Russia · Grade 12 · Practice Sheet 7

1. 1.

   Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A current of 0.7 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A device runs at 77 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A force of 88 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A body starts at 5 m/s and accelerates at 2.4 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

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

   Formula:Sum of a Geometric Series

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

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8. 8.

   A device runs at 106 V drawing 2.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A cone has base radius 11 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    An object with initial velocity 1 m/s accelerates at 3.7 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the population standard deviation of: 12, 4, 10, 4, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    In a triangle, a = 9, 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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14. 14.

    Find the gravitational potential energy of a 38 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A force of 120 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the population standard deviation of: 19, 18, 6, 13, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Find the momentum of a 42 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    An object with initial velocity 11 m/s accelerates at 4.1 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A device runs at 54 V drawing 6.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 29 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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