Qatar · Grade 12 · Practice Sheet 10

1. 1.

   A device runs at 53 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the force needed to accelerate a 22 kg mass at 8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   In a triangle, a = 13, b = 16 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Two masses 1,500 kg and 790 kg are 18 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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5. 5.

   In a triangle, a = 16, b = 6 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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6. 6.

   Two masses 5,600 kg and 880 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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7. 7.

   Find the momentum of a 59 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A population of 8,500 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Find the momentum of a 17 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 27 N moves an object 29 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 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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12. 12.

    In a triangle, a = 6, b = 13 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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13. 13.

    A force of 94 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A triangle has sides a = 20 cm and b = 17 cm with an included angle C = 45°. 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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15. 15.

    A population of 4,500 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A current of 7.5 A flows through a 33 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A wave has frequency 751 Hz and wavelength 2.7 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 8 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A force of 484 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the population standard deviation of: 19, 13, 18, 15, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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