South Korea · Grade 11 · Practice Sheet 35

1. 1.

   A wave has frequency 781 Hz and wavelength 1.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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3. 3.

   A force of 153 N acts on an area of 2.8 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 7 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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5. 5.

   Find the sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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6. 6.

   An object has mass 36.4 g and volume 28 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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7. 7.

   Find the force needed to accelerate a 36 kg mass at 4.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   ₩3,400 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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9. 9.

   Two masses 1,100 kg and 850 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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10. 10.

    In a triangle, a = 10, b = 16 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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11. 11.

    A right-angled triangle has legs of 7 cm and 8 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Two masses 6,900 kg and 360 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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13. 13.

    Find the momentum of a 48 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A cylinder has radius 5 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    A force of 71 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    An object has mass 264.6 g and volume 42 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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17. 17.

    A wave has frequency 756 Hz and wavelength 3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 258 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    In a triangle, a = 15, b = 17 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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20. 20.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 4 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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