Canada · Grade 12 · Practice Sheet 21

1. 1.

   Find the gravitational potential energy of a 17 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the force needed to accelerate a 36 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A 33 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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4. 4.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the force needed to accelerate a 44 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the momentum of a 24 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A 33 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   A wave has frequency 466 Hz and wavelength 0.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the gravitational potential energy of a 44 kg object raised 28 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the force needed to accelerate a 17 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A triangle has sides a = 13 cm and b = 16 cm with an included angle C = 90°. 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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12. 12.

    A current of 2.6 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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14. 14.

    Find the momentum of a 53 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    $2,100 is invested at 5% 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 20 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 84 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 5 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A cone has base radius 4 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    Find the force needed to accelerate a 42 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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