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

Mixed Topic Worksheet Grades 6/7: Day 082

Grades 6/7Calculator

  1. Question 1. A car is worth £10 000.
    Its value falls by 20% each year.
    Work out the value of the car after 2 years.

    Show worked answerHide worked answer
    1. M1: 100 - 20 = 80%
    2. M1: 10000 × 0.8 × 0.8
    3. A1: 6400
    Answer: £6,400
    Compound Decay
    [3 marks]

  2. Question 2. The diagram shows an isosceles triangle ABC with AB = AC = x cm. The area of the triangle is 50 cm². Work out the value of x. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × x × x × sin 40^° = 50
    2. M1: x² = 100/sin 40^°
    3. A1: 12.5
    Answer: 12.5
    Area of Triangles Using ½ab sin C
    x cmx cm40°ABCNot drawn accurately
    [3 marks]

  3. Question 3. Prove that 9(n + 7)² - (3n + 5)² is a multiple of 32 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 9(n² + 14n + 49) and (3n + 5)² = 9n² + 30n + 25
    2. M1: 96n + 416
    3. M1: 32(3n + 13)
    4. C1: 32(3n + 13) is a multiple of 32 for every integer n
    Answer: 32(3n + 13), a multiple of 32
    Proof with Multiples
    [4 marks]

  4. Question 4. Here is triangle PQR.
    Angle QPR = 53°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: QR² = 12² + 17² - 2 × 12 × 17 × cos 53^°
    2. M1: QR² = 433.00 - 245.54 = 187.46
    3. A1: QR = 13.7
    Answer: 13.7 cm
    Finding Side Lengths Using the Cosine Rule
    17 cm12 cm53°PQR
    [3 marks]

  5. Question 5. A circle has centre (0, 0) and radius 9
    Does the point (-5, 7) lie inside, on or outside the circle?
    You must show your working.

    Show worked answerHide worked answer
    1. B1: x² + y² = 81 (or r² = 81)
    2. M1: (-5)² + 7² = 25 + 49 = 74
    3. A1: 74 < 81, so the point lies inside the circle
    Answer: Inside, because (-5)² + 7² = 74 < 81
    Sketching Circles
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 082

Grades 6/7Calculator

  1. Question 1. A car is worth £10 000.
    Its value falls by 20% each year.
    Work out the value of the car after 2 years.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 100 - 20 = 80%
    2. M1: 10000 × 0.8 × 0.8
    3. A1: 6400
    Answer: £6,400
    Compound Decay

  2. Question 2. The diagram shows an isosceles triangle ABC with AB = AC = x cm. The area of the triangle is 50 cm². Work out the value of x. Give your answer to 1 decimal place.

    [3 marks]
    x cmx cm40°ABCNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × x × x × sin 40^° = 50
    2. M1: x² = 100/sin 40^°
    3. A1: 12.5
    Answer: 12.5
    Area of Triangles Using ½ab sin C

  3. Question 3. Prove that 9(n + 7)² - (3n + 5)² is a multiple of 32 for all integer values of n.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 9(n² + 14n + 49) and (3n + 5)² = 9n² + 30n + 25
    2. M1: 96n + 416
    3. M1: 32(3n + 13)
    4. C1: 32(3n + 13) is a multiple of 32 for every integer n
    Answer: 32(3n + 13), a multiple of 32
    Proof with Multiples

  4. Question 4. Here is triangle PQR.
    Angle QPR = 53°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    [3 marks]
    17 cm12 cm53°PQR
    Show worked answerHide worked answer
    1. M1: QR² = 12² + 17² - 2 × 12 × 17 × cos 53^°
    2. M1: QR² = 433.00 - 245.54 = 187.46
    3. A1: QR = 13.7
    Answer: 13.7 cm
    Finding Side Lengths Using the Cosine Rule

  5. Question 5. A circle has centre (0, 0) and radius 9
    Does the point (-5, 7) lie inside, on or outside the circle?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: x² + y² = 81 (or r² = 81)
    2. M1: (-5)² + 7² = 25 + 49 = 74
    3. A1: 74 < 81, so the point lies inside the circle
    Answer: Inside, because (-5)² + 7² = 74 < 81
    Sketching Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 082

Grades 6/7Calculator

  1. Question 1. A car is worth £10 000.
    Its value falls by 20% each year.
    Work out the value of the car after 2 years.

    Show worked answerHide worked answer
    1. M1: 100 - 20 = 80%
    2. M1: 10000 × 0.8 × 0.8
    3. A1: 6400
    Answer: £6,400
    Compound Decay
    [3 marks]

  2. Question 2. The diagram shows an isosceles triangle ABC with AB = AC = x cm. The area of the triangle is 50 cm². Work out the value of x. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × x × x × sin 40^° = 50
    2. M1: x² = 100/sin 40^°
    3. A1: 12.5
    Answer: 12.5
    Area of Triangles Using ½ab sin C
    x cmx cm40°ABCNot drawn accurately
    [3 marks]

  3. Question 3. Prove that 9(n + 7)² - (3n + 5)² is a multiple of 32 for all integer values of n.

    Show worked answerHide worked answer
    1. M1: 9(n² + 14n + 49) and (3n + 5)² = 9n² + 30n + 25
    2. M1: 96n + 416
    3. M1: 32(3n + 13)
    4. C1: 32(3n + 13) is a multiple of 32 for every integer n
    Answer: 32(3n + 13), a multiple of 32
    Proof with Multiples
    [4 marks]

  4. Question 4. Here is triangle PQR.
    Angle QPR = 53°.
    Work out the length of QR.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: QR² = 12² + 17² - 2 × 12 × 17 × cos 53^°
    2. M1: QR² = 433.00 - 245.54 = 187.46
    3. A1: QR = 13.7
    Answer: 13.7 cm
    Finding Side Lengths Using the Cosine Rule
    17 cm12 cm53°PQR
    [3 marks]

  5. Question 5. A circle has centre (0, 0) and radius 9
    Does the point (-5, 7) lie inside, on or outside the circle?
    You must show your working.

    Show worked answerHide worked answer
    1. B1: x² + y² = 81 (or r² = 81)
    2. M1: (-5)² + 7² = 25 + 49 = 74
    3. A1: 74 < 81, so the point lies inside the circle
    Answer: Inside, because (-5)² + 7² = 74 < 81
    Sketching Circles
    [3 marks]