France · Classe 12 · Practice Sheet 39

1. 1.

   A device runs at 211 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A body starts at 20 m/s and accelerates at 5.6 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A device runs at 152 V drawing 8.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the force needed to accelerate a 51 kg mass at 2.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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7. 7.

   Find the force needed to accelerate a 55 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the sum of the first 10 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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9. 9.

   A force of 76 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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11. 11.

    In a triangle, a = 17, b = 9 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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12. 12.

    €1,300 is invested at 3% compound interest per annum for 2 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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13. 13.

    A device runs at 132 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A body starts at 13 m/s and accelerates at 4.2 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 7.9 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Solve using the quadratic formula: x² + 0x − 25 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A population of 5,000 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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18. 18.

    Find the population standard deviation of: 12, 13, 2, 10, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A population of 7,300 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Find the momentum of a 2 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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