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

Mixed Topic Worksheet Grades 6/7: Day 030

Grades 6/7Calculator

  1. Question 1. The diagram shows a shape made from a rectangle and a semicircle.
    The diameter of the semicircle is equal to the width of the rectangle.
    Work out the perimeter of the shape.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: curved edge = π × 10 ÷ 2
    2. M1: 16 + 16 + 10 + curved edge
    3. A1: 57.7
    Answer: 57.7 cm
    Perimeter of Compound Shapes
    16 cm10 cmNot drawn accurately
    [3 marks]

  2. Question 2. n is an integer. n < √20 < n + 1 Work out the value of n.

    Show worked answerHide worked answer
    1. M1: 4² = 16 and 5² = 25
    2. A1: 4
    Answer: 4
    Estimating Roots
    [2 marks]

  3. Question 3. For every value of n, (n + a)² - (n - 3)² = 20(n + b) where a and b are positive integers. Find a and b.

    Show worked answerHide worked answer
    1. M1: (n + a)² - (n - 3)² = (2a + 6)n + a² - 9
    2. M1: 2a + 6 = 20 and a² - 9 = 20b
    3. A1: a = 7 and b = 2
    Answer: a = 7, b = 2
    Proof with Multiples
    [3 marks]

  4. Question 4. The region R is shaded. All the boundary lines are included in R.
    Write down the four inequalities that define R

    Show worked answerHide worked answer
    1. B1: x ≥ 1 and x ≤ 4
    2. B1: y ≥ 2 and y ≤ 5
    3. B1: all four with the correct signs
    Answer: x ≥ 1, x ≤ 4, y ≥ 2 and y ≤ 5
    Shading Regions with Graphical Inequalities
    Rxy246−11234560
    [3 marks]

  5. Question 5. The value of a machine falls by 10% each year.
    After 2 years the machine is worth £4 050.
    Work out the value of the machine when it was new.

    Show worked answerHide worked answer
    1. M1: 100 - 10 = 90%
    2. M1: 4050 ÷ 0.9 ÷ 0.9
    3. A1: 5000
    Answer: £5,000
    Finding the Initial Amount
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 030

Grades 6/7Calculator

  1. Question 1. The diagram shows a shape made from a rectangle and a semicircle.
    The diameter of the semicircle is equal to the width of the rectangle.
    Work out the perimeter of the shape.
    Give your answer to 1 decimal place.

    [3 marks]
    16 cm10 cmNot drawn accurately
    Show worked answerHide worked answer
    1. M1: curved edge = π × 10 ÷ 2
    2. M1: 16 + 16 + 10 + curved edge
    3. A1: 57.7
    Answer: 57.7 cm
    Perimeter of Compound Shapes

  2. Question 2. n is an integer. n < √20 < n + 1 Work out the value of n.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 4² = 16 and 5² = 25
    2. A1: 4
    Answer: 4
    Estimating Roots

  3. Question 3. For every value of n, (n + a)² - (n - 3)² = 20(n + b) where a and b are positive integers. Find a and b.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (n + a)² - (n - 3)² = (2a + 6)n + a² - 9
    2. M1: 2a + 6 = 20 and a² - 9 = 20b
    3. A1: a = 7 and b = 2
    Answer: a = 7, b = 2
    Proof with Multiples

  4. Question 4. The region R is shaded. All the boundary lines are included in R.
    Write down the four inequalities that define R

    [3 marks]
    Rxy246−11234560
    Show worked answerHide worked answer
    1. B1: x ≥ 1 and x ≤ 4
    2. B1: y ≥ 2 and y ≤ 5
    3. B1: all four with the correct signs
    Answer: x ≥ 1, x ≤ 4, y ≥ 2 and y ≤ 5
    Shading Regions with Graphical Inequalities

  5. Question 5. The value of a machine falls by 10% each year.
    After 2 years the machine is worth £4 050.
    Work out the value of the machine when it was new.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 - 10 = 90%
    2. M1: 4050 ÷ 0.9 ÷ 0.9
    3. A1: 5000
    Answer: £5,000
    Finding the Initial Amount
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 030

Grades 6/7Calculator

  1. Question 1. The diagram shows a shape made from a rectangle and a semicircle.
    The diameter of the semicircle is equal to the width of the rectangle.
    Work out the perimeter of the shape.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: curved edge = π × 10 ÷ 2
    2. M1: 16 + 16 + 10 + curved edge
    3. A1: 57.7
    Answer: 57.7 cm
    Perimeter of Compound Shapes
    16 cm10 cmNot drawn accurately
    [3 marks]

  2. Question 2. n is an integer. n < √20 < n + 1 Work out the value of n.

    Show worked answerHide worked answer
    1. M1: 4² = 16 and 5² = 25
    2. A1: 4
    Answer: 4
    Estimating Roots
    [2 marks]

  3. Question 3. For every value of n, (n + a)² - (n - 3)² = 20(n + b) where a and b are positive integers. Find a and b.

    Show worked answerHide worked answer
    1. M1: (n + a)² - (n - 3)² = (2a + 6)n + a² - 9
    2. M1: 2a + 6 = 20 and a² - 9 = 20b
    3. A1: a = 7 and b = 2
    Answer: a = 7, b = 2
    Proof with Multiples
    [3 marks]

  4. Question 4. The region R is shaded. All the boundary lines are included in R.
    Write down the four inequalities that define R

    Show worked answerHide worked answer
    1. B1: x ≥ 1 and x ≤ 4
    2. B1: y ≥ 2 and y ≤ 5
    3. B1: all four with the correct signs
    Answer: x ≥ 1, x ≤ 4, y ≥ 2 and y ≤ 5
    Shading Regions with Graphical Inequalities
    Rxy246−11234560
    [3 marks]

  5. Question 5. The value of a machine falls by 10% each year.
    After 2 years the machine is worth £4 050.
    Work out the value of the machine when it was new.

    Show worked answerHide worked answer
    1. M1: 100 - 10 = 90%
    2. M1: 4050 ÷ 0.9 ÷ 0.9
    3. A1: 5000
    Answer: £5,000
    Finding the Initial Amount
    [3 marks]