South Korea · Grade 12 · Practice Sheet 6

1. 1.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   In a triangle, a = 8, b = 6 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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3. 3.

   Find the force needed to accelerate a 35 kg mass at 4.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the population standard deviation of: 19, 20, 7, 12, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   In a triangle, a = 7, b = 9 and the included angle C = 60°. 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.

   A wave has frequency 296 Hz and wavelength 2.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A device runs at 226 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A wave has frequency 829 Hz and wavelength 2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   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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10. 10.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    Find the force needed to accelerate a 51 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A 30 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    Two masses 5,500 kg and 290 kg are 2 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 force of 177 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the momentum of a 18 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A body starts at 15 m/s and accelerates at 1.4 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Solve using the quadratic formula: x² + 3x − 18 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    ₩3,500 is invested at 5% compound interest per annum for 5 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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19. 19.

    A wave has frequency 748 Hz and wavelength 0.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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