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

Mixed Topic Worksheet Grades 6/7: Day 027

Grades 6/7Non-calculator

  1. Question 1. The table shows the heights of 40 plants. Work out the percentage of the plants with a height of 30 cm or less.

    Show worked answerHide worked answer
    1. M1: 6 + 13 + 16
    2. M1: 35 ÷ 40 × 100
    3. A1: 87.5%
    Answer: 87.5%
    Interpreting Grouped Frequency Tables
    Height, h (cm)Frequency0 < h ≤ 10610 < h ≤ 201320 < h ≤ 301630 < h ≤ 405
    [3 marks]

  2. Question 2. Ruth makes a 3-digit code.
    Each digit is chosen from 1 to 5.
    Digits can be used more than once.
    Ruth says, "There are 15 possible codes because 5 × 3 = 15."
    Is Ruth correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 5 × 5 × 5 or states that each of the 3 digits has 5 choices
    2. A1: No, there are 125 codes
    Answer: No. There are 125 codes, because each of the 3 digits has 5 choices: 5 × 5 × 5 = 125.
    Calculating Combinations
    [2 marks]

  3. Question 3. One of these numbers is irrational. Write down the irrational number.
    √25 √18 dfrac227 0.dot3 -4

    Show worked answerHide worked answer
    1. B1: √18
    Answer: √18
    Rational & Irrational Numbers
    [1 mark]

  4. Question 4. Line mathbfL_1 has equation 7y + 3x = 21
    Line mathbfL_2 has equation 6y + kx = 17
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: gradients -dfrac37 and -dfrack6, so -dfrac37 × ≤ft(-dfrack6) = -1
    2. A1: k = -14
    Answer: k = -14
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. Tia says that the sum of the squares of any two odd numbers is a multiple of 4.
    Is Tia correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (2m + 1)² + (2n + 1)² = 4m² + 4m + 4n² + 4n + 2
    2. A1: 4(m² + m + n² + n) + 2
    3. C1: this is 2 more than a multiple of 4, so Tia is not correct
    Answer: Tia is not correct
    Proof with Odd Numbers
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 027

Grades 6/7Non-calculator

  1. Question 1. The table shows the heights of 40 plants. Work out the percentage of the plants with a height of 30 cm or less.

    [3 marks]
    Height, h (cm)Frequency0 < h ≤ 10610 < h ≤ 201320 < h ≤ 301630 < h ≤ 405
    Show worked answerHide worked answer
    1. M1: 6 + 13 + 16
    2. M1: 35 ÷ 40 × 100
    3. A1: 87.5%
    Answer: 87.5%
    Interpreting Grouped Frequency Tables

  2. Question 2. Ruth makes a 3-digit code.
    Each digit is chosen from 1 to 5.
    Digits can be used more than once.
    Ruth says, "There are 15 possible codes because 5 × 3 = 15."
    Is Ruth correct?
    Give a reason for your answer.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5 × 5 × 5 or states that each of the 3 digits has 5 choices
    2. A1: No, there are 125 codes
    Answer: No. There are 125 codes, because each of the 3 digits has 5 choices: 5 × 5 × 5 = 125.
    Calculating Combinations

  3. Question 3. One of these numbers is irrational. Write down the irrational number.
    √25 √18 dfrac227 0.dot3 -4

    [1 mark]
    Show worked answerHide worked answer
    1. B1: √18
    Answer: √18
    Rational & Irrational Numbers

  4. Question 4. Line mathbfL_1 has equation 7y + 3x = 21
    Line mathbfL_2 has equation 6y + kx = 17
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: gradients -dfrac37 and -dfrack6, so -dfrac37 × ≤ft(-dfrack6) = -1
    2. A1: k = -14
    Answer: k = -14
    Properties of Perpendicular Lines

  5. Question 5. Tia says that the sum of the squares of any two odd numbers is a multiple of 4.
    Is Tia correct?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2m + 1)² + (2n + 1)² = 4m² + 4m + 4n² + 4n + 2
    2. A1: 4(m² + m + n² + n) + 2
    3. C1: this is 2 more than a multiple of 4, so Tia is not correct
    Answer: Tia is not correct
    Proof with Odd Numbers
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 027

Grades 6/7Non-calculator

  1. Question 1. The table shows the heights of 40 plants. Work out the percentage of the plants with a height of 30 cm or less.

    Show worked answerHide worked answer
    1. M1: 6 + 13 + 16
    2. M1: 35 ÷ 40 × 100
    3. A1: 87.5%
    Answer: 87.5%
    Interpreting Grouped Frequency Tables
    Height, h (cm)Frequency0 < h ≤ 10610 < h ≤ 201320 < h ≤ 301630 < h ≤ 405
    [3 marks]

  2. Question 2. Ruth makes a 3-digit code.
    Each digit is chosen from 1 to 5.
    Digits can be used more than once.
    Ruth says, "There are 15 possible codes because 5 × 3 = 15."
    Is Ruth correct?
    Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: 5 × 5 × 5 or states that each of the 3 digits has 5 choices
    2. A1: No, there are 125 codes
    Answer: No. There are 125 codes, because each of the 3 digits has 5 choices: 5 × 5 × 5 = 125.
    Calculating Combinations
    [2 marks]

  3. Question 3. One of these numbers is irrational. Write down the irrational number.
    √25 √18 dfrac227 0.dot3 -4

    Show worked answerHide worked answer
    1. B1: √18
    Answer: √18
    Rational & Irrational Numbers
    [1 mark]

  4. Question 4. Line mathbfL_1 has equation 7y + 3x = 21
    Line mathbfL_2 has equation 6y + kx = 17
    mathbfL_1 is perpendicular to mathbfL_2.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: gradients -dfrac37 and -dfrack6, so -dfrac37 × ≤ft(-dfrack6) = -1
    2. A1: k = -14
    Answer: k = -14
    Properties of Perpendicular Lines
    [2 marks]

  5. Question 5. Tia says that the sum of the squares of any two odd numbers is a multiple of 4.
    Is Tia correct?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: (2m + 1)² + (2n + 1)² = 4m² + 4m + 4n² + 4n + 2
    2. A1: 4(m² + m + n² + n) + 2
    3. C1: this is 2 more than a multiple of 4, so Tia is not correct
    Answer: Tia is not correct
    Proof with Odd Numbers
    [3 marks]