Czechia · Grade 12 · Practice Sheet 3

1. 1.

   A body starts at 7 m/s and accelerates at 3.8 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 2 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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3. 3.

   Kč 2,600 is invested at 4% compound interest per annum for 2 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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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 body starts at 12 m/s and accelerates at 5.9 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A cone has base radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A force of 194 N acts on an area of 5.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the gravitational potential energy of a 39 kg object raised 35 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A 33 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A population of 8,000 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A force of 88 N acts on an area of 9.1 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Find the momentum of a 41 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the force needed to accelerate a 55 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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15. 15.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Two masses 7,900 kg and 570 kg are 20 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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17. 17.

    Find the population standard deviation of: 5, 16, 17, 12, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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18. 18.

    A device runs at 54 V drawing 2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A 8 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A force of 42 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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