Taiwan · Grade 11 · Practice Sheet 38

1. 1.

   Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A 4 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A device runs at 85 V drawing 7.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the force needed to accelerate a 3 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A body starts at 14 m/s and accelerates at 4.1 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   An object with initial velocity 9 m/s accelerates at 2.6 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A cylinder has radius 11 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Two masses 7,200 kg and 370 kg are 4 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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9. 9.

   A force of 60 N acts on an area of 1.3 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A current of 5.5 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A device runs at 66 V drawing 1.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A 20 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A force of 5 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    In a triangle, a = 8, 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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15. 15.

    A body starts at 15 m/s and accelerates at 1.5 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    An object has mass 330 g and volume 50 cm³. Find its density.

    Formula:Density

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

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17. 17.

    NT$ 2,100 is invested at 6% compound interest per annum for 2 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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18. 18.

    A device runs at 115 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A current of 3.4 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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