Italy · Classe 11 · Practice Sheet 27

1. 1.

   A body starts at 2 m/s and accelerates at 4.5 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A device runs at 198 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 49 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   In a triangle, a = 15, b = 18 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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5. 5.

   A force of 50 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 5 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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7. 7.

   A force of 49 N moves an object 27 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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9. 9.

   €4,000 is invested at 8% 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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10. 10.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 6 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    Find the population standard deviation of: 2, 13, 10, 15, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A triangle has sides a = 11 cm and b = 10 cm with an included angle C = 30°. 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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13. 13.

    Find the population standard deviation of: 5, 8, 4, 4, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A force of 50 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A body starts at 13 m/s and accelerates at 1.7 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A current of 7.9 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the gravitational potential energy of a 15 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A current of 0.9 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    €2,600 is invested at 4% 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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