Poland · Klasa 12 · Practice Sheet 25

1. 1.

   Find the momentum of a 47 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Solve using the quadratic formula: x² − 7x + 12 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A force of 17 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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5. 5.

   zł 3,000 is invested at 3% 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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6. 6.

   Two masses 1,300 kg and 120 kg are 8 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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7. 7.

   A device runs at 103 V drawing 6.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the momentum of a 11 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the force needed to accelerate a 58 kg mass at 8.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object with initial velocity 4 m/s accelerates at 1.9 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    A device runs at 37 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A wave has frequency 625 Hz and wavelength 3.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the momentum of a 59 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    An object with initial velocity 15 m/s accelerates at 2.5 m/s² for 9 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 force needed to accelerate a 18 kg mass at 4.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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17. 17.

    A force of 89 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    In a triangle, a = 17, b = 7 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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19. 19.

    A population of 3,900 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 5 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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