United States · Grade 10 · Practice Sheet 36

1. 1.

   Find the gravitational potential energy of a 42 kg object raised 39 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 8 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A force of 65 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the force needed to accelerate a 23 kg mass at 7.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the momentum of a 34 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   In a triangle, a = 6, b = 13 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A triangle has sides a = 16 cm and b = 18 cm with an included angle C = 90°. 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 right-angled triangle has legs of 16 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   $3,100 is invested at 6% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    A force of 66 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A triangle has sides a = 6 cm and b = 7 cm with an included angle C = 90°. 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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12. 12.

    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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13. 13.

    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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14. 14.

    An object has mass 322 g and volume 46 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A force of 364 N acts on an area of 4.5 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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16. 16.

    A force of 36 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A current of 2.2 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A force of 307 N acts on an area of 7.5 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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19. 19.

    A wave has frequency 535 Hz and wavelength 3.82 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    An object has mass 241.4 g and volume 34 cm³. Find its density.

    Formula:Density

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

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