Argentina · Grado 12 · Practice Sheet 29

1. 1.

   A force of 417 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A 31 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A force of 38 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A device runs at 141 V drawing 6.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A population of 8,000 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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6. 6.

   Find the sum of the first 7 terms of a geometric series with first term a = 6 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.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 8 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   A force of 30 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A cone has base radius 10 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A body starts at 4 m/s and accelerates at 5.9 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A wave has frequency 70 Hz and wavelength 3.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    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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13. 13.

    A body starts at 20 m/s and accelerates at 3.1 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 4 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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15. 15.

    A device runs at 91 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 9 cm and b = 16 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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17. 17.

    A current of 6.3 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the force needed to accelerate a 7 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A wave has frequency 260 Hz and wavelength 3.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    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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