Hungary · Grade 10 · Practice Sheet 9

1. 1.

   A cylinder has radius 12 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   An object has mass 68.8 g and volume 8 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A triangle has sides a = 17 cm and b = 17 cm with an included angle C = 45°. 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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4. 4.

   A 18 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   An object with initial velocity 3 m/s accelerates at 1.7 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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6. 6.

   A right-angled triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A triangle has sides a = 15 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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8. 8.

   A current of 7 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 8 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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10. 10.

    Find the force needed to accelerate a 47 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object has mass 119 g and volume 34 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A cylinder has radius 9 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    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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14. 14.

    In a triangle, a = 12, b = 10 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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15. 15.

    A cylinder has radius 4 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A wave has frequency 470 Hz and wavelength 0.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A force of 98 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the gravitational potential energy of a 34 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A device runs at 237 V drawing 9.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    An object has mass 91.2 g and volume 12 cm³. Find its density.

    Formula:Density

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

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