Vietnam · Grade 11 · Practice Sheet 41

1. 1.

   Two masses 6,900 kg and 280 kg are 9 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.

   An object has mass 23.1 g and volume 11 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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4. 4.

   VND 1,400 is invested at 3% 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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5. 5.

   A force of 35 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   An object has mass 120.4 g and volume 43 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A cone has base radius 7 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A population of 8,500 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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9. 9.

   Find the force needed to accelerate a 44 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 82 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A force of 48 N acts on an area of 8.2 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A wave has frequency 851 Hz and wavelength 1.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    An object has mass 285.6 g and volume 42 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A cone has base radius 7 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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15. 15.

    A population of 8,200 grows 2% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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16. 16.

    A body starts at 15 m/s and accelerates at 3.2 m/s² for 11 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 − 5x + 6 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A triangle has sides a = 6 cm and b = 16 cm with an included angle C = 45°. 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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19. 19.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 11 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    In a triangle, a = 13, 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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