Thailand · Grade 12 · Practice Sheet 1

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 8 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.

   A current of 8 A flows through a 45 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the momentum of a 59 kg object moving at 11 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 168 N acts on an area of 6 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A wave has frequency 720 Hz and wavelength 3.94 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   In a triangle, a = 5, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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7. 7.

   A body starts at 17 m/s and accelerates at 5.1 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 2 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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9. 9.

   In a triangle, a = 7, b = 12 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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10. 10.

    A wave has frequency 882 Hz and wavelength 1.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    In a triangle, a = 10, b = 11 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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12. 12.

    Find the momentum of a 44 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the sum of the first 8 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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14. 14.

    ฿800 is invested at 6% 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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15. 15.

    In a triangle, a = 15, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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16. 16.

    A force of 474 N acts on an area of 1.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 10 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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18. 18.

    A device runs at 225 V drawing 8.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

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

    Formula:Volume of a Cone

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

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20. 20.

    A current of 7.5 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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