Uganda · Grade 12 · Practice Sheet 2

1. 1.

   Solve using the quadratic formula: x² + 7x + 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A population of 4,200 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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3. 3.

   A wave has frequency 33 Hz and wavelength 3.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A cone has base radius 5 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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5. 5.

   A force of 114 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the population standard deviation of: 15, 4, 7, 7, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   A force of 392 N acts on an area of 1.2 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A current of 7.7 A flows through a 4 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   An object with initial velocity 13 m/s accelerates at 3.7 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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10. 10.

    A body starts at 19 m/s and accelerates at 5.9 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A device runs at 207 V drawing 0.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A current of 7.6 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the momentum of a 20 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A device runs at 41 V drawing 3.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A force of 449 N acts on an area of 6.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A wave has frequency 65 Hz and wavelength 2.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A population of 4,700 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the momentum of a 32 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 118 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    In a triangle, a = 10, b = 13 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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