Vietnam · Grade 12 · Practice Sheet 2

1. 1.

   Find the population standard deviation of: 3, 19, 19, 14, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   Find the force needed to accelerate a 5 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the sum of the first 10 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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4. 4.

   Find the force needed to accelerate a 45 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A device runs at 135 V drawing 0.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Solve using the quadratic formula: x² − 1x − 30 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the gravitational potential energy of a 46 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Two masses 2,900 kg and 580 kg are 16 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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10. 10.

    Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A triangle has sides a = 18 cm and b = 17 cm with an included angle C = 30°. 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 device runs at 66 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A current of 6.9 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A triangle has sides a = 19 cm and b = 6 cm with an included angle C = 30°. 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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16. 16.

    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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17. 17.

    A wave has frequency 39 Hz and wavelength 1.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A device runs at 19 V drawing 3.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the force needed to accelerate a 8 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

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

    Formula:Quadratic Formula

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

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