Russia · Grade 9 · Practice Sheet 29

1. 1.

   Find the momentum of a 45 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A force of 6 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the gravitational potential energy of a 48 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A cone has base radius 9 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   Find the force needed to accelerate a 48 kg mass at 2.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A 13 kg object moves at 8 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A current of 6.6 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the gravitational potential energy of a 10 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A current of 7.9 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    ₽4,200 is invested at 4% 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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13. 13.

    A car travels 305 km in 5 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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14. 14.

    A right-angled triangle has legs of 11 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Solve for x: 5x + 19 = 44.

    Formula:Solving a Linear Equation

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

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16. 16.

    A cylinder has radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A value changes from 181 to 126. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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18. 18.

    A cone has base radius 7 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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19. 19.

    A right-angled triangle has legs of 6 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A cone has base radius 8 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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