Peru · Grado 12 · Practice Sheet 32

1. 1.

   In a triangle, a = 15, b = 13 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   Find the gravitational potential energy of a 45 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A current of 0.8 A flows through a 14 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the population standard deviation of: 10, 18, 6, 11, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A force of 184 N acts on an area of 5.1 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A triangle has sides a = 11 cm and b = 6 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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7. 7.

   An object with initial velocity 11 m/s accelerates at 1.2 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   A triangle has sides a = 7 cm and b = 19 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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9. 9.

   Two masses 8,900 kg and 760 kg are 14 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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10. 10.

    A cone has base radius 3 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the momentum of a 13 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    In a triangle, a = 9, b = 18 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    An object with initial velocity 14 m/s accelerates at 2.5 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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14. 14.

    Find the force needed to accelerate a 26 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A wave has frequency 733 Hz and wavelength 0.59 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve using the quadratic formula: x² + 7x + 10 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    Find the force needed to accelerate a 31 kg mass at 1.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A body starts at 16 m/s and accelerates at 2.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Two masses 8,000 kg and 430 kg are 19 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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20. 20.

    A population of 8,600 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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