. C1: -dfrac53 × dfrac35 = -1, so the lines are perpendicular
    Answer: gradients -dfrac53 and dfrac35, product -1
    Properties of Perpendicular Lines

  5. Question 5. A = x : 2x - 3 ; > ; 5
    B = x : x + 6 ; > ; 8
    Zoe says that A subset B
    Is Zoe correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2x > 8 so x > 4
    2. M1: x > 2 for B
    3. C1: every number greater than 4 is greater than 2 so A is a subset of B
    Answer: Yes, A = x : x > 4 and B = x : x > 2, and every x > 4 is greater than 2
    Sets & Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 091

Grades 6/7Non-calculator

  1. Question 1. A rod is 12 cm long, correct to the nearest cm.
    Sam says the rod could be exactly 12.5 cm long.
    Is Sam correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 12 + 0.5 = 12.5 as the upper bound
    2. C1: No, 12.5 is not included
    Answer: No: the interval is 11.5 ≤ x < 12.5, and 12.5 is not less than 12.5 (it would round to 13).
    Finding Bounds & Error Intervals
    [2 marks]

  2. Question 2. A translation has vector beginpmatrix 3 -2 endpmatrix.
    Write down the number of invariant points of this translation.

    Show worked answerHide worked answer
    1. B1: 0
    Answer: 0
    Invariant Points
    [1 mark]

  3. Question 3. n is an integer.
    Prove that (2n + 3)² - (2n - 1)² is a multiple of 8.

    Show worked answerHide worked answer
    1. M1: (2n + 3)² = 4n² + 12n + 9
    2. M1: (2n - 1)² = 4n² - 4n + 1
    3. A1: 4n² + 12n + 9 - (4n² - 4n + 1) = 16n + 8
    4. C1: 8(2n + 1), which is a multiple of 8
    Answer: 8(2n + 1), a multiple of 8
    Proof with Multiples
    [4 marks]

  4. Question 4. Line mathbfL_1 has equation 3y = -5x + 12
    Line mathbfL_2 has equation 5y - 3x = 40
    Show that mathbfL_1 and mathbfL_2 are perpendicular.

    Show worked answerHide worked answer
    1. M1: mathbfL_1 rearranged to y = -dfrac53x + 4; mathbfL_2 rearranged to y = dfrac35x + 8
    2. C1: -dfrac53 × dfrac35 = -1, so the lines are perpendicular
    Answer: gradients -dfrac53 and dfrac35, product -1
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. A = x : 2x - 3 ; > ; 5
    B = x : x + 6 ; > ; 8
    Zoe says that A subset B
    Is Zoe correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 2x > 8 so x > 4
    2. M1: x > 2 for B
    3. C1: every number greater than 4 is greater than 2 so A is a subset of B
    Answer: Yes, A = x : x > 4 and B = x : x > 2, and every x > 4 is greater than 2
    Sets & Inequalities
    [3 marks]