Chile · Grado 11 · Practice Sheet 6

1. 1.

   Find the sum of the first 4 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A wave has frequency 892 Hz and wavelength 1.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the gravitational potential energy of a 21 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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5. 5.

   An object with initial velocity 13 m/s accelerates at 3.2 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A 31 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A cylinder has radius 13 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   A population of 2,600 grows 3% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A cylinder has radius 2 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A cone has base radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A right-angled triangle has legs of 16 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A force of 83 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A wave has frequency 557 Hz and wavelength 3.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the gravitational potential energy of a 36 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the force needed to accelerate a 42 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A device runs at 175 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A current of 3.5 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A right-angled triangle has legs of 20 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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