šŸ“… Free live lesson: Tuesday 17th NovemberSave your free place ā†’

Mixed Topic Worksheet Grades 8/9: Day 049

Grades 8/9Non-calculator

  1. Question 1. Show that āˆš27 + āˆš12 = āˆš75.

    Show worked answerHide worked answer
    1. M1: āˆš27 = 3āˆš3 and āˆš12 = 2āˆš3
    2. M1: sum = 5āˆš3
    3. C1: āˆš75 = āˆš25 Ɨ 3 = 5āˆš3
    Answer: Both sides equal 5āˆš3
    Simplifying Surds
    [3 marks]

  2. Question 2. P(Acup B)=0.9, P(A)=0.55 and P(B)=0.6. Work out P(Amid B').

    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.55+0.6-0.9=0.25, so P(Acap B')=0.3
    2. M1: P(B')=0.4
    3. A1: 0.3/0.4=3/4
    Answer: 3/4
    Conditional Probability with Venn Diagrams
    [3 marks]

  3. Question 3. Solve xĀ² + 8x + 3 = 0 by completing the square
    Give the solutions in the form a Ā± āˆšb where a and b are integers.

    Show worked answerHide worked answer
    1. M1: (x + 4)Ā² - 16 + 3 = 0
    2. M1: (x + 4)Ā² = 13
    3. A1: first solution: x = -4 + āˆš13
    4. A1: second solution: x = -4 - āˆš13
    Answer: x = -4 Ā± āˆš13
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  4. Question 4. The sum of the squares of four consecutive positive integers is 366. Use algebra to work out the four integers.

    Show worked answerHide worked answer
    1. M1: nĀ² + (n + 1)Ā² + (n + 2)Ā² + (n + 3)Ā² = 366
    2. M1: 4nĀ² + 12n + 14 = 366 so nĀ² + 3n - 88 = 0
    3. M1: (n + 11)(n - 8) = 0
    4. A1: 8, 9, 10, 11
    Answer: 8, 9, 10 and 11
    Proof with Consecutive Numbers
    [4 marks]

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. M lies on AB with AM:MB=1:3. Find overrightarrowOM.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowAM=1/4mathbfc
    2. A1: overrightarrowOM=mathbfa+1/4mathbfc
    Answer: overrightarrowOM=mathbfa+1/4mathbfc
    Vector Ratio Problems
    [2 marks]
šŸ“… Free lesson: Tue 17th NovSave your place ā†’

Mixed Topic Worksheet Grades 8/9: Day 049

Grades 8/9Non-calculator

  1. Question 1. Show that āˆš27 + āˆš12 = āˆš75.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: āˆš27 = 3āˆš3 and āˆš12 = 2āˆš3
    2. M1: sum = 5āˆš3
    3. C1: āˆš75 = āˆš25 Ɨ 3 = 5āˆš3
    Answer: Both sides equal 5āˆš3
    Simplifying Surds

  2. Question 2. P(Acup B)=0.9, P(A)=0.55 and P(B)=0.6. Work out P(Amid B').

    [3 marks]
    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.55+0.6-0.9=0.25, so P(Acap B')=0.3
    2. M1: P(B')=0.4
    3. A1: 0.3/0.4=3/4
    Answer: 3/4
    Conditional Probability with Venn Diagrams

  3. Question 3. Solve xĀ² + 8x + 3 = 0 by completing the square
    Give the solutions in the form a Ā± āˆšb where a and b are integers.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (x + 4)Ā² - 16 + 3 = 0
    2. M1: (x + 4)Ā² = 13
    3. A1: first solution: x = -4 + āˆš13
    4. A1: second solution: x = -4 - āˆš13
    Answer: x = -4 Ā± āˆš13
    Solving Quadratics by Completing the Square (a = 1)

  4. Question 4. The sum of the squares of four consecutive positive integers is 366. Use algebra to work out the four integers.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: nĀ² + (n + 1)Ā² + (n + 2)Ā² + (n + 3)Ā² = 366
    2. M1: 4nĀ² + 12n + 14 = 366 so nĀ² + 3n - 88 = 0
    3. M1: (n + 11)(n - 8) = 0
    4. A1: 8, 9, 10, 11
    Answer: 8, 9, 10 and 11
    Proof with Consecutive Numbers

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. M lies on AB with AM:MB=1:3. Find overrightarrowOM.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowAM=1/4mathbfc
    2. A1: overrightarrowOM=mathbfa+1/4mathbfc
    Answer: overrightarrowOM=mathbfa+1/4mathbfc
    Vector Ratio Problems
šŸ“… Free live lesson: Tuesday 17th NovemberSave your free place ā†’

Mixed Topic Worksheet Grades 8/9: Day 049

Grades 8/9Non-calculator

  1. Question 1. Show that āˆš27 + āˆš12 = āˆš75.

    Show worked answerHide worked answer
    1. M1: āˆš27 = 3āˆš3 and āˆš12 = 2āˆš3
    2. M1: sum = 5āˆš3
    3. C1: āˆš75 = āˆš25 Ɨ 3 = 5āˆš3
    Answer: Both sides equal 5āˆš3
    Simplifying Surds
    [3 marks]

  2. Question 2. P(Acup B)=0.9, P(A)=0.55 and P(B)=0.6. Work out P(Amid B').

    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.55+0.6-0.9=0.25, so P(Acap B')=0.3
    2. M1: P(B')=0.4
    3. A1: 0.3/0.4=3/4
    Answer: 3/4
    Conditional Probability with Venn Diagrams
    [3 marks]

  3. Question 3. Solve xĀ² + 8x + 3 = 0 by completing the square
    Give the solutions in the form a Ā± āˆšb where a and b are integers.

    Show worked answerHide worked answer
    1. M1: (x + 4)Ā² - 16 + 3 = 0
    2. M1: (x + 4)Ā² = 13
    3. A1: first solution: x = -4 + āˆš13
    4. A1: second solution: x = -4 - āˆš13
    Answer: x = -4 Ā± āˆš13
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  4. Question 4. The sum of the squares of four consecutive positive integers is 366. Use algebra to work out the four integers.

    Show worked answerHide worked answer
    1. M1: nĀ² + (n + 1)Ā² + (n + 2)Ā² + (n + 3)Ā² = 366
    2. M1: 4nĀ² + 12n + 14 = 366 so nĀ² + 3n - 88 = 0
    3. M1: (n + 11)(n - 8) = 0
    4. A1: 8, 9, 10, 11
    Answer: 8, 9, 10 and 11
    Proof with Consecutive Numbers
    [4 marks]

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. M lies on AB with AM:MB=1:3. Find overrightarrowOM.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowAM=1/4mathbfc
    2. A1: overrightarrowOM=mathbfa+1/4mathbfc
    Answer: overrightarrowOM=mathbfa+1/4mathbfc
    Vector Ratio Problems
    [2 marks]