Poland · Klasa 12 · Practice Sheet 2

1. 1.

   A cone has base radius 7 cm and height 14 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.

   zł 2,600 is invested at 5% 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 − 1x − 12 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A wave has frequency 74 Hz and wavelength 1.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the force needed to accelerate a 53 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A population of 2,000 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A triangle has sides a = 10 cm and b = 11 cm with an included angle C = 90°. 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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8. 8.

   A device runs at 192 V drawing 9.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A cone has base radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A triangle has sides a = 17 cm and b = 7 cm with an included angle C = 90°. 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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11. 11.

    A device runs at 166 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A population of 7,300 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A device runs at 153 V drawing 9.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A wave has frequency 548 Hz and wavelength 3.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A cone has base radius 11 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A device runs at 63 V drawing 3.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Two masses 1,200 kg and 130 kg are 5 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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18. 18.

    Find the force needed to accelerate a 20 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Two masses 5,000 kg and 530 kg are 16 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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20. 20.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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