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

Mixed Topic Worksheet Grades 8/9: Day 100

Grades 8/9Calculator

  1. Question 1. Simplify fully sqrtdfrac1129

    Show worked answerHide worked answer
    1. M1: √112 = 4√7 and √9 = 3
    2. A1: dfrac4√73
    Answer: dfrac4√73
    Simplifying Surds
    [2 marks]

  2. Question 2. a = 7.2 and b = 0.9
    Each value is correct to 1 decimal place.
    Work out the upper bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.2 + 0.05 and 0.9 - 0.05
    2. M1: 7.25 ÷ 0.85
    3. A1: 8.53
    Answer: 8.53
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. The squares of the smallest and the largest of three consecutive integers are added together. Prove algebraically that the total is 2 more than twice the square of the middle integer.

    Show worked answerHide worked answer
    1. M1: (n - 1)² + (n + 1)²
    2. M1: n² - 2n + 1 + n² + 2n + 1
    3. C1: 2n² + 2 = 2 × n² + 2
    Answer: 2n² + 2
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. overrightarrowJK = 2mathbfa + 5mathbfb
    overrightarrowKN = 6mathbfa + kmathbfb
    J, K and N lie on a straight line.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: overrightarrowKN = 3overrightarrowJK because 6 ÷ 2 = 3
    2. A1: k = 3 × 5 = 15
    Answer: k = 15
    Vectors Along a Straight Line
    [2 marks]

  5. Question 5. Solve the simultaneous equations
    y = x² - 8
    y = -3x + 20

    Show worked answerHide worked answer
    1. M1: Equate: x² - 8 = -3x + 20
    2. M1: Collect and factorise: ≤ft(x - 4) ≤ft(x + 7) = 0
    3. A1: x = 4 and x = -7
    4. A1: y = 8 and y = 41
    Answer: x = 4, y = 8 and x = -7, y = 41
    Solving Quadratic Simultaneous Equations
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 100

Grades 8/9Calculator

  1. Question 1. Simplify fully sqrtdfrac1129

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √112 = 4√7 and √9 = 3
    2. A1: dfrac4√73
    Answer: dfrac4√73
    Simplifying Surds

  2. Question 2. a = 7.2 and b = 0.9
    Each value is correct to 1 decimal place.
    Work out the upper bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 7.2 + 0.05 and 0.9 - 0.05
    2. M1: 7.25 ÷ 0.85
    3. A1: 8.53
    Answer: 8.53
    Combining Upper & Lower Bounds

  3. Question 3. The squares of the smallest and the largest of three consecutive integers are added together. Prove algebraically that the total is 2 more than twice the square of the middle integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (n - 1)² + (n + 1)²
    2. M1: n² - 2n + 1 + n² + 2n + 1
    3. C1: 2n² + 2 = 2 × n² + 2
    Answer: 2n² + 2
    Proof with Consecutive Numbers

  4. Question 4. overrightarrowJK = 2mathbfa + 5mathbfb
    overrightarrowKN = 6mathbfa + kmathbfb
    J, K and N lie on a straight line.
    Work out the value of k.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowKN = 3overrightarrowJK because 6 ÷ 2 = 3
    2. A1: k = 3 × 5 = 15
    Answer: k = 15
    Vectors Along a Straight Line

  5. Question 5. Solve the simultaneous equations
    y = x² - 8
    y = -3x + 20

    [4 marks]
    Show worked answerHide worked answer
    1. M1: Equate: x² - 8 = -3x + 20
    2. M1: Collect and factorise: ≤ft(x - 4) ≤ft(x + 7) = 0
    3. A1: x = 4 and x = -7
    4. A1: y = 8 and y = 41
    Answer: x = 4, y = 8 and x = -7, y = 41
    Solving Quadratic Simultaneous Equations
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 100

Grades 8/9Calculator

  1. Question 1. Simplify fully sqrtdfrac1129

    Show worked answerHide worked answer
    1. M1: √112 = 4√7 and √9 = 3
    2. A1: dfrac4√73
    Answer: dfrac4√73
    Simplifying Surds
    [2 marks]

  2. Question 2. a = 7.2 and b = 0.9
    Each value is correct to 1 decimal place.
    Work out the upper bound of a ÷ b.
    Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.2 + 0.05 and 0.9 - 0.05
    2. M1: 7.25 ÷ 0.85
    3. A1: 8.53
    Answer: 8.53
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. The squares of the smallest and the largest of three consecutive integers are added together. Prove algebraically that the total is 2 more than twice the square of the middle integer.

    Show worked answerHide worked answer
    1. M1: (n - 1)² + (n + 1)²
    2. M1: n² - 2n + 1 + n² + 2n + 1
    3. C1: 2n² + 2 = 2 × n² + 2
    Answer: 2n² + 2
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. overrightarrowJK = 2mathbfa + 5mathbfb
    overrightarrowKN = 6mathbfa + kmathbfb
    J, K and N lie on a straight line.
    Work out the value of k.

    Show worked answerHide worked answer
    1. M1: overrightarrowKN = 3overrightarrowJK because 6 ÷ 2 = 3
    2. A1: k = 3 × 5 = 15
    Answer: k = 15
    Vectors Along a Straight Line
    [2 marks]

  5. Question 5. Solve the simultaneous equations
    y = x² - 8
    y = -3x + 20

    Show worked answerHide worked answer
    1. M1: Equate: x² - 8 = -3x + 20
    2. M1: Collect and factorise: ≤ft(x - 4) ≤ft(x + 7) = 0
    3. A1: x = 4 and x = -7
    4. A1: y = 8 and y = 41
    Answer: x = 4, y = 8 and x = -7, y = 41
    Solving Quadratic Simultaneous Equations
    [4 marks]