Ecuador · Grado 12 · Practice Sheet 1

1. 1.

   $1,800 is invested at 8% 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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2. 2.

   Find the population standard deviation of: 4, 16, 5, 7, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   $3,100 is invested at 3% 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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4. 4.

   A wave has frequency 220 Hz and wavelength 1.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   In a triangle, a = 5, b = 10 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Solve using the quadratic formula: x² − 1x − 30 = 0.

   Formula:Quadratic Formula

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

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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 gravitational potential energy of a 32 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the momentum of a 2 kg object moving at 8 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A force of 474 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A wave has frequency 764 Hz and wavelength 1.9 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the gravitational potential energy of a 29 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Two masses 4,000 kg and 260 kg are 15 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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14. 14.

    A 7 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A wave has frequency 451 Hz and wavelength 1.56 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    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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17. 17.

    A cone has base radius 11 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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18. 18.

    A wave has frequency 112 Hz and wavelength 4.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A force of 85 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A wave has frequency 378 Hz and wavelength 2.19 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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