Ukraine · Grade 10 · Practice Sheet 2

1. 1.

   Find the force needed to accelerate a 47 kg mass at 4.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the momentum of a 44 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A device runs at 210 V drawing 4.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the sum of the first 11 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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5. 5.

   A wave has frequency 323 Hz and wavelength 0.46 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A population of 8,600 grows 10% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A value changes from 180 to 44. 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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8. 8.

   Solve for x: 4x + 8 = 52.

   Formula:Solving a Linear Equation

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

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9. 9.

   Solve using the quadratic formula: x² + 7x + 6 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    Find the force needed to accelerate a 60 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    An object has mass 138 g and volume 23 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A 20 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A bag has 27 equally likely marbles, of which 21 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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14. 14.

    A triangle has sides a = 12 cm and b = 12 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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15. 15.

    A cylinder has radius 11 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A cone has base radius 6 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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17. 17.

    A right-angled triangle has legs of 6 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A value changes from 119 to 184. 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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19. 19.

    A current of 7.3 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A wave has frequency 852 Hz and wavelength 0.79 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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