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Mixed Topic Worksheet Grades 8/9: Day 054

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    AG = 14 cm
    Work out the length of AE.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 14² = 8² + 6² + AE²
    2. M1: AE² = 14² - 8² - 6²
    3. A1: AE = 9.8 from AE² = 96
    Answer: 9.8
    3D Pythagoras
    8 cmADBCFGEH6 cmNot drawn accurately
    [3 marks]

  2. Question 2. A metal block has mass 340 g, to the nearest 10 g, and volume 85 cm³, to the nearest 5 cm³. Work out the upper bound for the density. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the upper bound of mass and the lower bound of volume
    2. M1: 345 ÷ 82.5
    3. A1: 4.18 g/cm³
    Answer: 4.18 g/cm³
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Simplify fully dfracx² - 9x × dfracx²x + 3

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x × dfracx²x + 3
    2. M1 A1: x(x - 3)
    Answer: x(x - 3)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. Solve x² + 10x + 8 = 0 by completing the square
    Give each solution correct to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: (x + 5)² - 25 + 8 = 0
    2. M1: (x + 5)² = 17
    3. M1: x = -5 ± √17
    4. A1: -0.88 and -9.12
    Answer: -0.88 and -9.12
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  5. Question 5. The curve y = 6x - x² and the line y = 2x cross at the origin and at (4, 8). The region between them is shaded. Use 4 trapezia of equal width to estimate its area.

    Show worked answerHide worked answer
    1. M1: ½ × 1 × (0 + 8 + 2 × (5 + 8 + 9))
    2. M1: area under the line = ½ × 4 × 8 = 16
    3. A1: 26 − 16 = 10
    Answer: 10
    Estimating Areas Under Curves
    xy0246810y = 6x − x²y = 2x012345
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 054

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    AG = 14 cm
    Work out the length of AE.
    Give your answer to 1 decimal place.

    [3 marks]
    8 cmADBCFGEH6 cmNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 14² = 8² + 6² + AE²
    2. M1: AE² = 14² - 8² - 6²
    3. A1: AE = 9.8 from AE² = 96
    Answer: 9.8
    3D Pythagoras

  2. Question 2. A metal block has mass 340 g, to the nearest 10 g, and volume 85 cm³, to the nearest 5 cm³. Work out the upper bound for the density. Give your answer to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: use the upper bound of mass and the lower bound of volume
    2. M1: 345 ÷ 82.5
    3. A1: 4.18 g/cm³
    Answer: 4.18 g/cm³
    Combining Upper & Lower Bounds

  3. Question 3. Simplify fully dfracx² - 9x × dfracx²x + 3

    [3 marks]
    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x × dfracx²x + 3
    2. M1 A1: x(x - 3)
    Answer: x(x - 3)
    Multiplying & Dividing Algebraic Fractions

  4. Question 4. Solve x² + 10x + 8 = 0 by completing the square
    Give each solution correct to 2 decimal places.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (x + 5)² - 25 + 8 = 0
    2. M1: (x + 5)² = 17
    3. M1: x = -5 ± √17
    4. A1: -0.88 and -9.12
    Answer: -0.88 and -9.12
    Solving Quadratics by Completing the Square (a = 1)

  5. Question 5. The curve y = 6x - x² and the line y = 2x cross at the origin and at (4, 8). The region between them is shaded. Use 4 trapezia of equal width to estimate its area.

    [3 marks]
    xy0246810y = 6x − x²y = 2x012345
    Show worked answerHide worked answer
    1. M1: ½ × 1 × (0 + 8 + 2 × (5 + 8 + 9))
    2. M1: area under the line = ½ × 4 × 8 = 16
    3. A1: 26 − 16 = 10
    Answer: 10
    Estimating Areas Under Curves
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 054

Grades 8/9Calculator

  1. Question 1. ABCDEFGH is a cuboid.
    AG = 14 cm
    Work out the length of AE.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 14² = 8² + 6² + AE²
    2. M1: AE² = 14² - 8² - 6²
    3. A1: AE = 9.8 from AE² = 96
    Answer: 9.8
    3D Pythagoras
    8 cmADBCFGEH6 cmNot drawn accurately
    [3 marks]

  2. Question 2. A metal block has mass 340 g, to the nearest 10 g, and volume 85 cm³, to the nearest 5 cm³. Work out the upper bound for the density. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the upper bound of mass and the lower bound of volume
    2. M1: 345 ÷ 82.5
    3. A1: 4.18 g/cm³
    Answer: 4.18 g/cm³
    Combining Upper & Lower Bounds
    [3 marks]

  3. Question 3. Simplify fully dfracx² - 9x × dfracx²x + 3

    Show worked answerHide worked answer
    1. M1: dfrac(x - 3)(x + 3)x × dfracx²x + 3
    2. M1 A1: x(x - 3)
    Answer: x(x - 3)
    Multiplying & Dividing Algebraic Fractions
    [3 marks]

  4. Question 4. Solve x² + 10x + 8 = 0 by completing the square
    Give each solution correct to 2 decimal places.

    Show worked answerHide worked answer
    1. M1: (x + 5)² - 25 + 8 = 0
    2. M1: (x + 5)² = 17
    3. M1: x = -5 ± √17
    4. A1: -0.88 and -9.12
    Answer: -0.88 and -9.12
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  5. Question 5. The curve y = 6x - x² and the line y = 2x cross at the origin and at (4, 8). The region between them is shaded. Use 4 trapezia of equal width to estimate its area.

    Show worked answerHide worked answer
    1. M1: ½ × 1 × (0 + 8 + 2 × (5 + 8 + 9))
    2. M1: area under the line = ½ × 4 × 8 = 16
    3. A1: 26 − 16 = 10
    Answer: 10
    Estimating Areas Under Curves
    xy0246810y = 6x − x²y = 2x012345
    [3 marks]