United Kingdom · Year 9 · Practice Sheet 21

1. 1.

   A bag has 23 equally likely marbles, of which 20 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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2. 2.

   A force of 30 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the gravitational potential energy of a 23 kg object raised 17 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A force of 96 N moves an object 5 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   Find the circumference of a circle whose radius is 26 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   A cone has base radius 8 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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7. 7.

   A train moves at 55 km/h for 5.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   A cylinder has radius 6 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Find the force needed to accelerate a 25 kg mass at 3.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A train moves at 37 km/h for 3.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    Solve for x: 9x + 14 = 50.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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12. 12.

    Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    Find the gravitational potential energy of a 34 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A right-angled triangle has legs of 19 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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15. 15.

    A train moves at 64 km/h for 3.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    Find the force needed to accelerate a 16 kg mass at 0.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cone has base radius 4 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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18. 18.

    A bag has 28 equally likely marbles, of which 21 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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19. 19.

    Find the gravitational potential energy of a 2 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A device runs at 47 V drawing 1.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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