Poland · Klasa 11 · Practice Sheet 50

1. 1.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A wave has frequency 393 Hz and wavelength 4.12 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Solve using the quadratic formula: x² + 0x − 1 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A cylinder has radius 4 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   A triangle has sides a = 18 cm and b = 13 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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6. 6.

   A device runs at 104 V drawing 1.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A current of 4.5 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A body starts at 19 m/s and accelerates at 2.5 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   An object with initial velocity 11 m/s accelerates at 2.8 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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10. 10.

    A wave has frequency 348 Hz and wavelength 3.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A current of 7.3 A flows through a 17 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the force needed to accelerate a 17 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the momentum of a 18 kg object moving at 16 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    zł 4,000 is invested at 3% compound interest per annum for 3 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 sum of the first 4 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A wave has frequency 31 Hz and wavelength 3.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A current of 4 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the population standard deviation of: 7, 4, 10, 19, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 3 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    Find the gravitational potential energy of a 28 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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