Russia · Grade 9 · Practice Sheet 12

1. 1.

   A 34 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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2. 2.

   Solve for x: 2x + 2 = 14.

   Formula:Solving a Linear Equation

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

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3. 3.

   A train moves at 84 km/h for 2.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   Find the force needed to accelerate a 49 kg mass at 4.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A bag has 30 equally likely marbles, of which 11 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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6. 6.

   An object has mass 192 g and volume 32 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A force of 62 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A cylinder has radius 14 cm and height 30 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 gravitational potential energy of a 15 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    ₽3,700 is invested at 4% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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11. 11.

    A train moves at 70 km/h for 4.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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12. 12.

    A force of 38 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A bag has 14 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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14. 14.

    ₽162 is shared in the ratio 3 : 3. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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15. 15.

    Find the circumference of a circle whose radius is 11 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    Find the gravitational potential energy of a 31 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A wave has frequency 501 Hz and wavelength 1.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Find the force needed to accelerate a 16 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 382 N acts on an area of 9.6 m². Find the pressure.

    Formula:Pressure

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

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