Peru · Grado 12 · Practice Sheet 26

1. 1.

   A 27 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A force of 31 N acts on an area of 10 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A wave has frequency 670 Hz and wavelength 2.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Solve using the quadratic formula: x² − 1x − 30 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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5. 5.

   Find the momentum of a 57 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the sum of the first 6 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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7. 7.

   A body starts at 4 m/s and accelerates at 3.2 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A triangle has sides a = 19 cm and b = 7 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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9. 9.

   A wave has frequency 535 Hz and wavelength 4.74 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A body starts at 17 m/s and accelerates at 4.5 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A cone has base radius 5 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A current of 5.9 A flows through a 51 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the momentum of a 3 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A population of 2,700 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A force of 61 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A body starts at 16 m/s and accelerates at 5.9 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A population of 5,300 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A force of 118 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the gravitational potential energy of a 2 kg object raised 34 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A triangle has sides a = 7 cm and b = 7 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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