Hungary · Grade 10 · Practice Sheet 47

1. 1.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Find the momentum of a 13 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   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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4. 4.

   A current of 7 A flows through a 51 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the sum of the first 16 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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7. 7.

   A triangle has sides a = 17 cm and b = 13 cm with an included angle C = 60°. 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.

   Find the momentum of a 29 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A current of 2.9 A flows through a 10 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

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

    Formula:Quadratic Formula

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

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11. 11.

    Find the momentum of a 58 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the gravitational potential energy of a 44 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A body starts at 14 m/s and accelerates at 2.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    A value changes from 171 to 77. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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15. 15.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A device runs at 110 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 2 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    Solve for x: 7x + 14 = 77.

    Formula:Solving a Linear Equation

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

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19. 19.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    Find the momentum of a 29 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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