Germany · Klasse 11 · Practice Sheet 6

1. 1.

   A cone has base radius 8 cm and height 12 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.

   A wave has frequency 527 Hz and wavelength 2.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   In a triangle, a = 14, b = 18 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A right-angled triangle has legs of 20 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   A population of 5,000 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A 21 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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7. 7.

   A cone has base radius 12 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A wave has frequency 298 Hz and wavelength 3.95 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A device runs at 39 V drawing 3.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the momentum of a 19 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the gravitational potential energy of a 14 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 1 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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14. 14.

    Find the force needed to accelerate a 45 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A right-angled triangle has legs of 17 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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16. 16.

    A device runs at 138 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 54 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 33 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A triangle has sides a = 19 cm and b = 15 cm with an included angle C = 120°. 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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20. 20.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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