Mexico · Grado 12 · Practice Sheet 41

1. 1.

   Find the sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 4.

   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 671 Hz and wavelength 1.33 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the gravitational potential energy of a 28 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the momentum of a 29 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A cone has base radius 11 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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6. 6.

   Find the force needed to accelerate a 46 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A cone has base radius 11 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   A device runs at 6 V drawing 2.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    An object with initial velocity 13 m/s accelerates at 3.8 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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11. 11.

    A population of 1,700 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    An object with initial velocity 13 m/s accelerates at 2.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A body starts at 8 m/s and accelerates at 3.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A cone has base radius 2 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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16. 16.

    A 36 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A wave has frequency 662 Hz and wavelength 3.92 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A 5 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A device runs at 56 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A cone has base radius 3 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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