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

Mixed Topic Worksheet Grades 6/7: Day 089

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of sand against its mass.
    Hamid pays £14 for sand.
    Work out the mass of sand he buys.

    Show worked answerHide worked answer
    1. M1: 14 ÷ 2, or reads across from 14 to the line
    2. A1: 7
    Answer: 7 kg
    Direct Proportion Graphs
    Mass (kg)Cost (£)051015200246810
    [2 marks]

  2. Question 2. Line segment AB has A(2, 1) and B(5, 5).
    Line segment AB is enlarged by scale factor -3 with centre (0, 0).
    The image is the line segment A'B'.
    Work out the length of A'B'.

    Show worked answerHide worked answer
    1. M1: length of AB from the difference in coordinates, √3² + 4²
    2. A1: 15
    Answer: 15
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. n is a positive integer.
    The cube root of n is rounded to the nearest integer and the answer is 4
    Work out the greatest possible value of n.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: sqrt[3]n < 4.5
    2. M1: 4.5³ = 91.125, so n < 91.125
    3. A1: 91
    Answer: 91
    Estimating Roots
    [3 marks]

  4. Question 4. The cost £C of a circular tablecloth is directly proportional to the square of its radius r cm.
    A tablecloth with r = 60 costs £36.
    Work out the cost of a tablecloth with r = 90.

    Show worked answerHide worked answer
    1. M1: 36 = k × 60²
    2. M1: C = 0.01 × 90²
    3. A1: £81
    Answer: £81
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. Here are the first five terms of a quadratic sequence.
    9 qquad 8 qquad 9 qquad 12 qquad 17 qquad ldots
    Find an expression, in terms of n, for the nth term of this sequence.

    Show worked answerHide worked answer
    1. M1: differences -1, 1, 3, 5 so the second difference is 2, giving n²
    2. M1: the remainders 8, 4, 0, -4, -8 are 12 - 4n
    3. A1: n² - 4n + 12
    Answer: n² - 4n + 12
    nth Term of Quadratic Sequences
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 089

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of sand against its mass.
    Hamid pays £14 for sand.
    Work out the mass of sand he buys.

    [2 marks]
    Mass (kg)Cost (£)051015200246810
    Show worked answerHide worked answer
    1. M1: 14 ÷ 2, or reads across from 14 to the line
    2. A1: 7
    Answer: 7 kg
    Direct Proportion Graphs

  2. Question 2. Line segment AB has A(2, 1) and B(5, 5).
    Line segment AB is enlarged by scale factor -3 with centre (0, 0).
    The image is the line segment A'B'.
    Work out the length of A'B'.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: length of AB from the difference in coordinates, √3² + 4²
    2. A1: 15
    Answer: 15
    Enlargements with Negative Integer Scale Factors

  3. Question 3. n is a positive integer.
    The cube root of n is rounded to the nearest integer and the answer is 4
    Work out the greatest possible value of n.
    Give your answer as an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: sqrt[3]n < 4.5
    2. M1: 4.5³ = 91.125, so n < 91.125
    3. A1: 91
    Answer: 91
    Estimating Roots

  4. Question 4. The cost £C of a circular tablecloth is directly proportional to the square of its radius r cm.
    A tablecloth with r = 60 costs £36.
    Work out the cost of a tablecloth with r = 90.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 36 = k × 60²
    2. M1: C = 0.01 × 90²
    3. A1: £81
    Answer: £81
    Algebraic Direct Proportion

  5. Question 5. Here are the first five terms of a quadratic sequence.
    9 qquad 8 qquad 9 qquad 12 qquad 17 qquad ldots
    Find an expression, in terms of n, for the nth term of this sequence.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: differences -1, 1, 3, 5 so the second difference is 2, giving n²
    2. M1: the remainders 8, 4, 0, -4, -8 are 12 - 4n
    3. A1: n² - 4n + 12
    Answer: n² - 4n + 12
    nth Term of Quadratic Sequences
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 089

Grades 6/7Non-calculator

  1. Question 1. The graph shows the cost of sand against its mass.
    Hamid pays £14 for sand.
    Work out the mass of sand he buys.

    Show worked answerHide worked answer
    1. M1: 14 ÷ 2, or reads across from 14 to the line
    2. A1: 7
    Answer: 7 kg
    Direct Proportion Graphs
    Mass (kg)Cost (£)051015200246810
    [2 marks]

  2. Question 2. Line segment AB has A(2, 1) and B(5, 5).
    Line segment AB is enlarged by scale factor -3 with centre (0, 0).
    The image is the line segment A'B'.
    Work out the length of A'B'.

    Show worked answerHide worked answer
    1. M1: length of AB from the difference in coordinates, √3² + 4²
    2. A1: 15
    Answer: 15
    Enlargements with Negative Integer Scale Factors
    [2 marks]

  3. Question 3. n is a positive integer.
    The cube root of n is rounded to the nearest integer and the answer is 4
    Work out the greatest possible value of n.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: sqrt[3]n < 4.5
    2. M1: 4.5³ = 91.125, so n < 91.125
    3. A1: 91
    Answer: 91
    Estimating Roots
    [3 marks]

  4. Question 4. The cost £C of a circular tablecloth is directly proportional to the square of its radius r cm.
    A tablecloth with r = 60 costs £36.
    Work out the cost of a tablecloth with r = 90.

    Show worked answerHide worked answer
    1. M1: 36 = k × 60²
    2. M1: C = 0.01 × 90²
    3. A1: £81
    Answer: £81
    Algebraic Direct Proportion
    [3 marks]

  5. Question 5. Here are the first five terms of a quadratic sequence.
    9 qquad 8 qquad 9 qquad 12 qquad 17 qquad ldots
    Find an expression, in terms of n, for the nth term of this sequence.

    Show worked answerHide worked answer
    1. M1: differences -1, 1, 3, 5 so the second difference is 2, giving n²
    2. M1: the remainders 8, 4, 0, -4, -8 are 12 - 4n
    3. A1: n² - 4n + 12
    Answer: n² - 4n + 12
    nth Term of Quadratic Sequences
    [3 marks]