Ukraine · Grade 10 · Practice Sheet 42

1. 1.

   Find the gravitational potential energy of a 25 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A device runs at 216 V drawing 1.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 3 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Solve for x: 3x + 1 = 34.

   Formula:Solving a Linear Equation

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

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5. 5.

   In a triangle, a = 12, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Find the momentum of a 19 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A value changes from 100 to 106. 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.

   Find the gravitational potential energy of a 38 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A current of 6.5 A flows through a 18 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    An object has mass 39.6 g and volume 36 cm³. Find its density.

    Formula:Density

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

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11. 11.

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

    Formula:Volume of a Cone

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

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12. 12.

    A value changes from 127 to 164. 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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13. 13.

    ₴4,300 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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14. 14.

    A value changes from 69 to 256. 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 14 terms of an arithmetic series with first term a = 5 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    An object has mass 123.5 g and volume 19 cm³. Find its density.

    Formula:Density

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

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17. 17.

    A value changes from 82 to 187. 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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18. 18.

    A 19 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A triangle has sides a = 19 cm and b = 19 cm with an included angle C = 120°. 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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20. 20.

    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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