Ecuador · Grado 12 · Practice Sheet 3

1. 1.

   A triangle has sides a = 16 cm and b = 10 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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2. 2.

   Find the momentum of a 60 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A body starts at 6 m/s and accelerates at 2.1 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Two masses 9,000 kg and 520 kg are 16 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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5. 5.

   $900 is invested at 4% compound interest per annum for 2 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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6. 6.

   A wave has frequency 598 Hz and wavelength 4.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A device runs at 238 V drawing 7.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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9. 9.

   $1,500 is invested at 8% compound interest per annum for 2 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.

    Find the gravitational potential energy of a 23 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Solve using the quadratic formula: x² + 5x + 6 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    A wave has frequency 826 Hz and wavelength 2.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A cone has base radius 9 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    Find the gravitational potential energy of a 3 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    In a triangle, a = 9, b = 12 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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17. 17.

    A 31 kg object moves at 23 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    An object with initial velocity 13 m/s accelerates at 4 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A force of 5 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A force of 470 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

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