Russia · Grade 9 · Practice Sheet 45

1. 1.

   A bag has 15 equally likely marbles, of which 13 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.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A bag has 27 equally likely marbles, of which 19 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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5. 5.

   A force of 17 N moves an object 24 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A 37 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   A force of 287 N acts on an area of 9.3 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A wave has frequency 578 Hz and wavelength 2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A bag has 25 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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10. 10.

    A force of 9 N moves an object 8 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    ₽3,900 is invested at 6% 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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12. 12.

    A cone has base radius 7 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    Find the gravitational potential energy of a 33 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A car travels 220 km in 4 hours. Find its average speed.

    Formula:Speed

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

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15. 15.

    A wave has frequency 638 Hz and wavelength 0.9 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A cylinder has radius 7 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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18. 18.

    A force of 37 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A cylinder has radius 5 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A wave has frequency 67 Hz and wavelength 2.44 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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