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

Mixed Topic Worksheet Grades 8/9: Day 039

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 4 cm by 4 cm by 7 cm. Work out the length of a diagonal joining two opposite corners of the cuboid.

    Show worked answerHide worked answer
    1. M1: √4² + 4² + 7²
    2. A1: 9 cm
    Answer: 9 cm
    3D Pythagoras
    [2 marks]

  2. Question 2. The graph of y = f(x), where f(x) = 3x² - 4, is translated 2 units to the left to give the graph of y = g(x). Find g(x). Give your answer in the form y = ax² + bx + c where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: g(x) = 3(x + 2)² - 4
    2. M1: 3(x² + 4x + 4) - 4
    3. A1: y = 3x² + 12x + 8
    Answer: y = 3x² + 12x + 8
    Translations Along the x- & y-Axes
    [3 marks]

  3. Question 3. Prove that the sum of the squares of two consecutive integers is always odd.

    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = 2n² + 2n + 1
    2. M1 A1: = 2(n² + n) + 1, which is odd
    Answer: 2(n² + n) + 1 is odd
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. A, B, C and D are on a circle.
    AB = BC and angle ADC = 112^°
    Work out angle BAC.
    Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: 180 - 112
    2. M1: (180 - 68) ÷ 2
    3. A1: angle BAC = 56^°
    4. C1: opposite angles of a cyclic quadrilateral add to 180^°; ABC is isosceles
    Answer: 56^°
    Combining Circle Theorems
    112°ABCDNot drawn accurately
    [4 marks]

  5. Question 5. Write 4x² - 24x + 31 in the form a(x + p)² + q

    Show worked answerHide worked answer
    1. M1: 4(x² - 6x) + 31
    2. M1: 4≤ft((x - 3)² - 9) + 31
    3. A1: 4(x - 3)² - 5
    Answer: 4(x - 3)² - 5
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 039

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 4 cm by 4 cm by 7 cm. Work out the length of a diagonal joining two opposite corners of the cuboid.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √4² + 4² + 7²
    2. A1: 9 cm
    Answer: 9 cm
    3D Pythagoras

  2. Question 2. The graph of y = f(x), where f(x) = 3x² - 4, is translated 2 units to the left to give the graph of y = g(x). Find g(x). Give your answer in the form y = ax² + bx + c where a, b and c are integers.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: g(x) = 3(x + 2)² - 4
    2. M1: 3(x² + 4x + 4) - 4
    3. A1: y = 3x² + 12x + 8
    Answer: y = 3x² + 12x + 8
    Translations Along the x- & y-Axes

  3. Question 3. Prove that the sum of the squares of two consecutive integers is always odd.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = 2n² + 2n + 1
    2. M1 A1: = 2(n² + n) + 1, which is odd
    Answer: 2(n² + n) + 1 is odd
    Proof with Consecutive Numbers

  4. Question 4. A, B, C and D are on a circle.
    AB = BC and angle ADC = 112^°
    Work out angle BAC.
    Give reasons for each stage.

    [4 marks]
    112°ABCDNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 180 - 112
    2. M1: (180 - 68) ÷ 2
    3. A1: angle BAC = 56^°
    4. C1: opposite angles of a cyclic quadrilateral add to 180^°; ABC is isosceles
    Answer: 56^°
    Combining Circle Theorems

  5. Question 5. Write 4x² - 24x + 31 in the form a(x + p)² + q

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 4(x² - 6x) + 31
    2. M1: 4≤ft((x - 3)² - 9) + 31
    3. A1: 4(x - 3)² - 5
    Answer: 4(x - 3)² - 5
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 039

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 4 cm by 4 cm by 7 cm. Work out the length of a diagonal joining two opposite corners of the cuboid.

    Show worked answerHide worked answer
    1. M1: √4² + 4² + 7²
    2. A1: 9 cm
    Answer: 9 cm
    3D Pythagoras
    [2 marks]

  2. Question 2. The graph of y = f(x), where f(x) = 3x² - 4, is translated 2 units to the left to give the graph of y = g(x). Find g(x). Give your answer in the form y = ax² + bx + c where a, b and c are integers.

    Show worked answerHide worked answer
    1. M1: g(x) = 3(x + 2)² - 4
    2. M1: 3(x² + 4x + 4) - 4
    3. A1: y = 3x² + 12x + 8
    Answer: y = 3x² + 12x + 8
    Translations Along the x- & y-Axes
    [3 marks]

  3. Question 3. Prove that the sum of the squares of two consecutive integers is always odd.

    Show worked answerHide worked answer
    1. M1: n² + (n + 1)² = 2n² + 2n + 1
    2. M1 A1: = 2(n² + n) + 1, which is odd
    Answer: 2(n² + n) + 1 is odd
    Proof with Consecutive Numbers
    [3 marks]

  4. Question 4. A, B, C and D are on a circle.
    AB = BC and angle ADC = 112^°
    Work out angle BAC.
    Give reasons for each stage.

    Show worked answerHide worked answer
    1. M1: 180 - 112
    2. M1: (180 - 68) ÷ 2
    3. A1: angle BAC = 56^°
    4. C1: opposite angles of a cyclic quadrilateral add to 180^°; ABC is isosceles
    Answer: 56^°
    Combining Circle Theorems
    112°ABCDNot drawn accurately
    [4 marks]

  5. Question 5. Write 4x² - 24x + 31 in the form a(x + p)² + q

    Show worked answerHide worked answer
    1. M1: 4(x² - 6x) + 31
    2. M1: 4≤ft((x - 3)² - 9) + 31
    3. A1: 4(x - 3)² - 5
    Answer: 4(x - 3)² - 5
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]