Hungary · Grade 10 · Practice Sheet 19

1. 1.

   Find the momentum of a 51 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A right-angled triangle has legs of 10 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Solve using the quadratic formula: x² − 3x + 0 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   Find the momentum of a 9 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A cylinder has radius 14 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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7. 7.

   Find the momentum of a 29 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A population of 7,800 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   Solve for x: 5x + 17 = 37.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the momentum of a 49 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A value changes from 149 to 38. 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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12. 12.

    A body starts at 20 m/s and accelerates at 2.3 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    An object has mass 399.5 g and volume 47 cm³. Find its density.

    Formula:Density

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

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14. 14.

    Solve for x: 2x + 1 = 7.

    Formula:Solving a Linear Equation

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

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15. 15.

    A wave has frequency 685 Hz and wavelength 3.48 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A right-angled triangle has legs of 11 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    A force of 112 N moves an object 19 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 force needed to accelerate a 23 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Solve for x: 3x + 13 = 40.

    Formula:Solving a Linear Equation

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

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20. 20.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 12 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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