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

Mixed Topic Worksheet Grades 8/9: Day 033

Grades 8/9Non-calculator

  1. Question 1. Prove algebraically that the sum of six consecutive integers is 3 more than a multiple of 6.

    Show worked answerHide worked answer
    1. M1: n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)
    2. A1: 6n + 15
    3. C1: 6(n + 2) + 3, which is 3 more than a multiple of 6
    Answer: 6(n + 2) + 3
    Proof with Consecutive Numbers
    [3 marks]

  2. Question 2. Simplify fully dfracx5×dfrac10x²

    Show worked answerHide worked answer
    1. M1: dfrac10x5x²
    2. A1: dfrac2x
    Answer: dfrac2x
    Multiplying & Dividing Algebraic Fractions
    [2 marks]

  3. Question 3. y is inversely proportional to the cube root of x.
    y = 10 when x = 8
    Find the value of y when x = 125

    Show worked answerHide worked answer
    1. M1: y = dfracksqrt[3]x and 10 = dfrack2
    2. A1: k = 20
    3. A1: y = dfrac205 = 4
    Answer: 4
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. A rectangle has a perimeter of 54 cm and an area of 180 cm²
    Work out the length and the width of the rectangle.

    Show worked answerHide worked answer
    1. M1: Form l + w = 27 and lw = 180, then substitute: w(27 - w) = 180
    2. M1: Rearrange and factorise: (w - 12)(w - 15) = 0
    3. A1: w = 12 and w = 15
    4. A1: length 15 cm, width 12 cm
    Answer: length = 15 cm, width = 12 cm
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The diagram shows a rectangle with an area of 10 cm² and a width of (4 - √6) cm. Work out the length of the rectangle, giving your answer in its simplest form.

    Show worked answerHide worked answer
    1. M1: length = dfrac104 - √6
    2. M1: dfrac10(4 + √6)(4 - √6)(4 + √6) = dfrac10(4 + √6)10
    3. A1: 4 + √6 cm
    Answer: (4 + √6) cm
    Rationalising Denominators of the Form a ± √b
    (4 − √6) cmArea = 10 cm²Not drawn accurately
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 033

Grades 8/9Non-calculator

  1. Question 1. Prove algebraically that the sum of six consecutive integers is 3 more than a multiple of 6.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)
    2. A1: 6n + 15
    3. C1: 6(n + 2) + 3, which is 3 more than a multiple of 6
    Answer: 6(n + 2) + 3
    Proof with Consecutive Numbers

  2. Question 2. Simplify fully dfracx5×dfrac10x²

    [2 marks]
    Show worked answerHide worked answer
    1. M1: dfrac10x5x²
    2. A1: dfrac2x
    Answer: dfrac2x
    Multiplying & Dividing Algebraic Fractions

  3. Question 3. y is inversely proportional to the cube root of x.
    y = 10 when x = 8
    Find the value of y when x = 125

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = dfracksqrt[3]x and 10 = dfrack2
    2. A1: k = 20
    3. A1: y = dfrac205 = 4
    Answer: 4
    Direct & Inverse Proportion with Functions

  4. Question 4. A rectangle has a perimeter of 54 cm and an area of 180 cm²
    Work out the length and the width of the rectangle.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: Form l + w = 27 and lw = 180, then substitute: w(27 - w) = 180
    2. M1: Rearrange and factorise: (w - 12)(w - 15) = 0
    3. A1: w = 12 and w = 15
    4. A1: length 15 cm, width 12 cm
    Answer: length = 15 cm, width = 12 cm
    Solving Quadratic Simultaneous Equations

  5. Question 5. The diagram shows a rectangle with an area of 10 cm² and a width of (4 - √6) cm. Work out the length of the rectangle, giving your answer in its simplest form.

    [3 marks]
    (4 − √6) cmArea = 10 cm²Not drawn accurately
    Show worked answerHide worked answer
    1. M1: length = dfrac104 - √6
    2. M1: dfrac10(4 + √6)(4 - √6)(4 + √6) = dfrac10(4 + √6)10
    3. A1: 4 + √6 cm
    Answer: (4 + √6) cm
    Rationalising Denominators of the Form a ± √b
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 033

Grades 8/9Non-calculator

  1. Question 1. Prove algebraically that the sum of six consecutive integers is 3 more than a multiple of 6.

    Show worked answerHide worked answer
    1. M1: n + (n + 1) + (n + 2) + (n + 3) + (n + 4) + (n + 5)
    2. A1: 6n + 15
    3. C1: 6(n + 2) + 3, which is 3 more than a multiple of 6
    Answer: 6(n + 2) + 3
    Proof with Consecutive Numbers
    [3 marks]

  2. Question 2. Simplify fully dfracx5×dfrac10x²

    Show worked answerHide worked answer
    1. M1: dfrac10x5x²
    2. A1: dfrac2x
    Answer: dfrac2x
    Multiplying & Dividing Algebraic Fractions
    [2 marks]

  3. Question 3. y is inversely proportional to the cube root of x.
    y = 10 when x = 8
    Find the value of y when x = 125

    Show worked answerHide worked answer
    1. M1: y = dfracksqrt[3]x and 10 = dfrack2
    2. A1: k = 20
    3. A1: y = dfrac205 = 4
    Answer: 4
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. A rectangle has a perimeter of 54 cm and an area of 180 cm²
    Work out the length and the width of the rectangle.

    Show worked answerHide worked answer
    1. M1: Form l + w = 27 and lw = 180, then substitute: w(27 - w) = 180
    2. M1: Rearrange and factorise: (w - 12)(w - 15) = 0
    3. A1: w = 12 and w = 15
    4. A1: length 15 cm, width 12 cm
    Answer: length = 15 cm, width = 12 cm
    Solving Quadratic Simultaneous Equations
    [4 marks]

  5. Question 5. The diagram shows a rectangle with an area of 10 cm² and a width of (4 - √6) cm. Work out the length of the rectangle, giving your answer in its simplest form.

    Show worked answerHide worked answer
    1. M1: length = dfrac104 - √6
    2. M1: dfrac10(4 + √6)(4 - √6)(4 + √6) = dfrac10(4 + √6)10
    3. A1: 4 + √6 cm
    Answer: (4 + √6) cm
    Rationalising Denominators of the Form a ± √b
    (4 − √6) cmArea = 10 cm²Not drawn accurately
    [3 marks]