Romania · Grade 12 · Practice Sheet 11

1. 1.

   lei 3,300 is invested at 5% compound interest per annum for 3 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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2. 2.

   Two masses 8,500 kg and 770 kg are 4 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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3. 3.

   A force of 111 N acts on an area of 3.2 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Find the population standard deviation of: 20, 11, 10, 5, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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5. 5.

   A cone has base radius 12 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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6. 6.

   Find the gravitational potential energy of a 10 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A body starts at 0 m/s and accelerates at 3.7 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A wave has frequency 87 Hz and wavelength 2.52 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A current of 4.4 A flows through a 19 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A population of 2,900 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    Find the gravitational potential energy of a 33 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    An object with initial velocity 0 m/s accelerates at 2.3 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    A current of 0.7 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the force needed to accelerate a 50 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A cone has base radius 11 cm and height 22 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.

    Find the sum of the first 8 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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17. 17.

    Find the force needed to accelerate a 55 kg mass at 6.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Two masses 8,500 kg and 870 kg are 9 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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20. 20.

    A device runs at 223 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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