Germany · Klasse 12 · Practice Sheet 50

1. 1.

   A population of 3,600 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A current of 2 A flows through a 8 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the force needed to accelerate a 23 kg mass at 7.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A 35 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   An object with initial velocity 11 m/s accelerates at 4.8 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A body starts at 5 m/s and accelerates at 6 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A triangle has sides a = 8 cm and b = 15 cm with an included angle C = 60°. 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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8. 8.

   A current of 2.4 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A triangle has sides a = 8 cm and b = 7 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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10. 10.

    Find the momentum of a 14 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    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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12. 12.

    €1,700 is invested at 8% compound interest per annum for 3 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 body starts at 1 m/s and accelerates at 4.5 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    An object with initial velocity 14 m/s accelerates at 1.8 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    In a triangle, a = 11, b = 9 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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16. 16.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 10 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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17. 17.

    Find the gravitational potential energy of a 23 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A force of 6 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the force needed to accelerate a 58 kg mass at 1.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

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

    Formula:Quadratic Formula

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

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