Russia · Grade 10 · Practice Sheet 39

1. 1.

   A cone has base radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the force needed to accelerate a 17 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 104 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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4. 4.

   ₽2,800 is invested at 10% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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5. 5.

   Find the momentum of a 25 kg object moving at 9 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Solve for x: 3x + 12 = 24.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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7. 7.

   A force of 19 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 9 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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9. 9.

   Solve for x: 7x + 15 = 71.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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10. 10.

    A triangle has sides a = 11 cm and b = 14 cm with an included angle C = 120°. 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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11. 11.

    A 30 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    An object has mass 179.8 g and volume 31 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A current of 6.2 A flows through a 28 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A body starts at 6 m/s and accelerates at 5.1 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A current of 1.5 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the force needed to accelerate a 30 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Solve using the quadratic formula: x² + 6x + 5 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A wave has frequency 82 Hz and wavelength 2.77 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Solve for x: 5x + 18 = 63.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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20. 20.

    A force of 90 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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