Switzerland · Grade 12 · Practice Sheet 32

1. 1.

   Find the momentum of a 56 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   CHF 4,000 is invested at 3% 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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3. 3.

   Two masses 2,200 kg and 840 kg are 18 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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4. 4.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 2 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A force of 33 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A wave has frequency 238 Hz and wavelength 0.52 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A population of 3,600 grows 2% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A cone has base radius 8 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    In a triangle, a = 12, b = 9 and the included angle C = 40°. 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.

    Two masses 3,500 kg and 480 kg are 12 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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12. 12.

    A wave has frequency 216 Hz and wavelength 3.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A triangle has sides a = 8 cm and b = 5 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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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 4 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A wave has frequency 591 Hz and wavelength 2.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A device runs at 216 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A current of 0.7 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the population standard deviation of: 17, 18, 20, 16, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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19. 19.

    Find the force needed to accelerate a 26 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A population of 7,900 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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