Saudi Arabia · Grade 12 · Practice Sheet 5

1. 1.

   Find the population standard deviation of: 3, 13, 18, 19, 7 (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 sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   In a triangle, a = 12, 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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5. 5.

   SAR 2,000 is invested at 8% 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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6. 6.

   A body starts at 0 m/s and accelerates at 4 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A force of 142 N acts on an area of 7.4 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the momentum of a 25 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the force needed to accelerate a 17 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 7 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the population standard deviation of: 15, 10, 18, 15, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the force needed to accelerate a 9 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 103 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the force needed to accelerate a 35 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A device runs at 57 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the momentum of a 54 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A wave has frequency 648 Hz and wavelength 2.37 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A device runs at 174 V drawing 7.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

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

    Formula:Sum of a Geometric Series

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

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20. 20.

    A current of 7 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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