Germany · Klasse 10 · Practice Sheet 48

1. 1.

   A device runs at 102 V drawing 4.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A population of 5,600 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Solve for x: 5x + 16 = 56.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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4. 4.

   A wave has frequency 834 Hz and wavelength 2.26 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 12 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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6. 6.

   A device runs at 198 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 10 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   Find the momentum of a 13 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A value changes from 192 to 232. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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10. 10.

    €500 is invested at 8% compound interest per annum for 5 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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11. 11.

    A 36 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A cylinder has radius 7 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    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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14. 14.

    Find the force needed to accelerate a 15 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    An object with initial velocity 11 m/s accelerates at 2.3 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    Find the momentum of a 9 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    €1,800 is invested at 3% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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19. 19.

    A cylinder has radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A current of 1.4 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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