Germany · Klasse 11 · Practice Sheet 34

1. 1.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 5 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A population of 5,600 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A triangle has sides a = 15 cm and b = 19 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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4. 4.

   A device runs at 200 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the momentum of a 21 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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7. 7.

   An object with initial velocity 2 m/s accelerates at 4.9 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A force of 31 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   In a triangle, a = 15, b = 7 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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10. 10.

    A device runs at 200 V drawing 6.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 2 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A force of 10 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Find the momentum of a 29 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A wave has frequency 247 Hz and wavelength 3.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the momentum of a 3 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    €2,800 is invested at 6% 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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17. 17.

    An object has mass 327.6 g and volume 39 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A current of 6.9 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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