Germany · Klasse 12 · Practice Sheet 48

1. 1.

   In a triangle, a = 12, 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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2. 2.

   A force of 131 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the force needed to accelerate a 51 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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5. 5.

   Find the momentum of a 52 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 36 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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8. 8.

   A current of 4.2 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A device runs at 113 V drawing 8.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A force of 231 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Two masses 8,400 kg and 800 kg are 19 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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12. 12.

    A body starts at 3 m/s and accelerates at 1.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the force needed to accelerate a 25 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    €2,800 is invested at 6% 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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15. 15.

    Find the population standard deviation of: 18, 15, 18, 16, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    A force of 24 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A wave has frequency 373 Hz and wavelength 1.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A cone has base radius 9 cm and height 21 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.

    A force of 57 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A population of 1,400 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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