Greece · Grade 10 · Practice Sheet 33

1. 1.

   A wave has frequency 618 Hz and wavelength 3.7 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A current of 3.8 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A force of 116 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A bag has 13 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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5. 5.

   An object has mass 219.6 g and volume 36 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   An object with initial velocity 5 m/s accelerates at 2 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   A force of 22 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   An object has mass 75.9 g and volume 11 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the force needed to accelerate a 2 kg mass at 8.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A force of 94 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Solve for x: 6x + 3 = 15.

    Formula:Solving a Linear Equation

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

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14. 14.

    A right-angled triangle has legs of 16 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A body starts at 1 m/s and accelerates at 3.9 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    An object with initial velocity 5 m/s accelerates at 1.2 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the gravitational potential energy of a 35 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 6 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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19. 19.

    Solve using the quadratic formula: x² − 4x − 5 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A triangle has sides a = 17 cm and b = 9 cm with an included angle C = 30°. 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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