Czechia · Grade 12 · Practice Sheet 19

1. 1.

   In a triangle, a = 13, b = 9 and the included angle C = 60°. 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.

   Find the population standard deviation of: 16, 13, 20, 8, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A force of 54 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A force of 101 N acts on an area of 2.5 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 4 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 device runs at 167 V drawing 4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A triangle has sides a = 19 cm and b = 8 cm with an included angle C = 60°. 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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9. 9.

   A current of 0.7 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A force of 73 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A force of 28 N acts on an area of 6.9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    Find the population standard deviation of: 13, 10, 18, 11, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    Find the force needed to accelerate a 18 kg mass at 6.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A wave has frequency 859 Hz and wavelength 2.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the population standard deviation of: 9, 15, 7, 8, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 2.

    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 42 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the gravitational potential energy of a 22 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A population of 6,100 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    A wave has frequency 200 Hz and wavelength 3.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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