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Mixed Topic Worksheet Grades 8/9: Day 018

Grades 8/9Calculator

  1. Question 1. cos 40° = 0.766 correct to 3 significant figures. Find the other value of x between 0° and 360° for which cos x = 0.766.

    Show worked answerHide worked answer
    1. M1: symmetry of the cosine graph about x = 180°
    2. A1: 360° - 40° = 320°
    Answer: 320°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Prove algebraically that the sum of four consecutive even integers is 4 more than a multiple of 8.

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    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. M1: 8n + 12
    3. C1: 8n + 12 = 8(n + 1) + 4, which is 4 more than a multiple of 8
    Answer: 8(n + 1) + 4, 4 more than a multiple of 8
    Proof with Consecutive Numbers
    [3 marks]

  3. Question 3. A chord AB of length 8 cm is drawn in a circle with centre O and radius 5 cm. Work out the size of angle AOB. Give your answer correct to 1 decimal place.

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    1. M1: right-angled triangle with hypotenuse 5 cm and opposite side 8 ÷ 2 = 4 cm
    2. M1: sin≤ft(tfracAOB2) = dfrac45, so half the angle is 53.13°
    3. A1: 106.3°
    Answer: 106.3°
    Circle Theorems
    [3 marks]

  4. Question 4. The resistance R ohms of a wire is directly proportional to its length L metres and inversely proportional to the square of its diameter d mm.
    L = 5, d = 0.5 gives R = 40.
    A second wire has L = 20 and R = 10.
    Work out its diameter.

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    1. M1: 40 = k × 5 ÷ 0.5²
    2. M1: 10 = 2 × 20 ÷ d²
    3. M1: d² = 4
    4. A1: 2 mm
    Answer: 2 mm
    Direct & Inverse Proportion with Functions
    [4 marks]

  5. Question 5. Find the coordinates of the turning point of y = 5x² + 20x + 7.

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    1. M1: 5(x + 2)² - 20 + 7
    2. A1: 5(x + 2)² - 13
    3. A1: (-2, -13)
    Answer: (-2, -13)
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 018

Grades 8/9Calculator

  1. Question 1. cos 40° = 0.766 correct to 3 significant figures. Find the other value of x between 0° and 360° for which cos x = 0.766.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: symmetry of the cosine graph about x = 180°
    2. A1: 360° - 40° = 320°
    Answer: 320°
    Sketching sin, cos & tan

  2. Question 2. Prove algebraically that the sum of four consecutive even integers is 4 more than a multiple of 8.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. M1: 8n + 12
    3. C1: 8n + 12 = 8(n + 1) + 4, which is 4 more than a multiple of 8
    Answer: 8(n + 1) + 4, 4 more than a multiple of 8
    Proof with Consecutive Numbers

  3. Question 3. A chord AB of length 8 cm is drawn in a circle with centre O and radius 5 cm. Work out the size of angle AOB. Give your answer correct to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: right-angled triangle with hypotenuse 5 cm and opposite side 8 ÷ 2 = 4 cm
    2. M1: sin≤ft(tfracAOB2) = dfrac45, so half the angle is 53.13°
    3. A1: 106.3°
    Answer: 106.3°
    Circle Theorems

  4. Question 4. The resistance R ohms of a wire is directly proportional to its length L metres and inversely proportional to the square of its diameter d mm.
    L = 5, d = 0.5 gives R = 40.
    A second wire has L = 20 and R = 10.
    Work out its diameter.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 40 = k × 5 ÷ 0.5²
    2. M1: 10 = 2 × 20 ÷ d²
    3. M1: d² = 4
    4. A1: 2 mm
    Answer: 2 mm
    Direct & Inverse Proportion with Functions

  5. Question 5. Find the coordinates of the turning point of y = 5x² + 20x + 7.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 5(x + 2)² - 20 + 7
    2. A1: 5(x + 2)² - 13
    3. A1: (-2, -13)
    Answer: (-2, -13)
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 018

Grades 8/9Calculator

  1. Question 1. cos 40° = 0.766 correct to 3 significant figures. Find the other value of x between 0° and 360° for which cos x = 0.766.

    Show worked answerHide worked answer
    1. M1: symmetry of the cosine graph about x = 180°
    2. A1: 360° - 40° = 320°
    Answer: 320°
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. Prove algebraically that the sum of four consecutive even integers is 4 more than a multiple of 8.

    Show worked answerHide worked answer
    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. M1: 8n + 12
    3. C1: 8n + 12 = 8(n + 1) + 4, which is 4 more than a multiple of 8
    Answer: 8(n + 1) + 4, 4 more than a multiple of 8
    Proof with Consecutive Numbers
    [3 marks]

  3. Question 3. A chord AB of length 8 cm is drawn in a circle with centre O and radius 5 cm. Work out the size of angle AOB. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: right-angled triangle with hypotenuse 5 cm and opposite side 8 ÷ 2 = 4 cm
    2. M1: sin≤ft(tfracAOB2) = dfrac45, so half the angle is 53.13°
    3. A1: 106.3°
    Answer: 106.3°
    Circle Theorems
    [3 marks]

  4. Question 4. The resistance R ohms of a wire is directly proportional to its length L metres and inversely proportional to the square of its diameter d mm.
    L = 5, d = 0.5 gives R = 40.
    A second wire has L = 20 and R = 10.
    Work out its diameter.

    Show worked answerHide worked answer
    1. M1: 40 = k × 5 ÷ 0.5²
    2. M1: 10 = 2 × 20 ÷ d²
    3. M1: d² = 4
    4. A1: 2 mm
    Answer: 2 mm
    Direct & Inverse Proportion with Functions
    [4 marks]

  5. Question 5. Find the coordinates of the turning point of y = 5x² + 20x + 7.

    Show worked answerHide worked answer
    1. M1: 5(x + 2)² - 20 + 7
    2. A1: 5(x + 2)² - 13
    3. A1: (-2, -13)
    Answer: (-2, -13)
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]