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

Mixed Topic Worksheet Grades 8/9: Day 007

Grades 8/9Non-calculator

  1. Question 1. Simplify fully dfrac2x²+5x-3x²+3x

    Show worked answerHide worked answer
    1. M1: (2x-1)(x+3)
    2. M1: x(x+3)
    3. A1: dfrac2x-1x
    Answer: dfrac2x-1x
    Algebraic Fractions Involving Factorising
    [3 marks]

  2. Question 2. Two bars: 20 < x ≤ 25 has frequency density 4.8 and 25 < x ≤ 40 has frequency density 1.6. Work out the frequency of each class.

    Show worked answerHide worked answer
    1. M1: frequency = density × width
    2. M1: 4.8 × 5 and 1.6 × 15
    3. A1: 24 and 24
    Answer: 24 and 24
    Sketching Histograms
    [3 marks]

  3. Question 3. Simplify fully dfracx² - 43x ÷ dfracx + 26

    Show worked answerHide worked answer
    1. M1: dfrac(x - 2)(x + 2)3x × dfrac6x + 2
    2. M1 A1: dfrac2(x - 2)x
    Answer: dfrac2(x - 2)x
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. P(A)=0.6, P(Bmid A)=0.5 and P(Bmid A')=0.2. Work out P(B).

    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.6×0.5=0.3 and P(A'cap B)=0.4×0.2=0.08
    2. M1: add
    3. A1: 0.38
    Answer: 0.38
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. N lies on AB with AN:NB=3:1. Find overrightarrowCN in terms of mathbfa and mathbfc.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowON=mathbfa+3/4mathbfc
    2. M1: overrightarrowCN=-mathbfc+overrightarrowON
    3. A1: mathbfa-1/4mathbfc
    Answer: overrightarrowCN=mathbfa-1/4mathbfc
    Vector Ratio Problems
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 007

Grades 8/9Non-calculator

  1. Question 1. Simplify fully dfrac2x²+5x-3x²+3x

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2x-1)(x+3)
    2. M1: x(x+3)
    3. A1: dfrac2x-1x
    Answer: dfrac2x-1x
    Algebraic Fractions Involving Factorising

  2. Question 2. Two bars: 20 < x ≤ 25 has frequency density 4.8 and 25 < x ≤ 40 has frequency density 1.6. Work out the frequency of each class.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: frequency = density × width
    2. M1: 4.8 × 5 and 1.6 × 15
    3. A1: 24 and 24
    Answer: 24 and 24
    Sketching Histograms

  3. Question 3. Simplify fully dfracx² - 43x ÷ dfracx + 26

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac(x - 2)(x + 2)3x × dfrac6x + 2
    2. M1 A1: dfrac2(x - 2)x
    Answer: dfrac2(x - 2)x
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. P(A)=0.6, P(Bmid A)=0.5 and P(Bmid A')=0.2. Work out P(B).

    [3 marks]
    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.6×0.5=0.3 and P(A'cap B)=0.4×0.2=0.08
    2. M1: add
    3. A1: 0.38
    Answer: 0.38
    Conditional Probability with Venn Diagrams

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. N lies on AB with AN:NB=3:1. Find overrightarrowCN in terms of mathbfa and mathbfc.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowON=mathbfa+3/4mathbfc
    2. M1: overrightarrowCN=-mathbfc+overrightarrowON
    3. A1: mathbfa-1/4mathbfc
    Answer: overrightarrowCN=mathbfa-1/4mathbfc
    Vector Ratio Problems
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 007

Grades 8/9Non-calculator

  1. Question 1. Simplify fully dfrac2x²+5x-3x²+3x

    Show worked answerHide worked answer
    1. M1: (2x-1)(x+3)
    2. M1: x(x+3)
    3. A1: dfrac2x-1x
    Answer: dfrac2x-1x
    Algebraic Fractions Involving Factorising
    [3 marks]

  2. Question 2. Two bars: 20 < x ≤ 25 has frequency density 4.8 and 25 < x ≤ 40 has frequency density 1.6. Work out the frequency of each class.

    Show worked answerHide worked answer
    1. M1: frequency = density × width
    2. M1: 4.8 × 5 and 1.6 × 15
    3. A1: 24 and 24
    Answer: 24 and 24
    Sketching Histograms
    [3 marks]

  3. Question 3. Simplify fully dfracx² - 43x ÷ dfracx + 26

    Show worked answerHide worked answer
    1. M1: dfrac(x - 2)(x + 2)3x × dfrac6x + 2
    2. M1 A1: dfrac2(x - 2)x
    Answer: dfrac2(x - 2)x
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. P(A)=0.6, P(Bmid A)=0.5 and P(Bmid A')=0.2. Work out P(B).

    Show worked answerHide worked answer
    1. M1: P(Acap B)=0.6×0.5=0.3 and P(A'cap B)=0.4×0.2=0.08
    2. M1: add
    3. A1: 0.38
    Answer: 0.38
    Conditional Probability with Venn Diagrams
    [3 marks]

  5. Question 5. OABC is a parallelogram with overrightarrowOA=mathbfa and overrightarrowOC=mathbfc. N lies on AB with AN:NB=3:1. Find overrightarrowCN in terms of mathbfa and mathbfc.

    Show worked answerHide worked answer
    1. M1: overrightarrowAB=mathbfc, so overrightarrowON=mathbfa+3/4mathbfc
    2. M1: overrightarrowCN=-mathbfc+overrightarrowON
    3. A1: mathbfa-1/4mathbfc
    Answer: overrightarrowCN=mathbfa-1/4mathbfc
    Vector Ratio Problems
    [3 marks]