Germany · Klasse 12 · Practice Sheet 37

1. 1.

   A body starts at 15 m/s and accelerates at 5.4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Two masses 1,100 kg and 240 kg are 15 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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3. 3.

   A device runs at 82 V drawing 4.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A triangle has sides a = 11 cm and b = 18 cm with an included angle C = 90°. 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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5. 5.

   A force of 294 N acts on an area of 9.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A wave has frequency 514 Hz and wavelength 1.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the sum of the first 5 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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8. 8.

   A body starts at 2 m/s and accelerates at 5.1 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 14 terms of an arithmetic series with first term a = 1 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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10. 10.

    Find the sum of the first 8 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A 12 kg object moves at 21 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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12. 12.

    Find the force needed to accelerate a 20 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    In a triangle, a = 12, b = 9 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Solve using the quadratic formula: x² + 9x + 18 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A device runs at 188 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A population of 5,100 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A wave has frequency 531 Hz and wavelength 2.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A triangle has sides a = 6 cm and b = 12 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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19. 19.

    A force of 493 N acts on an area of 0.6 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Solve using the quadratic formula: x² + 4x + 3 = 0.

    Formula:Quadratic Formula

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

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