Czechia · Grade 12 · Practice Sheet 9

1. 1.

   A force of 462 N acts on an area of 6.4 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A wave has frequency 143 Hz and wavelength 1.45 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A current of 7.6 A flows through a 31 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 11 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A triangle has sides a = 15 cm and b = 19 cm with an included angle C = 45°. 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 14 V drawing 4.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A wave has frequency 585 Hz and wavelength 4.01 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Solve using the quadratic formula: x² + 1x − 30 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A device runs at 39 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A 17 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Kč 1,400 is invested at 3% 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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12. 12.

    A triangle has sides a = 6 cm and b = 11 cm with an included angle C = 45°. 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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13. 13.

    A body starts at 3 m/s and accelerates at 4.8 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A current of 6.8 A flows through a 21 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A body starts at 11 m/s and accelerates at 1.2 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the gravitational potential energy of a 47 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Solve using the quadratic formula: x² − 4x + 3 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A device runs at 209 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A body starts at 17 m/s and accelerates at 3.3 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the force needed to accelerate a 49 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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