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

Mixed Topic Worksheet Grades 6/7: Day 098

Grades 6/7Calculator

  1. Question 1. The diagram shows an isosceles triangle.
    Work out the perimeter of the triangle.

    Show worked answerHide worked answer
    1. M1: 5x − 7 = 2x + 8 (equal sides)
    2. M1: 3x = 15 and x = 5
    3. M1: 5 × 5 − 7 = 18 (equal side)
    4. A1: 49
    Answer: 49 cm
    Solving Harder Equations
    13 cm(5x − 7) cm(2x + 8) cmNot drawn accurately
    [4 marks]

  2. Question 2. Write down an irrational number that is greater than 4 and less than 5.

    Show worked answerHide worked answer
    1. B1: a correct irrational number, for example √17
    Answer: For example √17
    Rational & Irrational Numbers
    [1 mark]

  3. Question 3. The diagram shows triangle STU. Work out the area of triangle STU. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 11 × 8 × sin 38^°
    2. A1: 27.1
    Answer: 27.1 cm²
    Area of Triangles Using ½ab sin C
    11 cm8 cm38°TSUNot drawn accurately
    [2 marks]

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8.4² + 12.7² - 2 × 8.4 × 12.7 × cos 58^°
    2. M1: BC² = 231.85 - 113.06 = 118.79
    3. A1: BC = 10.9
    Answer: 10.9 cm
    Finding Side Lengths Using the Cosine Rule
    12.7 cm8.4 cm58°ABC
    [3 marks]

  5. Question 5. An isosceles triangle has two equal sides of length x cm. The angle between them is 50° and the area is 20 cm². Work out x. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 1/2x² sin 50° = 20
    2. M1: x² = frac40sin 50° = 52.2...
    3. A1: x = 7.23
    Answer: x = 7.23
    Calculating Side Lengths Using ½ab sin C
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 098

Grades 6/7Calculator

  1. Question 1. The diagram shows an isosceles triangle.
    Work out the perimeter of the triangle.

    [4 marks]
    13 cm(5x − 7) cm(2x + 8) cmNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 5x − 7 = 2x + 8 (equal sides)
    2. M1: 3x = 15 and x = 5
    3. M1: 5 × 5 − 7 = 18 (equal side)
    4. A1: 49
    Answer: 49 cm
    Solving Harder Equations

  2. Question 2. Write down an irrational number that is greater than 4 and less than 5.

    [1 mark]
    Show worked answerHide worked answer
    1. B1: a correct irrational number, for example √17
    Answer: For example √17
    Rational & Irrational Numbers

  3. Question 3. The diagram shows triangle STU. Work out the area of triangle STU. Give your answer to 1 decimal place.

    [2 marks]
    11 cm8 cm38°TSUNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 1/2 × 11 × 8 × sin 38^°
    2. A1: 27.1
    Answer: 27.1 cm²
    Area of Triangles Using ½ab sin C

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    [3 marks]
    12.7 cm8.4 cm58°ABC
    Show worked answerHide worked answer
    1. M1: BC² = 8.4² + 12.7² - 2 × 8.4 × 12.7 × cos 58^°
    2. M1: BC² = 231.85 - 113.06 = 118.79
    3. A1: BC = 10.9
    Answer: 10.9 cm
    Finding Side Lengths Using the Cosine Rule

  5. Question 5. An isosceles triangle has two equal sides of length x cm. The angle between them is 50° and the area is 20 cm². Work out x. Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 1/2x² sin 50° = 20
    2. M1: x² = frac40sin 50° = 52.2...
    3. A1: x = 7.23
    Answer: x = 7.23
    Calculating Side Lengths Using ½ab sin C
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 098

Grades 6/7Calculator

  1. Question 1. The diagram shows an isosceles triangle.
    Work out the perimeter of the triangle.

    Show worked answerHide worked answer
    1. M1: 5x − 7 = 2x + 8 (equal sides)
    2. M1: 3x = 15 and x = 5
    3. M1: 5 × 5 − 7 = 18 (equal side)
    4. A1: 49
    Answer: 49 cm
    Solving Harder Equations
    13 cm(5x − 7) cm(2x + 8) cmNot drawn accurately
    [4 marks]

  2. Question 2. Write down an irrational number that is greater than 4 and less than 5.

    Show worked answerHide worked answer
    1. B1: a correct irrational number, for example √17
    Answer: For example √17
    Rational & Irrational Numbers
    [1 mark]

  3. Question 3. The diagram shows triangle STU. Work out the area of triangle STU. Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 11 × 8 × sin 38^°
    2. A1: 27.1
    Answer: 27.1 cm²
    Area of Triangles Using ½ab sin C
    11 cm8 cm38°TSUNot drawn accurately
    [2 marks]

  4. Question 4. Here is triangle ABC.
    Work out the length of BC.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: BC² = 8.4² + 12.7² - 2 × 8.4 × 12.7 × cos 58^°
    2. M1: BC² = 231.85 - 113.06 = 118.79
    3. A1: BC = 10.9
    Answer: 10.9 cm
    Finding Side Lengths Using the Cosine Rule
    12.7 cm8.4 cm58°ABC
    [3 marks]

  5. Question 5. An isosceles triangle has two equal sides of length x cm. The angle between them is 50° and the area is 20 cm². Work out x. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 1/2x² sin 50° = 20
    2. M1: x² = frac40sin 50° = 52.2...
    3. A1: x = 7.23
    Answer: x = 7.23
    Calculating Side Lengths Using ½ab sin C
    [3 marks]