United States · Grade 9 · Practice Sheet 14

1. 1.

   A value changes from 105 to 55. 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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2. 2.

   A right-angled triangle has legs of 13 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A 9 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   A force of 86 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 31 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   $330 is shared in the ratio 5 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   An object has mass 231.4 g and volume 26 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the gravitational potential energy of a 21 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A 28 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    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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12. 12.

    A wave has frequency 750 Hz and wavelength 0.68 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the force needed to accelerate a 48 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the gravitational potential energy of a 28 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A current of 4.7 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    Solve for x: 4x + 6 = 30.

    Formula:Solving a Linear Equation

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

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18. 18.

    An object has mass 124.2 g and volume 27 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A wave has frequency 137 Hz and wavelength 3.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the gravitational potential energy of a 45 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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