Russia · Grade 11 · Practice Sheet 23

1. 1.

   A right-angled triangle has legs of 17 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A population of 1,300 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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3. 3.

   Find the momentum of a 9 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   ₽3,300 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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5. 5.

   Two masses 8,300 kg and 140 kg are 17 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   A device runs at 170 V drawing 4.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the gravitational potential energy of a 12 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A population of 6,600 grows 3% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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9. 9.

   A cone has base radius 11 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A device runs at 178 V drawing 1.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A current of 4.3 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the force needed to accelerate a 41 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    An object has mass 146.2 g and volume 34 cm³. Find its density.

    Formula:Density

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

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14. 14.

    Find the force needed to accelerate a 57 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the momentum of a 48 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A force of 437 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the gravitational potential energy of a 26 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 3 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A 6 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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20. 20.

    A cone has base radius 9 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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