Japan · Grade 9 · Practice Sheet 1

1. 1.

   A car travels 174 km in 3 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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2. 2.

   Find the gravitational potential energy of a 7 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A 39 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A force of 382 N acts on an area of 5 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A right-angled triangle has legs of 5 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   An object has mass 190.8 g and volume 36 cm³. Find its density.

   Formula:Density

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

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7. 7.

   Find the momentum of a 43 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A cone has base radius 6 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A train moves at 86 km/h for 5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    A wave has frequency 236 Hz and wavelength 4.93 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Solve for x: 8x + 1 = 33.

    Formula:Solving a Linear Equation

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

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12. 12.

    A 11 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A force of 185 N acts on an area of 4.9 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A car travels 186 km in 3 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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15. 15.

    A bag has 13 equally likely marbles, of which 1 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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16. 16.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A right-angled triangle has legs of 15 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A car travels 824 km in 8 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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19. 19.

    Solve for x: 7x + 16 = 79.

    Formula:Solving a Linear Equation

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

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20. 20.

    Find the momentum of a 14 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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