Poland · Klasa 11 · Practice Sheet 7

1. 1.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 10 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   An object has mass 274.4 g and volume 49 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   A triangle has sides a = 7 cm and b = 17 cm with an included angle C = 120°. 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.

   In a triangle, a = 18, b = 8 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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5. 5.

   A cone has base radius 5 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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6. 6.

   Find the gravitational potential energy of a 9 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A device runs at 64 V drawing 4.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A cylinder has radius 10 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A current of 1.9 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A force of 98 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    An object with initial velocity 11 m/s accelerates at 1.6 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    Find the momentum of a 16 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    A force of 93 N moves an object 28 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    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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17. 17.

    A force of 78 N moves an object 23 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A right-angled triangle has legs of 9 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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19. 19.

    A cylinder has radius 2 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A force of 440 N acts on an area of 4.6 m². Find the pressure.

    Formula:Pressure

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

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