Denmark · Grade 12 · Practice Sheet 36

1. 1.

   Find the population standard deviation of: 17, 14, 15, 5, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A wave has frequency 530 Hz and wavelength 1.04 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   An object with initial velocity 5 m/s accelerates at 3.5 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   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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5. 5.

   Two masses 5,600 kg and 420 kg are 14 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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6. 6.

   A current of 2.7 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   A triangle has sides a = 20 cm and b = 7 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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8. 8.

   A device runs at 96 V drawing 2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the momentum of a 55 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 475 N acts on an area of 7.9 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    In a triangle, a = 18, b = 5 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    A force of 445 N acts on an area of 1.9 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A wave has frequency 738 Hz and wavelength 1.82 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the gravitational potential energy of a 44 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A force of 133 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 52 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    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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19. 19.

    Find the population standard deviation of: 15, 14, 12, 2, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A population of 3,400 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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