Russia · Grade 10 · Practice Sheet 23

1. 1.

   A force of 303 N acts on an area of 6.7 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the force needed to accelerate a 8 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the gravitational potential energy of a 5 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   An object has mass 374.1 g and volume 43 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A cone has base radius 12 cm and height 8 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 volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   An object has mass 60.8 g and volume 16 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A body starts at 17 m/s and accelerates at 3.9 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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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.

    A 7 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A body starts at 4 m/s and accelerates at 1.3 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A 19 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 11 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

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

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 11 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A right-angled triangle has legs of 9 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    ₽1,500 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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18. 18.

    An object with initial velocity 3 m/s accelerates at 1.7 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    ₽3,100 is invested at 10% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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20. 20.

    A device runs at 71 V drawing 5.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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