Philippines · Grade 11 · Practice Sheet 43

1. 1.

   A cylinder has radius 9 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the sum of the first 5 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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3. 3.

   A triangle has sides a = 7 cm and b = 16 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.

   In a triangle, a = 17, b = 15 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.

   A body starts at 15 m/s and accelerates at 4.4 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A force of 379 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the population standard deviation of: 20, 5, 7, 16, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the gravitational potential energy of a 10 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A force of 167 N acts on an area of 2.5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 611 Hz and wavelength 1.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object has mass 147 g and volume 30 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Find the momentum of a 7 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A wave has frequency 662 Hz and wavelength 3.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the gravitational potential energy of a 41 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 1 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A wave has frequency 264 Hz and wavelength 0.65 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A cylinder has radius 5 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    A device runs at 113 V drawing 2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Two masses 2,600 kg and 890 kg are 18 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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20. 20.

    A triangle has sides a = 10 cm and b = 13 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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