Ukraine · Grade 12 · Practice Sheet 15

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   Find the population standard deviation of: 17, 4, 15, 6, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the momentum of a 45 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 12 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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5. 5.

   A current of 1.9 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A triangle has sides a = 16 cm and b = 11 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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7. 7.

   Find the force needed to accelerate a 56 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   An object with initial velocity 11 m/s accelerates at 4.7 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   In a triangle, a = 17, b = 6 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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10. 10.

    A device runs at 57 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A wave has frequency 144 Hz and wavelength 3.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the population standard deviation of: 13, 17, 9, 17, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A current of 5.7 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A wave has frequency 840 Hz and wavelength 3.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 9 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    In a triangle, a = 7, b = 10 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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18. 18.

    Find the population standard deviation of: 14, 5, 10, 8, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the force needed to accelerate a 28 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the momentum of a 5 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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