Czechia · Grade 12 · Practice Sheet 40

1. 1.

   A cone has base radius 8 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the force needed to accelerate a 51 kg mass at 2.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A wave has frequency 158 Hz and wavelength 3.15 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A cone has base radius 8 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the momentum of a 1 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the gravitational potential energy of a 25 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 147 V drawing 7.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A wave has frequency 227 Hz and wavelength 3.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A population of 1,700 grows 8% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A force of 35 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A 18 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A force of 492 N acts on an area of 4.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A device runs at 136 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    An object with initial velocity 1 m/s accelerates at 3.3 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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15. 15.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A force of 31 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.

    Find the force needed to accelerate a 28 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A population of 1,100 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 1 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    A force of 351 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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