Germany · Klasse 12 · Practice Sheet 26

1. 1.

   Find the population standard deviation of: 8, 8, 4, 9, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   In a triangle, a = 9, 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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3. 3.

   €3,200 is invested at 3% 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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4. 4.

   In a triangle, a = 10, b = 9 and the included angle C = 70°. 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.

   Find the population standard deviation of: 3, 9, 3, 16, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A population of 2,900 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A force of 62 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   In a triangle, a = 17, b = 18 and the included angle C = 50°. 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.

   A force of 76 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    In a triangle, a = 13, b = 6 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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11. 11.

    A current of 2 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Solve using the quadratic formula: x² + 0x − 16 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A device runs at 95 V drawing 3.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    €1,200 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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15. 15.

    A 2 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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16. 16.

    A force of 165 N acts on an area of 4.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    In a triangle, a = 13, b = 12 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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18. 18.

    A device runs at 65 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A current of 2.2 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A body starts at 18 m/s and accelerates at 5.8 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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