Bahrain · Grade 11 · Practice Sheet 21

1. 1.

   A population of 6,100 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A cylinder has radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 7 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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4. 4.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   A device runs at 43 V drawing 4.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A cylinder has radius 3 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   Find the momentum of a 47 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A force of 276 N acts on an area of 6.3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   In a triangle, a = 5, b = 16 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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10. 10.

    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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11. 11.

    Find the force needed to accelerate a 33 kg mass at 7.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    An object with initial velocity 3 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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13. 13.

    Find the population standard deviation of: 17, 5, 4, 18, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    Find the gravitational potential energy of a 9 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Two masses 6,500 kg and 610 kg are 3 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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16. 16.

    Find the force needed to accelerate a 2 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A right-angled triangle has legs of 16 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A wave has frequency 861 Hz and wavelength 2.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A right-angled triangle has legs of 6 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A wave has frequency 98 Hz and wavelength 4.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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