Russia · Grade 11 · Practice Sheet 18

1. 1.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 9 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   ₽3,400 is invested at 5% compound interest per annum for 4 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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3. 3.

   Two masses 7,300 kg and 200 kg are 8 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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4. 4.

   A force of 38 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A 3 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the momentum of a 6 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   ₽3,300 is invested at 3% compound interest per annum for 4 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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9. 9.

   A cylinder has radius 11 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A body starts at 4 m/s and accelerates at 3.3 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    An object has mass 352.8 g and volume 49 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A force of 95 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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13. 13.

    A body starts at 20 m/s and accelerates at 1.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A current of 2.6 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the momentum of a 14 kg object moving at 24 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A force of 41 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the force needed to accelerate a 25 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the momentum of a 53 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A body starts at 13 m/s and accelerates at 4.6 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A device runs at 110 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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