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

Mixed Topic Worksheet Grades 8/9: Day 008

Grades 8/9Calculator

  1. Question 1. P is directly proportional to r². r increases by 30%. Work out the percentage increase in P.

    Show worked answerHide worked answer
    1. M1: P is multiplied by ≤ft(dfrac130100)²
    2. A1: 1.69, an increase of 69%
    Answer: 69%
    Direct & Inverse Proportion with Functions
    [2 marks]

  2. Question 2. The probability of rain is 0.4. If it rains, Sam walks with probability 0.1. If not, he walks with probability 0.7. Given that Sam walks, find the probability that it rained. Give your answer to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: P(walk) = 0.4 × 0.1 + 0.6 × 0.7
    2. M1: dfrac0.040.46
    3. A1: 0.09
    Answer: 0.09
    Conditional Probability with Tree Diagrams
    [3 marks]

  3. Question 3. A rectangle has length √448 cm and width √175 cm. Work out the perimeter of the rectangle, giving your answer in the form a√7 cm where a is an integer.

    Show worked answerHide worked answer
    1. M1: √448 = 8√7
    2. M1: √175 = 5√7
    3. M1: 2 × (8√7 + 5√7)
    4. A1: 26√7 cm
    Answer: 26√7 cm
    Simplifying Surds
    [4 marks]

  4. Question 4. The histogram shows information about the lengths, h cm, of some beans.
    Work out the frequency for the class 20 < h ≤ 40.

    Show worked answerHide worked answer
    1. M1: 1.5 × (40 - 20)
    2. A1: 30
    Answer: 30
    Interpreting Histograms
    Length, h (cm)Frequency density01234010203040
    [2 marks]

  5. Question 5. The equation x² + kx + 9 = 0 has no real solutions Work out the possible values of k

    Show worked answerHide worked answer
    1. M1: no real solutions so b² - 4ac < 0
    2. M1: k² - 36 is negative so k² < 36
    3. A1: -6 < k < 6
    Answer: -6 < k < 6
    Solving Quadratic Inequalities
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 008

Grades 8/9Calculator

  1. Question 1. P is directly proportional to r². r increases by 30%. Work out the percentage increase in P.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: P is multiplied by ≤ft(dfrac130100)²
    2. A1: 1.69, an increase of 69%
    Answer: 69%
    Direct & Inverse Proportion with Functions

  2. Question 2. The probability of rain is 0.4. If it rains, Sam walks with probability 0.1. If not, he walks with probability 0.7. Given that Sam walks, find the probability that it rained. Give your answer to 2 decimal places.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: P(walk) = 0.4 × 0.1 + 0.6 × 0.7
    2. M1: dfrac0.040.46
    3. A1: 0.09
    Answer: 0.09
    Conditional Probability with Tree Diagrams

  3. Question 3. A rectangle has length √448 cm and width √175 cm. Work out the perimeter of the rectangle, giving your answer in the form a√7 cm where a is an integer.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: √448 = 8√7
    2. M1: √175 = 5√7
    3. M1: 2 × (8√7 + 5√7)
    4. A1: 26√7 cm
    Answer: 26√7 cm
    Simplifying Surds

  4. Question 4. The histogram shows information about the lengths, h cm, of some beans.
    Work out the frequency for the class 20 < h ≤ 40.

    [2 marks]
    Length, h (cm)Frequency density01234010203040
    Show worked answerHide worked answer
    1. M1: 1.5 × (40 - 20)
    2. A1: 30
    Answer: 30
    Interpreting Histograms

  5. Question 5. The equation x² + kx + 9 = 0 has no real solutions Work out the possible values of k

    [3 marks]
    Show worked answerHide worked answer
    1. M1: no real solutions so b² - 4ac < 0
    2. M1: k² - 36 is negative so k² < 36
    3. A1: -6 < k < 6
    Answer: -6 < k < 6
    Solving Quadratic Inequalities
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 008

Grades 8/9Calculator

  1. Question 1. P is directly proportional to r². r increases by 30%. Work out the percentage increase in P.

    Show worked answerHide worked answer
    1. M1: P is multiplied by ≤ft(dfrac130100)²
    2. A1: 1.69, an increase of 69%
    Answer: 69%
    Direct & Inverse Proportion with Functions
    [2 marks]

  2. Question 2. The probability of rain is 0.4. If it rains, Sam walks with probability 0.1. If not, he walks with probability 0.7. Given that Sam walks, find the probability that it rained. Give your answer to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: P(walk) = 0.4 × 0.1 + 0.6 × 0.7
    2. M1: dfrac0.040.46
    3. A1: 0.09
    Answer: 0.09
    Conditional Probability with Tree Diagrams
    [3 marks]

  3. Question 3. A rectangle has length √448 cm and width √175 cm. Work out the perimeter of the rectangle, giving your answer in the form a√7 cm where a is an integer.

    Show worked answerHide worked answer
    1. M1: √448 = 8√7
    2. M1: √175 = 5√7
    3. M1: 2 × (8√7 + 5√7)
    4. A1: 26√7 cm
    Answer: 26√7 cm
    Simplifying Surds
    [4 marks]

  4. Question 4. The histogram shows information about the lengths, h cm, of some beans.
    Work out the frequency for the class 20 < h ≤ 40.

    Show worked answerHide worked answer
    1. M1: 1.5 × (40 - 20)
    2. A1: 30
    Answer: 30
    Interpreting Histograms
    Length, h (cm)Frequency density01234010203040
    [2 marks]

  5. Question 5. The equation x² + kx + 9 = 0 has no real solutions Work out the possible values of k

    Show worked answerHide worked answer
    1. M1: no real solutions so b² - 4ac < 0
    2. M1: k² - 36 is negative so k² < 36
    3. A1: -6 < k < 6
    Answer: -6 < k < 6
    Solving Quadratic Inequalities
    [3 marks]