Greece · Grade 12 · Practice Sheet 13

1. 1.

   Find the population standard deviation of: 3, 3, 10, 11, 2 (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 momentum of a 42 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   €2,000 is invested at 6% 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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4. 4.

   Find the force needed to accelerate a 25 kg mass at 7.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A force of 21 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 99 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Two masses 6,100 kg and 560 kg are 4 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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8. 8.

   Find the momentum of a 38 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A wave has frequency 197 Hz and wavelength 4.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A 9 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Find the population standard deviation of: 5, 9, 19, 12, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A force of 463 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    In a triangle, a = 7, b = 7 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A population of 8,400 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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15. 15.

    Find the force needed to accelerate a 11 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    An object with initial velocity 4 m/s accelerates at 2.4 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A device runs at 235 V drawing 8.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A 11 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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19. 19.

    In a triangle, a = 17, b = 12 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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20. 20.

    A triangle has sides a = 16 cm and b = 13 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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