Ecuador · Grado 10 · Practice Sheet 27

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   A body starts at 18 m/s and accelerates at 5.2 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A current of 6.1 A flows through a 59 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A wave has frequency 767 Hz and wavelength 0.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A device runs at 49 V drawing 3.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A wave has frequency 765 Hz and wavelength 4.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A force of 325 N acts on an area of 2.6 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 5 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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9. 9.

   Solve using the quadratic formula: x² + 7x + 12 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A wave has frequency 761 Hz and wavelength 1.05 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the force needed to accelerate a 53 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A body starts at 3 m/s and accelerates at 2.3 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A wave has frequency 772 Hz and wavelength 3.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 8 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the momentum of a 58 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A body starts at 2 m/s and accelerates at 5.9 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Solve using the quadratic formula: x² + 8x + 12 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A triangle has sides a = 18 cm and b = 9 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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