Australia · Year 9 · Practice Sheet 22

1. 1.

   Solve for x: 6x + 1 = 31.

   Formula:Solving a Linear Equation

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

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2. 2.

   Find the gravitational potential energy of a 38 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A cylinder has radius 14 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A 36 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   $108 is shared in the ratio 2 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   A wave has frequency 874 Hz and wavelength 2.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   $800 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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8. 8.

   A device runs at 197 V drawing 4.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   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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10. 10.

    Solve for x: 3x + 4 = 13.

    Formula:Solving a Linear Equation

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

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11. 11.

    Find the gravitational potential energy of a 18 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A right-angled triangle has legs of 4 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Find the gravitational potential energy of a 47 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A force of 221 N acts on an area of 9.1 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the momentum of a 43 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    An object has mass 58.5 g and volume 39 cm³. Find its density.

    Formula:Density

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

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17. 17.

    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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18. 18.

    A cylinder has radius 6 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A bag has 23 equally likely marbles, of which 14 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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20. 20.

    A force of 84 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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