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

Mixed Topic Worksheet Grades 8/9: Day 076

Grades 8/9Calculator

  1. Question 1. A right-angled triangle has shorter sides 8 cm and 15 cm, both to the nearest cm. Work out the upper bound of the hypotenuse. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the upper bound of both shorter sides
    2. M1: √8.5² + 15.5²
    3. A1: 17.7 cm
    Answer: 17.7 cm
    Combining Upper & Lower Bounds
    [3 marks]

  2. Question 2. A circle has radius 13 cm. A chord is 5 cm from the centre of the circle. Work out the length of the chord.

    Show worked answerHide worked answer
    1. B1: the perpendicular from the centre bisects the chord
    2. M1: half-chord = √13² - 5² = 12
    3. A1: 24
    Answer: 24 cm
    Circle Theorems
    [3 marks]

  3. Question 3. y is directly proportional to x³. When x=2, y=40. Work out x when y=135.

    Show worked answerHide worked answer
    1. M2: y=5x³, so 5x³=135, x³=27
    2. A1: x=3
    Answer: x=3
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. ABCDE is a pyramid with square base ABCD; E is vertically above the centre of the base. AE = 16 cm
    Work out the height of the pyramid to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 14² + 14²
    2. M1: AC ÷ 2 = √392 ÷ 2
    3. M1: height² = 16² - (AC ÷ 2)²
    4. A1: height = 12.6
    Answer: 12.6
    3D Pythagoras
    14 cm14 cmABCDENot drawn accurately
    [4 marks]

  5. Question 5. The graph shows the power, in kilowatts, of a heater over 6 hours.
    Use 3 trapezia of equal width to work out an estimate for the area under the graph.

    Show worked answerHide worked answer
    1. M1: readings at 0, 2, 4, 6 hours: 3, 6, 9, 8
    2. M1: 1/2 × 2 × (3 + 8 + 2 × (6 + 9))
    3. A1: 41
    Answer: 41 (kilowatt-hours)
    Estimating Areas Under Curves
    Time (hours)Power (kW)048120123456
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 076

Grades 8/9Calculator

  1. Question 1. A right-angled triangle has shorter sides 8 cm and 15 cm, both to the nearest cm. Work out the upper bound of the hypotenuse. Give your answer to 3 significant figures.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: use the upper bound of both shorter sides
    2. M1: √8.5² + 15.5²
    3. A1: 17.7 cm
    Answer: 17.7 cm
    Combining Upper & Lower Bounds

  2. Question 2. A circle has radius 13 cm. A chord is 5 cm from the centre of the circle. Work out the length of the chord.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: the perpendicular from the centre bisects the chord
    2. M1: half-chord = √13² - 5² = 12
    3. A1: 24
    Answer: 24 cm
    Circle Theorems

  3. Question 3. y is directly proportional to x³. When x=2, y=40. Work out x when y=135.

    [3 marks]
    Show worked answerHide worked answer
    1. M2: y=5x³, so 5x³=135, x³=27
    2. A1: x=3
    Answer: x=3
    Direct & Inverse Proportion with Functions

  4. Question 4. ABCDE is a pyramid with square base ABCD; E is vertically above the centre of the base. AE = 16 cm
    Work out the height of the pyramid to 1 decimal place.

    [4 marks]
    14 cm14 cmABCDENot drawn accurately
    Show worked answerHide worked answer
    1. M1: AC² = 14² + 14²
    2. M1: AC ÷ 2 = √392 ÷ 2
    3. M1: height² = 16² - (AC ÷ 2)²
    4. A1: height = 12.6
    Answer: 12.6
    3D Pythagoras

  5. Question 5. The graph shows the power, in kilowatts, of a heater over 6 hours.
    Use 3 trapezia of equal width to work out an estimate for the area under the graph.

    [3 marks]
    Time (hours)Power (kW)048120123456
    Show worked answerHide worked answer
    1. M1: readings at 0, 2, 4, 6 hours: 3, 6, 9, 8
    2. M1: 1/2 × 2 × (3 + 8 + 2 × (6 + 9))
    3. A1: 41
    Answer: 41 (kilowatt-hours)
    Estimating Areas Under Curves
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 076

Grades 8/9Calculator

  1. Question 1. A right-angled triangle has shorter sides 8 cm and 15 cm, both to the nearest cm. Work out the upper bound of the hypotenuse. Give your answer to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: use the upper bound of both shorter sides
    2. M1: √8.5² + 15.5²
    3. A1: 17.7 cm
    Answer: 17.7 cm
    Combining Upper & Lower Bounds
    [3 marks]

  2. Question 2. A circle has radius 13 cm. A chord is 5 cm from the centre of the circle. Work out the length of the chord.

    Show worked answerHide worked answer
    1. B1: the perpendicular from the centre bisects the chord
    2. M1: half-chord = √13² - 5² = 12
    3. A1: 24
    Answer: 24 cm
    Circle Theorems
    [3 marks]

  3. Question 3. y is directly proportional to x³. When x=2, y=40. Work out x when y=135.

    Show worked answerHide worked answer
    1. M2: y=5x³, so 5x³=135, x³=27
    2. A1: x=3
    Answer: x=3
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. ABCDE is a pyramid with square base ABCD; E is vertically above the centre of the base. AE = 16 cm
    Work out the height of the pyramid to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: AC² = 14² + 14²
    2. M1: AC ÷ 2 = √392 ÷ 2
    3. M1: height² = 16² - (AC ÷ 2)²
    4. A1: height = 12.6
    Answer: 12.6
    3D Pythagoras
    14 cm14 cmABCDENot drawn accurately
    [4 marks]

  5. Question 5. The graph shows the power, in kilowatts, of a heater over 6 hours.
    Use 3 trapezia of equal width to work out an estimate for the area under the graph.

    Show worked answerHide worked answer
    1. M1: readings at 0, 2, 4, 6 hours: 3, 6, 9, 8
    2. M1: 1/2 × 2 × (3 + 8 + 2 × (6 + 9))
    3. A1: 41
    Answer: 41 (kilowatt-hours)
    Estimating Areas Under Curves
    Time (hours)Power (kW)048120123456
    [3 marks]