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

Mixed Topic Worksheet Grades 8/9: Day 065

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 6 cm by 8 cm by 24 cm. Work out the length of a space diagonal.

    Show worked answerHide worked answer
    1. M1: √6² + 8² + 24²
    2. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras
    [2 marks]

  2. Question 2. 200 people: 120 use the bus, 80 use the train and 30 use both. One of the people who use at least one of these is chosen. Work out the probability that this person uses both.

    Show worked answerHide worked answer
    1. M1: at least one =120+80-30=170
    2. A1: 30/170=3/17
    Answer: 3/17
    Conditional Probability with Venn Diagrams
    [2 marks]

  3. Question 3. The rectangle has area (3x²+10x-8) cm².
    Work out an expression, in terms of x, for the length p cm.

    Show worked answerHide worked answer
    1. M1: p=dfrac3x²+10x-8x+4
    2. M1: 3x²+10x-8=(3x-2)(x+4)
    3. A1: 3x-2
    Answer: 3x-2
    Algebraic Fractions Involving Factorising
    p cm(x + 4) cmABCDNot drawn accurately
    [3 marks]

  4. Question 4. The solutions of x² + bx + c = 0 are
    x = -7 + √10
    x = -7 - √10
    Work out the value of b and the value of c

    Show worked answerHide worked answer
    1. M1: (x + 7)² = 10
    2. M1: expand: x² + 14x + 49 - 10 = 0
    3. A1: b = 14
    4. A1: c = 39
    Answer: b = 14, c = 39
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  5. Question 5. An estimate of the area under a graph of speed (km/h) against time (minutes) is 90 Work out the distance travelled in kilometres

    Show worked answerHide worked answer
    1. M1: area is in km/h × minutes, so divide by 60 to change minutes to hours
    2. A1: 1.5 km
    Answer: 1.5 km
    Estimating Areas Under Curves
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 065

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 6 cm by 8 cm by 24 cm. Work out the length of a space diagonal.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: √6² + 8² + 24²
    2. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras

  2. Question 2. 200 people: 120 use the bus, 80 use the train and 30 use both. One of the people who use at least one of these is chosen. Work out the probability that this person uses both.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: at least one =120+80-30=170
    2. A1: 30/170=3/17
    Answer: 3/17
    Conditional Probability with Venn Diagrams

  3. Question 3. The rectangle has area (3x²+10x-8) cm².
    Work out an expression, in terms of x, for the length p cm.

    [3 marks]
    p cm(x + 4) cmABCDNot drawn accurately
    Show worked answerHide worked answer
    1. M1: p=dfrac3x²+10x-8x+4
    2. M1: 3x²+10x-8=(3x-2)(x+4)
    3. A1: 3x-2
    Answer: 3x-2
    Algebraic Fractions Involving Factorising

  4. Question 4. The solutions of x² + bx + c = 0 are
    x = -7 + √10
    x = -7 - √10
    Work out the value of b and the value of c

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (x + 7)² = 10
    2. M1: expand: x² + 14x + 49 - 10 = 0
    3. A1: b = 14
    4. A1: c = 39
    Answer: b = 14, c = 39
    Solving Quadratics by Completing the Square (a = 1)

  5. Question 5. An estimate of the area under a graph of speed (km/h) against time (minutes) is 90 Work out the distance travelled in kilometres

    [2 marks]
    Show worked answerHide worked answer
    1. M1: area is in km/h × minutes, so divide by 60 to change minutes to hours
    2. A1: 1.5 km
    Answer: 1.5 km
    Estimating Areas Under Curves
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 065

Grades 8/9Non-calculator

  1. Question 1. A cuboid measures 6 cm by 8 cm by 24 cm. Work out the length of a space diagonal.

    Show worked answerHide worked answer
    1. M1: √6² + 8² + 24²
    2. A1: 26 cm
    Answer: 26 cm
    3D Pythagoras
    [2 marks]

  2. Question 2. 200 people: 120 use the bus, 80 use the train and 30 use both. One of the people who use at least one of these is chosen. Work out the probability that this person uses both.

    Show worked answerHide worked answer
    1. M1: at least one =120+80-30=170
    2. A1: 30/170=3/17
    Answer: 3/17
    Conditional Probability with Venn Diagrams
    [2 marks]

  3. Question 3. The rectangle has area (3x²+10x-8) cm².
    Work out an expression, in terms of x, for the length p cm.

    Show worked answerHide worked answer
    1. M1: p=dfrac3x²+10x-8x+4
    2. M1: 3x²+10x-8=(3x-2)(x+4)
    3. A1: 3x-2
    Answer: 3x-2
    Algebraic Fractions Involving Factorising
    p cm(x + 4) cmABCDNot drawn accurately
    [3 marks]

  4. Question 4. The solutions of x² + bx + c = 0 are
    x = -7 + √10
    x = -7 - √10
    Work out the value of b and the value of c

    Show worked answerHide worked answer
    1. M1: (x + 7)² = 10
    2. M1: expand: x² + 14x + 49 - 10 = 0
    3. A1: b = 14
    4. A1: c = 39
    Answer: b = 14, c = 39
    Solving Quadratics by Completing the Square (a = 1)
    [4 marks]

  5. Question 5. An estimate of the area under a graph of speed (km/h) against time (minutes) is 90 Work out the distance travelled in kilometres

    Show worked answerHide worked answer
    1. M1: area is in km/h × minutes, so divide by 60 to change minutes to hours
    2. A1: 1.5 km
    Answer: 1.5 km
    Estimating Areas Under Curves
    [2 marks]