China · Grade 11 · Practice Sheet 16

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   Find the force needed to accelerate a 28 kg mass at 8.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A device runs at 113 V drawing 1.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A wave has frequency 237 Hz and wavelength 1.7 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 3 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   A body starts at 11 m/s and accelerates at 3.2 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A device runs at 25 V drawing 3.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the force needed to accelerate a 41 kg mass at 2.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A right-angled triangle has legs of 10 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    Two masses 5,000 kg and 870 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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11. 11.

    A right-angled triangle has legs of 19 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 1 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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13. 13.

    A current of 4.9 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A 38 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the sum of the first 5 terms of a geometric series with first term a = 8 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A triangle has sides a = 16 cm and b = 14 cm with an included angle C = 30°. 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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17. 17.

    A population of 3,700 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    ¥600 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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19. 19.

    Find the force needed to accelerate a 22 kg mass at 8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A device runs at 203 V drawing 9.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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