Ukraine · Grade 11 · Practice Sheet 2

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 3 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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2. 2.

   An object has mass 20.8 g and volume 13 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the momentum of a 41 kg object moving at 2 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 202 N acts on an area of 6.1 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A 30 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   A right-angled triangle has legs of 11 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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8. 8.

   A wave has frequency 301 Hz and wavelength 4.78 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   ₴3,500 is invested at 3% 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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10. 10.

    An object has mass 170.1 g and volume 21 cm³. Find its density.

    Formula:Density

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

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11. 11.

    An object with initial velocity 10 m/s accelerates at 1.8 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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12. 12.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 11 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A force of 420 N acts on an area of 4.8 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A device runs at 182 V drawing 0.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    An object with initial velocity 4 m/s accelerates at 2.3 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the force needed to accelerate a 30 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A right-angled triangle has legs of 20 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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19. 19.

    An object with initial velocity 13 m/s accelerates at 4 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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20. 20.

    An object has mass 85 g and volume 34 cm³. Find its density.

    Formula:Density

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

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