Czechia · Grade 9 · Practice Sheet 3

1. 1.

   Find the force needed to accelerate a 51 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A right-angled triangle has legs of 17 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the force needed to accelerate a 50 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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6. 6.

   A value changes from 113 to 253. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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7. 7.

   An object has mass 126 g and volume 35 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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8. 8.

   Find the momentum of a 8 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A force of 353 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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10. 10.

    A bag has 22 equally likely marbles, of which 17 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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11. 11.

    A cylinder has radius 9 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A current of 3.1 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A 28 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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14. 14.

    A force of 100 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A wave has frequency 234 Hz and wavelength 1.01 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    Find the force needed to accelerate a 59 kg mass at 5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    A train moves at 25 km/h for 4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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20. 20.

    A current of 2.4 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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