Qatar · Grade 11 · Practice Sheet 27

1. 1.

   A force of 90 N moves an object 24 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A right-angled triangle has legs of 8 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   An object has mass 398.4 g and volume 48 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Two masses 4,000 kg and 200 kg are 17 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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5. 5.

   Find the population standard deviation of: 10, 17, 14, 20, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A population of 5,700 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A body starts at 7 m/s and accelerates at 5.3 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A wave has frequency 349 Hz and wavelength 2.75 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   QAR 1,100 is invested at 3% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    A cylinder has radius 8 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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11. 11.

    A current of 5 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A 9 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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13. 13.

    A wave has frequency 693 Hz and wavelength 2.84 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A force of 59 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 10 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 5 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    A current of 4 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the force needed to accelerate a 28 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    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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