France · Classe 12 · Practice Sheet 16

1. 1.

   A population of 8,500 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   €600 is invested at 4% compound interest per annum for 5 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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3. 3.

   A 7 kg object moves at 10 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   An object with initial velocity 6 m/s accelerates at 3.9 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A triangle has sides a = 16 cm and b = 9 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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6. 6.

   A wave has frequency 25 Hz and wavelength 1.33 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

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

   Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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9. 9.

   A 21 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

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

    Formula:Quadratic Formula

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

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11. 11.

    A wave has frequency 411 Hz and wavelength 4.9 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the force needed to accelerate a 50 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

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

    Formula:Exponential Growth

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

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14. 14.

    A device runs at 221 V drawing 8.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A body starts at 0 m/s and accelerates at 3.7 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A wave has frequency 219 Hz and wavelength 1.55 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 7 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 61 N acts on an area of 4.2 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the momentum of a 50 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A cone has base radius 6 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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