United States · Grade 12 · Practice Sheet 9

1. 1.

   A wave has frequency 411 Hz and wavelength 1.16 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A current of 7.9 A flows through a 38 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the gravitational potential energy of a 17 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   Solve using the quadratic formula: x² + 1x − 20 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   A triangle has sides a = 5 cm and b = 7 cm with an included angle C = 120°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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7. 7.

   Find the gravitational potential energy of a 21 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   Find the momentum of a 34 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    In a triangle, a = 5, b = 17 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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11. 11.

    Find the force needed to accelerate a 33 kg mass at 6.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A force of 49 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the force needed to accelerate a 16 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A body starts at 9 m/s and accelerates at 2.7 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the population standard deviation of: 12, 9, 11, 3, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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16. 16.

    Find the force needed to accelerate a 59 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    $2,800 is invested at 3% 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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18. 18.

    A force of 450 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A 6 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A cone has base radius 7 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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