Greece · Grade 12 · Practice Sheet 17

1. 1.

   €3,900 is invested at 8% compound interest per annum for 4 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.

   Find the force needed to accelerate a 15 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the momentum of a 24 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A wave has frequency 256 Hz and wavelength 0.51 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the gravitational potential energy of a 42 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   €600 is invested at 4% 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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7. 7.

   Find the population standard deviation of: 6, 3, 15, 18, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the momentum of a 6 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A cone has base radius 9 cm and height 4 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 current of 7.3 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A wave has frequency 336 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Two masses 8,100 kg and 260 kg are 14 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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13. 13.

    A triangle has sides a = 9 cm and b = 19 cm with an included angle C = 45°. 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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14. 14.

    A force of 81 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A device runs at 103 V drawing 5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 1 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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17. 17.

    A cone has base radius 9 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    €600 is invested at 8% 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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19. 19.

    Find the force needed to accelerate a 37 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    In a triangle, a = 14, b = 18 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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