Greece · Grade 12 · Practice Sheet 2

1. 1.

   Find the gravitational potential energy of a 47 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   An object with initial velocity 10 m/s accelerates at 2.9 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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3. 3.

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

   Formula:Volume of a Cone

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

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4. 4.

   A force of 245 N acts on an area of 9.4 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A body starts at 8 m/s and accelerates at 4.2 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the gravitational potential energy of a 24 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A current of 1.5 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A body starts at 4 m/s and accelerates at 4.4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   €3,200 is invested at 6% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 7 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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12. 12.

    A population of 7,000 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A force of 354 N acts on an area of 4.3 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the force needed to accelerate a 46 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 296 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the momentum of a 25 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

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

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A cone has base radius 8 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    An object with initial velocity 4 m/s accelerates at 2.9 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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20. 20.

    A 10 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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