Greece · Grade 12 · Practice Sheet 10

1. 1.

   Find the gravitational potential energy of a 50 kg object raised 24 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 35 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A triangle has sides a = 14 cm and b = 19 cm with an included angle C = 60°. 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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4. 4.

   Find the gravitational potential energy of a 50 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Solve using the quadratic formula: x² − 8x + 12 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the force needed to accelerate a 3 kg mass at 5.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the sum of the first 7 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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8. 8.

   Find the population standard deviation of: 15, 4, 11, 18, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A wave has frequency 513 Hz and wavelength 4.11 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Two masses 3,200 kg and 650 kg are 19 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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11. 11.

    A current of 7 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A device runs at 209 V drawing 4.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the force needed to accelerate a 26 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A 26 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A population of 4,000 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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16. 16.

    In a triangle, a = 9, b = 15 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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17. 17.

    A force of 51 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the population standard deviation of: 15, 5, 19, 17, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A population of 4,100 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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20. 20.

    A force of 79 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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