Russia · Grade 11 · Practice Sheet 44

1. 1.

   Find the momentum of a 24 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the force needed to accelerate a 53 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A body starts at 10 m/s and accelerates at 1.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A triangle has sides a = 12 cm and b = 13 cm with an included angle C = 45°. 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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5. 5.

   A cone has base radius 4 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Find the momentum of a 59 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the sum of the first 3 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A 36 kg object moves at 15 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the momentum of a 29 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A current of 0.6 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A force of 65 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    An object has mass 167.4 g and volume 31 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A wave has frequency 89 Hz and wavelength 2.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 3 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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16. 16.

    A current of 0.7 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A body starts at 6 m/s and accelerates at 5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the momentum of a 8 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    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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20. 20.

    ₽3,600 is invested at 5% 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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