Saudi Arabia · Grade 11 · Practice Sheet 28

1. 1.

   Find the population standard deviation of: 18, 9, 3, 11, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A current of 7.8 A flows through a 46 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A force of 42 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   An object with initial velocity 13 m/s accelerates at 2.1 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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6. 6.

   Find the gravitational potential energy of a 23 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A force of 20 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A force of 47 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the force needed to accelerate a 5 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Solve using the quadratic formula: x² + 6x + 8 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A triangle has sides a = 16 cm and b = 13 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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12. 12.

    A population of 6,900 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 11 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the population standard deviation of: 16, 19, 9, 18, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Solve using the quadratic formula: x² − 8x + 12 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A device runs at 210 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A wave has frequency 856 Hz and wavelength 3.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the population standard deviation of: 19, 14, 3, 14, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A force of 111 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    SAR 3,200 is invested at 5% 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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