Greece · Grade 10 · Practice Sheet 37

1. 1.

   A body starts at 5 m/s and accelerates at 1.9 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A population of 3,900 grows 10% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A force of 389 N acts on an area of 5.7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A current of 5.4 A flows through a 54 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A wave has frequency 582 Hz and wavelength 2.39 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the momentum of a 57 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A population of 8,400 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

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

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Find the force needed to accelerate a 24 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 34 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A body starts at 17 m/s and accelerates at 1.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the gravitational potential energy of a 15 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A wave has frequency 722 Hz and wavelength 2.73 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    An object has mass 64.8 g and volume 24 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 1 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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17. 17.

    Solve using the quadratic formula: x² + 2x − 15 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    An object with initial velocity 2 m/s accelerates at 3.7 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    Find the sum of the first 12 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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20. 20.

    A wave has frequency 338 Hz and wavelength 0.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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