Qatar · Grade 11 · Practice Sheet 43

1. 1.

   A population of 8,000 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   A wave has frequency 334 Hz and wavelength 2.15 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A force of 39 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   In a triangle, a = 14, b = 10 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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5. 5.

   A cylinder has radius 9 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   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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7. 7.

   A device runs at 112 V drawing 8.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the population standard deviation of: 16, 11, 14, 16, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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9. 9.

   A current of 3.6 A flows through a 27 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A device runs at 92 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    In a triangle, a = 17, b = 15 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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12. 12.

    Two masses 5,800 kg and 350 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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13. 13.

    A right-angled triangle has legs of 12 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    Solve using the quadratic formula: x² − 4x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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15. 15.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 8 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 cylinder has radius 13 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A wave has frequency 662 Hz and wavelength 3.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 171 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A body starts at 11 m/s and accelerates at 3.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Solve using the quadratic formula: x² − 10x + 24 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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