United States · Grade 10 · Practice Sheet 30

1. 1.

   An object has mass 16.2 g and volume 6 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A value changes from 77 to 244. 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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3. 3.

   Solve for x: 9x + 14 = 122.

   Formula:Solving a Linear Equation

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

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4. 4.

   A wave has frequency 250 Hz and wavelength 1.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A current of 1.4 A flows through a 49 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   An object with initial velocity 9 m/s accelerates at 3.2 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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7. 7.

   A device runs at 194 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Solve using the quadratic formula: x² − 8x + 15 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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9. 9.

   A device runs at 69 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A 28 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A cone has base radius 8 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Solve using the quadratic formula: x² − 7x + 12 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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13. 13.

    A wave has frequency 803 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the force needed to accelerate a 54 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    $1,100 is invested at 6% compound interest per annum for 4 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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16. 16.

    Find the momentum of a 43 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A cylinder has radius 9 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

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

    Formula:Volume of a Cone

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

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19. 19.

    A device runs at 14 V drawing 1.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 5 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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