Poland · Klasa 12 · Practice Sheet 44

1. 1.

   A population of 4,200 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   In a triangle, a = 6, b = 10 and the included angle C = 40°. 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.

   A triangle has sides a = 17 cm and b = 17 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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4. 4.

   A force of 8 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A population of 3,900 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A wave has frequency 526 Hz and wavelength 2.16 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 112 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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8. 8.

   A force of 177 N acts on an area of 8.3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the sum of the first 6 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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10. 10.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the population standard deviation of: 4, 8, 8, 10, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A current of 3.3 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A body starts at 5 m/s and accelerates at 5.4 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Find the force needed to accelerate a 12 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    An object with initial velocity 1 m/s accelerates at 4.6 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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16. 16.

    Find the sum of the first 7 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    An object with initial velocity 0 m/s accelerates at 3.1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    Two masses 1,100 kg and 730 kg are 4 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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19. 19.

    Find the sum of the first 3 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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20. 20.

    A device runs at 36 V drawing 7.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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