Italy · Classe 12 · Practice Sheet 36

1. 1.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 12 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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2. 2.

   A device runs at 35 V drawing 4.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A triangle has sides a = 8 cm and b = 12 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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4. 4.

   A wave has frequency 510 Hz and wavelength 3.34 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A current of 0.6 A flows through a 45 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   An object with initial velocity 5 m/s accelerates at 3.7 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A force of 5 N moves an object 36 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A 3 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   In a triangle, a = 18, b = 11 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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10. 10.

    Find the force needed to accelerate a 35 kg mass at 4.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 395 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A population of 5,400 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Solve using the quadratic formula: x² + 5x + 0 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A device runs at 199 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the momentum of a 31 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    An object with initial velocity 12 m/s accelerates at 4.9 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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17. 17.

    A triangle has sides a = 13 cm and b = 20 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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18. 18.

    An object with initial velocity 8 m/s accelerates at 4.1 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A triangle has sides a = 11 cm and b = 10 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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20. 20.

    A cone has base radius 5 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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