Hungary · Grade 12 · Practice Sheet 42

1. 1.

   Find the force needed to accelerate a 47 kg mass at 0.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   An object with initial velocity 14 m/s accelerates at 4.7 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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3. 3.

   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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4. 4.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   A triangle has sides a = 6 cm and b = 18 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.

   An object with initial velocity 14 m/s accelerates at 1.8 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the sum of the first 9 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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8. 8.

   A 38 kg object moves at 20 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 = 17, b = 10 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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10. 10.

    A current of 2.6 A flows through a 30 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A force of 289 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Solve using the quadratic formula: x² + 1x − 6 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    In a triangle, a = 17, b = 14 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.

    An object with initial velocity 8 m/s accelerates at 3.7 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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15. 15.

    Find the momentum of a 34 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A wave has frequency 507 Hz and wavelength 0.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the force needed to accelerate a 25 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 103 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A body starts at 3 m/s and accelerates at 2.6 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A current of 0.6 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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