Czechia · Grade 12 · Practice Sheet 29

1. 1.

   A force of 111 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Kč 3,200 is invested at 3% compound interest per annum for 4 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.

   Solve using the quadratic formula: x² − 5x + 4 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the momentum of a 53 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A device runs at 26 V drawing 6.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 34 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the force needed to accelerate a 30 kg mass at 3.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Two masses 7,800 kg and 840 kg are 3 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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9. 9.

   Kč 2,300 is invested at 5% 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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10. 10.

    A population of 8,400 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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11. 11.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 4 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    Find the force needed to accelerate a 45 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A 4 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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14. 14.

    Kč 1,400 is invested at 6% 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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15. 15.

    Find the gravitational potential energy of a 5 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A device runs at 93 V drawing 8.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the force needed to accelerate a 54 kg mass at 8.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A cone has base radius 3 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    Find the momentum of a 38 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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