Colombia · Grado 11 · Practice Sheet 5

1. 1.

   A right-angled triangle has legs of 17 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A triangle has sides a = 10 cm and b = 10 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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3. 3.

   Find the momentum of a 52 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A right-angled triangle has legs of 14 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   An object has mass 113.4 g and volume 14 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A force of 471 N acts on an area of 7.5 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A 36 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Find the momentum of a 59 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the population standard deviation of: 11, 6, 11, 20, 5 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A current of 7.7 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the momentum of a 3 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A current of 3.6 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A population of 1,800 grows 5% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    An object has mass 110.7 g and volume 41 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A body starts at 19 m/s and accelerates at 4 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the force needed to accelerate a 44 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A 15 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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18. 18.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the force needed to accelerate a 55 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the gravitational potential energy of a 35 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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