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

Mixed Topic Worksheet Grades 8/9: Day 079

Grades 8/9Non-calculator

  1. Question 1. n is a positive integer. √n = 6√5. Work out the value of n.

    Show worked answerHide worked answer
    1. M1: n = (6√5)² = 36 × 5
    2. A1: 180
    Answer: 180
    Simplifying Surds
    [2 marks]

  2. Question 2. On a histogram, the class 20 < h ≤ 50 has frequency 45. Work out the height of its bar.

    Show worked answerHide worked answer
    1. M1: 45 ÷ 30
    2. A1: 1.5
    Answer: 1.5
    Interpreting Histograms
    [2 marks]

  3. Question 3. Simplify fully dfracx² - 94x + 8 × dfracx + 2x - 3

    Show worked answerHide worked answer
    1. M1: x² - 9 = (x - 3)(x + 3)
    2. M1: 4x + 8 = 4(x + 2)
    3. A1: dfracx + 34
    Answer: dfracx + 34
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. y is inversely proportional to the cube of x. When x=2, y=12. Work out the value of x when y=1.5.

    Show worked answerHide worked answer
    1. M1: y=dfrackx³, 12=dfrack8, k=96
    2. M1: 1.5=dfrac96x³, x³=64
    3. A1: x=4
    Answer: x=4
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The line y = x + k is a tangent to the circle x² + y² = 18. Work out the two possible values of k

    Show worked answerHide worked answer
    1. M1: x² + (x + k)² = 18 gives 2x² + 2kx + k² - 18 = 0
    2. M1: tangent means one solution, so (2k)² - 8(k² - 18) = 0
    3. A2: k² = 36, so k = 6 or k = -6
    Answer: k = 6 or k = -6
    Finding Equations of Tangents to Circles
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 079

Grades 8/9Non-calculator

  1. Question 1. n is a positive integer. √n = 6√5. Work out the value of n.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: n = (6√5)² = 36 × 5
    2. A1: 180
    Answer: 180
    Simplifying Surds

  2. Question 2. On a histogram, the class 20 < h ≤ 50 has frequency 45. Work out the height of its bar.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 45 ÷ 30
    2. A1: 1.5
    Answer: 1.5
    Interpreting Histograms

  3. Question 3. Simplify fully dfracx² - 94x + 8 × dfracx + 2x - 3

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x² - 9 = (x - 3)(x + 3)
    2. M1: 4x + 8 = 4(x + 2)
    3. A1: dfracx + 34
    Answer: dfracx + 34
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. y is inversely proportional to the cube of x. When x=2, y=12. Work out the value of x when y=1.5.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y=dfrackx³, 12=dfrack8, k=96
    2. M1: 1.5=dfrac96x³, x³=64
    3. A1: x=4
    Answer: x=4
    Direct & Inverse Proportion with Functions

  5. Question 5. The line y = x + k is a tangent to the circle x² + y² = 18. Work out the two possible values of k

    [4 marks]
    Show worked answerHide worked answer
    1. M1: x² + (x + k)² = 18 gives 2x² + 2kx + k² - 18 = 0
    2. M1: tangent means one solution, so (2k)² - 8(k² - 18) = 0
    3. A2: k² = 36, so k = 6 or k = -6
    Answer: k = 6 or k = -6
    Finding Equations of Tangents to Circles
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 079

Grades 8/9Non-calculator

  1. Question 1. n is a positive integer. √n = 6√5. Work out the value of n.

    Show worked answerHide worked answer
    1. M1: n = (6√5)² = 36 × 5
    2. A1: 180
    Answer: 180
    Simplifying Surds
    [2 marks]

  2. Question 2. On a histogram, the class 20 < h ≤ 50 has frequency 45. Work out the height of its bar.

    Show worked answerHide worked answer
    1. M1: 45 ÷ 30
    2. A1: 1.5
    Answer: 1.5
    Interpreting Histograms
    [2 marks]

  3. Question 3. Simplify fully dfracx² - 94x + 8 × dfracx + 2x - 3

    Show worked answerHide worked answer
    1. M1: x² - 9 = (x - 3)(x + 3)
    2. M1: 4x + 8 = 4(x + 2)
    3. A1: dfracx + 34
    Answer: dfracx + 34
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. y is inversely proportional to the cube of x. When x=2, y=12. Work out the value of x when y=1.5.

    Show worked answerHide worked answer
    1. M1: y=dfrackx³, 12=dfrack8, k=96
    2. M1: 1.5=dfrac96x³, x³=64
    3. A1: x=4
    Answer: x=4
    Direct & Inverse Proportion with Functions
    [3 marks]

  5. Question 5. The line y = x + k is a tangent to the circle x² + y² = 18. Work out the two possible values of k

    Show worked answerHide worked answer
    1. M1: x² + (x + k)² = 18 gives 2x² + 2kx + k² - 18 = 0
    2. M1: tangent means one solution, so (2k)² - 8(k² - 18) = 0
    3. A2: k² = 36, so k = 6 or k = -6
    Answer: k = 6 or k = -6
    Finding Equations of Tangents to Circles
    [4 marks]