South Korea · Grade 11 · Practice Sheet 24

1. 1.

   Two masses 3,400 kg and 400 kg are 7 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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2. 2.

   ₩2,700 is invested at 5% 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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3. 3.

   A right-angled triangle has legs of 17 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   ₩2,700 is invested at 4% 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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5. 5.

   A force of 52 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 171 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   ₩1,900 is invested at 4% 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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8. 8.

   A 24 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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9. 9.

   A triangle has sides a = 15 cm and b = 8 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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10. 10.

    A body starts at 9 m/s and accelerates at 5.6 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A triangle has sides a = 13 cm and b = 20 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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12. 12.

    A cone has base radius 4 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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13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the gravitational potential energy of a 37 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A wave has frequency 346 Hz and wavelength 0.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    An object with initial velocity 8 m/s accelerates at 2.3 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    Find the force needed to accelerate a 11 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    In a triangle, a = 17, b = 18 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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19. 19.

    A cone has base radius 9 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    An object with initial velocity 15 m/s accelerates at 4 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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