Poland · Klasa 11 · Practice Sheet 12

1. 1.

   zł 700 is invested at 8% 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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2. 2.

   A cylinder has radius 9 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the force needed to accelerate a 25 kg mass at 5.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 65 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.

   A device runs at 176 V drawing 4.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 42 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 gravitational potential energy of a 3 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A force of 96 N moves an object 15 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A body starts at 3 m/s and accelerates at 5.3 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A population of 1,900 grows 2% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Find the gravitational potential energy of a 22 kg object raised 4 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A wave has frequency 573 Hz and wavelength 3.27 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A triangle has sides a = 6 cm and b = 13 cm with an included angle C = 30°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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14. 14.

    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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15. 15.

    Find the population standard deviation of: 18, 3, 11, 14, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A cone has base radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    An object has mass 56 g and volume 20 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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18. 18.

    Find the momentum of a 19 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A cylinder has radius 8 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A cone has base radius 11 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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