Greece · Grade 11 · Practice Sheet 35

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 9 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Find the force needed to accelerate a 28 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A triangle has sides a = 10 cm and b = 5 cm with an included angle C = 90°. 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 = 13 and the included angle C = 80°. 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 momentum of a 52 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 334 N acts on an area of 2.8 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Two masses 2,900 kg and 410 kg are 8 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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8. 8.

   An object has mass 100 g and volume 40 cm³. Find its density.

   Formula:Density

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

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9. 9.

   Find the population standard deviation of: 17, 13, 5, 5, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A cylinder has radius 13 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Find the momentum of a 20 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    In a triangle, a = 7, b = 8 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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13. 13.

    An object with initial velocity 1 m/s accelerates at 1.2 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 population standard deviation of: 7, 20, 13, 7, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Find the force needed to accelerate a 17 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A triangle has sides a = 20 cm and b = 14 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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17. 17.

    A device runs at 172 V drawing 0.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A cylinder has radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A wave has frequency 53 Hz and wavelength 2.07 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A force of 353 N acts on an area of 0.9 m². Find the pressure.

    Formula:Pressure

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

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