Portugal · Ano 12 · Practice Sheet 4

1. 1.

   A device runs at 69 V drawing 4.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the force needed to accelerate a 56 kg mass at 6.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the population standard deviation of: 13, 17, 2, 2, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the momentum of a 25 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   An object with initial velocity 0 m/s accelerates at 3.7 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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6. 6.

   €2,600 is invested at 6% compound interest per annum for 2 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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7. 7.

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

   Formula:Volume of a Cone

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

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8. 8.

   A wave has frequency 347 Hz and wavelength 2.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Solve using the quadratic formula: x² − 1x − 20 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A force of 47 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A device runs at 77 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object with initial velocity 4 m/s accelerates at 1.8 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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14. 14.

    A device runs at 97 V drawing 4.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A current of 5.8 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    An object with initial velocity 12 m/s accelerates at 2.5 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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17. 17.

    In a triangle, a = 5, b = 10 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    €2,500 is invested at 8% compound interest per annum for 2 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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19. 19.

    In a triangle, a = 8, b = 5 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    An object with initial velocity 7 m/s accelerates at 3.7 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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