Portugal · Ano 12 · Practice Sheet 32

1. 1.

   Find the gravitational potential energy of a 7 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   An object with initial velocity 1 m/s accelerates at 2.5 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A current of 3.1 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the gravitational potential energy of a 42 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the force needed to accelerate a 37 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 68 N acts on an area of 9.2 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   An object with initial velocity 1 m/s accelerates at 1.9 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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8. 8.

   In a triangle, a = 17, b = 7 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Solve using the quadratic formula: x² + 5x + 0 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    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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11. 11.

    In a triangle, a = 17, 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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12. 12.

    A force of 464 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A 23 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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14. 14.

    Find the gravitational potential energy of a 48 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A force of 242 N acts on an area of 1.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A population of 5,900 grows 8% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

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

    Formula:Sum of a Geometric Series

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

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18. 18.

    A body starts at 8 m/s and accelerates at 1.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A device runs at 99 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A current of 3 A flows through a 39 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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