Romania · Grade 12 · Practice Sheet 21

1. 1.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   Find the gravitational potential energy of a 48 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 6 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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4. 4.

   A wave has frequency 386 Hz and wavelength 1.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the force needed to accelerate a 32 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

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

   Formula:Quadratic Formula

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

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7. 7.

   A wave has frequency 240 Hz and wavelength 3.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A cone has base radius 4 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A force of 87 N moves an object 19 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A current of 3.6 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A device runs at 180 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A current of 7.6 A flows through a 23 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Two masses 5,900 kg and 590 kg are 14 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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14. 14.

    Find the sum of the first 7 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    An object with initial velocity 12 m/s accelerates at 2.1 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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16. 16.

    A force of 36 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A population of 2,300 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Solve using the quadratic formula: x² + 11x + 30 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the force needed to accelerate a 15 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A population of 7,700 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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