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

Mixed Topic Worksheet Grades 8/9: Day 064

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    Work out the size of the angle between the line AG and the plane ABCD.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 8² + 5²
    2. M1: tan GAC = dfrac7AC
    3. A1: angle GAC = 36.6^° from tan GAC = 7 ÷ 9.43
    Answer: 36.6^°
    3D Trigonometry
    8 cm7 cmADBCFGEH5 cm
    [3 marks]

  2. Question 2. x = 1, y = 12; x = 2, y = 6; x = 4, y = 3
    Zoe says y is inversely proportional to the square of x.
    Is Zoe correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 1² × 12 = 12 and 2² × 6 = 24
    2. M1: 4² × 3 = 48
    3. A1: No, x² × y is not the same each time
    Answer: No
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. A train travels dfrac4x+8x km at an average speed of dfracx+2x-1 km/h. Work out the time taken in hours.

    Show worked answerHide worked answer
    1. M1: dfrac4x+8x÷dfracx+2x-1
    2. M2: 4(x+2), then cancels (x+2)
    3. A1: dfrac4(x-1)x
    Answer: dfrac4(x-1)x hours
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  4. Question 4. Frequency density is 3.2 for 5 < x ≤ 15 and 1.1 for 15 < x ≤ 35. Work out the total frequency.

    Show worked answerHide worked answer
    1. M1: 3.2 × 10 = 32 and 1.1 × 20 = 22
    2. M1: 32 + 22
    3. A1: 54
    Answer: 54
    Sketching Histograms
    [3 marks]

  5. Question 5. Tia says that the equation 3x² + 12x + 10 = 0 has no solutions
    Is Tia correct?
    Use completing the square and show how you know.

    Show worked answerHide worked answer
    1. M1: 3(x² + 4x) + 10 = 0 so 3≤ft((x + 2)² - 4) + 10 = 0
    2. M1: 3(x + 2)² - 2 = 0 so (x + 2)² = dfrac23
    3. A1: No, there are two solutions because dfrac23 has two square roots
    Answer: No, Tia is not correct
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 064

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    Work out the size of the angle between the line AG and the plane ABCD.
    Give your answer to 1 decimal place.

    [3 marks]
    8 cm7 cmADBCFGEH5 cm
    Show worked answerHide worked answer
    1. M1: AC² = 8² + 5²
    2. M1: tan GAC = dfrac7AC
    3. A1: angle GAC = 36.6^° from tan GAC = 7 ÷ 9.43
    Answer: 36.6^°
    3D Trigonometry

  2. Question 2. x = 1, y = 12; x = 2, y = 6; x = 4, y = 3
    Zoe says y is inversely proportional to the square of x.
    Is Zoe correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 1² × 12 = 12 and 2² × 6 = 24
    2. M1: 4² × 3 = 48
    3. A1: No, x² × y is not the same each time
    Answer: No
    Direct & Inverse Proportion with Functions

  3. Question 3. A train travels dfrac4x+8x km at an average speed of dfracx+2x-1 km/h. Work out the time taken in hours.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: dfrac4x+8x÷dfracx+2x-1
    2. M2: 4(x+2), then cancels (x+2)
    3. A1: dfrac4(x-1)x
    Answer: dfrac4(x-1)x hours
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. Frequency density is 3.2 for 5 < x ≤ 15 and 1.1 for 15 < x ≤ 35. Work out the total frequency.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3.2 × 10 = 32 and 1.1 × 20 = 22
    2. M1: 32 + 22
    3. A1: 54
    Answer: 54
    Sketching Histograms

  5. Question 5. Tia says that the equation 3x² + 12x + 10 = 0 has no solutions
    Is Tia correct?
    Use completing the square and show how you know.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3(x² + 4x) + 10 = 0 so 3≤ft((x + 2)² - 4) + 10 = 0
    2. M1: 3(x + 2)² - 2 = 0 so (x + 2)² = dfrac23
    3. A1: No, there are two solutions because dfrac23 has two square roots
    Answer: No, Tia is not correct
    Solving Quadratics by Completing the Square (a > 1)
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 064

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    Work out the size of the angle between the line AG and the plane ABCD.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 8² + 5²
    2. M1: tan GAC = dfrac7AC
    3. A1: angle GAC = 36.6^° from tan GAC = 7 ÷ 9.43
    Answer: 36.6^°
    3D Trigonometry
    8 cm7 cmADBCFGEH5 cm
    [3 marks]

  2. Question 2. x = 1, y = 12; x = 2, y = 6; x = 4, y = 3
    Zoe says y is inversely proportional to the square of x.
    Is Zoe correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: 1² × 12 = 12 and 2² × 6 = 24
    2. M1: 4² × 3 = 48
    3. A1: No, x² × y is not the same each time
    Answer: No
    Direct & Inverse Proportion with Functions
    [3 marks]

  3. Question 3. A train travels dfrac4x+8x km at an average speed of dfracx+2x-1 km/h. Work out the time taken in hours.

    Show worked answerHide worked answer
    1. M1: dfrac4x+8x÷dfracx+2x-1
    2. M2: 4(x+2), then cancels (x+2)
    3. A1: dfrac4(x-1)x
    Answer: dfrac4(x-1)x hours
    Multiplying & Dividing Algebraic Fractions
    [4 marks]

  4. Question 4. Frequency density is 3.2 for 5 < x ≤ 15 and 1.1 for 15 < x ≤ 35. Work out the total frequency.

    Show worked answerHide worked answer
    1. M1: 3.2 × 10 = 32 and 1.1 × 20 = 22
    2. M1: 32 + 22
    3. A1: 54
    Answer: 54
    Sketching Histograms
    [3 marks]

  5. Question 5. Tia says that the equation 3x² + 12x + 10 = 0 has no solutions
    Is Tia correct?
    Use completing the square and show how you know.

    Show worked answerHide worked answer
    1. M1: 3(x² + 4x) + 10 = 0 so 3≤ft((x + 2)² - 4) + 10 = 0
    2. M1: 3(x + 2)² - 2 = 0 so (x + 2)² = dfrac23
    3. A1: No, there are two solutions because dfrac23 has two square roots
    Answer: No, Tia is not correct
    Solving Quadratics by Completing the Square (a > 1)
    [3 marks]