Peru · Grado 11 · Practice Sheet 18

1. 1.

   A triangle has sides a = 20 cm and b = 14 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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2. 2.

   A force of 459 N acts on an area of 2.3 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Two masses 4,600 kg and 790 kg are 5 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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4. 4.

   A force of 74 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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5. 5.

   Find the population standard deviation of: 19, 16, 18, 13, 7 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   Find the force needed to accelerate a 30 kg mass at 2.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A 25 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   S/ 1,600 is invested at 3% compound interest per annum for 4 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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9. 9.

   A current of 3.4 A flows through a 31 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A right-angled triangle has legs of 5 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the momentum of a 30 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A body starts at 10 m/s and accelerates at 1.3 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    An object has mass 102 g and volume 17 cm³. Find its density.

    Formula:Density

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

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14. 14.

    Find the momentum of a 55 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the sum of the first 3 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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16. 16.

    Find the force needed to accelerate a 21 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cylinder has radius 8 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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18. 18.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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19. 19.

    A wave has frequency 249 Hz and wavelength 0.96 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A current of 5.4 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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