Colombia · Grado 12 · Practice Sheet 10

1. 1.

   Find the population standard deviation of: 15, 7, 10, 3, 8 (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 17 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A force of 85 N acts on an area of 6.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   $500 is invested at 3% compound interest per annum for 5 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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5. 5.

   Solve using the quadratic formula: x² + 4x + 0 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the population standard deviation of: 8, 20, 10, 6, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 7 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   A body starts at 1 m/s and accelerates at 2.6 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 3 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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10. 10.

    Find the gravitational potential energy of a 18 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A population of 2,700 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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12. 12.

    In a triangle, a = 10, b = 13 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A force of 82 N acts on an area of 3.1 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the momentum of a 9 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A device runs at 228 V drawing 3.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Solve using the quadratic formula: x² + 4x − 12 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A current of 4.4 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A wave has frequency 408 Hz and wavelength 2.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Find the gravitational potential energy of a 43 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A force of 59 N acts on an area of 5.8 m². Find the pressure.

    Formula:Pressure

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

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