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

Mixed Topic Worksheet Grades 4/5: Day 054

Grades 4/5Calculator

  1. Question 1. A class has 40 students.
    dfrac35 of the students walk to school.
    Work out the number of students who walk to school.

    Show worked answerHide worked answer
    1. M1: 40 ÷ 5 = 8 then 8 × 3
    2. A1: 24
    Answer: 24
    Multiplying Fractions
    [2 marks]

  2. Question 2. Triangle PQR has a right angle at Q.
    PQ = 9 cm
    PR = 15 cm
    Work out the length of QR.

    Show worked answerHide worked answer
    1. M1: QR² = 15² - 9²
    2. A1: QR = 12
    Answer: 12
    Drawing a 90° Angle
    [2 marks]

  3. Question 3. ABC is a right-angled triangle.
    Calculate the length of AC.
    Round your answer to one decimal place.

    Show worked answerHide worked answer
    1. M1: 12² + 19²
    2. M1: √12² + 19² = 22.4722ldots
    3. A1: 22.5 m
    Answer: 22.5 m
    Using Pythagoras to Find a Hypotenuse
    12 m19 mBAC
    [3 marks]

  4. Question 4. The graph of the amount of water in a tank (litres) against time (minutes) is a straight line from (0, 40) to (10, 10).
    What does the gradient tell you about the water in the tank? [2]

    Show worked answerHide worked answer
    1. M1: gradient = 10 - 40/10 = -3
    2. A1: water is leaving at 3 litres per minute
    Answer: Gradient -3: the tank loses 3 litres every minute
    Gradient as a Rate of Change
    [2 marks]

  5. Question 5. Bulb A costs £1.50 and lasts 1000 hours.
    Bulb B costs £4 and lasts 3000 hours.

    A hall needs light for 6000 hours.

    Work out how much less it costs to use bulb B than bulb A.

    Show worked answerHide worked answer
    1. M1: 6000 ÷ 1000 = 6 bulbs, so 6 × 1.50 = 9
    2. M1: 6000 ÷ 3000 = 2 bulbs, so 2 × 4.00 = 8
    3. M1: 9 - 8
    4. A1: £1
    Answer: £1
    Applied Best Buys
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 4/5: Day 054

Grades 4/5Calculator

  1. Question 1. A class has 40 students.
    dfrac35 of the students walk to school.
    Work out the number of students who walk to school.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 40 ÷ 5 = 8 then 8 × 3
    2. A1: 24
    Answer: 24
    Multiplying Fractions

  2. Question 2. Triangle PQR has a right angle at Q.
    PQ = 9 cm
    PR = 15 cm
    Work out the length of QR.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: QR² = 15² - 9²
    2. A1: QR = 12
    Answer: 12
    Drawing a 90° Angle

  3. Question 3. ABC is a right-angled triangle.
    Calculate the length of AC.
    Round your answer to one decimal place.

    [3 marks]
    12 m19 mBAC
    Show worked answerHide worked answer
    1. M1: 12² + 19²
    2. M1: √12² + 19² = 22.4722ldots
    3. A1: 22.5 m
    Answer: 22.5 m
    Using Pythagoras to Find a Hypotenuse

  4. Question 4. The graph of the amount of water in a tank (litres) against time (minutes) is a straight line from (0, 40) to (10, 10).
    What does the gradient tell you about the water in the tank? [2]

    [2 marks]
    Show worked answerHide worked answer
    1. M1: gradient = 10 - 40/10 = -3
    2. A1: water is leaving at 3 litres per minute
    Answer: Gradient -3: the tank loses 3 litres every minute
    Gradient as a Rate of Change

  5. Question 5. Bulb A costs £1.50 and lasts 1000 hours.
    Bulb B costs £4 and lasts 3000 hours.

    A hall needs light for 6000 hours.

    Work out how much less it costs to use bulb B than bulb A.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: 6000 ÷ 1000 = 6 bulbs, so 6 × 1.50 = 9
    2. M1: 6000 ÷ 3000 = 2 bulbs, so 2 × 4.00 = 8
    3. M1: 9 - 8
    4. A1: £1
    Answer: £1
    Applied Best Buys
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 4/5: Day 054

Grades 4/5Calculator

  1. Question 1. A class has 40 students.
    dfrac35 of the students walk to school.
    Work out the number of students who walk to school.

    Show worked answerHide worked answer
    1. M1: 40 ÷ 5 = 8 then 8 × 3
    2. A1: 24
    Answer: 24
    Multiplying Fractions
    [2 marks]

  2. Question 2. Triangle PQR has a right angle at Q.
    PQ = 9 cm
    PR = 15 cm
    Work out the length of QR.

    Show worked answerHide worked answer
    1. M1: QR² = 15² - 9²
    2. A1: QR = 12
    Answer: 12
    Drawing a 90° Angle
    [2 marks]

  3. Question 3. ABC is a right-angled triangle.
    Calculate the length of AC.
    Round your answer to one decimal place.

    Show worked answerHide worked answer
    1. M1: 12² + 19²
    2. M1: √12² + 19² = 22.4722ldots
    3. A1: 22.5 m
    Answer: 22.5 m
    Using Pythagoras to Find a Hypotenuse
    12 m19 mBAC
    [3 marks]

  4. Question 4. The graph of the amount of water in a tank (litres) against time (minutes) is a straight line from (0, 40) to (10, 10).
    What does the gradient tell you about the water in the tank? [2]

    Show worked answerHide worked answer
    1. M1: gradient = 10 - 40/10 = -3
    2. A1: water is leaving at 3 litres per minute
    Answer: Gradient -3: the tank loses 3 litres every minute
    Gradient as a Rate of Change
    [2 marks]

  5. Question 5. Bulb A costs £1.50 and lasts 1000 hours.
    Bulb B costs £4 and lasts 3000 hours.

    A hall needs light for 6000 hours.

    Work out how much less it costs to use bulb B than bulb A.

    Show worked answerHide worked answer
    1. M1: 6000 ÷ 1000 = 6 bulbs, so 6 × 1.50 = 9
    2. M1: 6000 ÷ 3000 = 2 bulbs, so 2 × 4.00 = 8
    3. M1: 9 - 8
    4. A1: £1
    Answer: £1
    Applied Best Buys
    [4 marks]