United States · Grade 10 · Practice Sheet 32

1. 1.

   A current of 6.2 A flows through a 49 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   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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3. 3.

   An object has mass 85.5 g and volume 19 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A wave has frequency 157 Hz and wavelength 2.33 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   An object with initial velocity 0 m/s accelerates at 2.3 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   Find the force needed to accelerate a 31 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A bag has 28 equally likely marbles, of which 2 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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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 force of 6 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A cone has base radius 5 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    A force of 28 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A wave has frequency 360 Hz and wavelength 1.56 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A current of 4.2 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A cylinder has radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A right-angled triangle has legs of 3 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A body starts at 15 m/s and accelerates at 4.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A force of 29 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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18. 18.

    Solve for x: 5x + 20 = 80.

    Formula:Solving a Linear Equation

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

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19. 19.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 11 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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20. 20.

    A value changes from 123 to 24. 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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