Singapore · Grade 12 · Practice Sheet 20

1. 1.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 4 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Find the momentum of a 36 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Find the gravitational potential energy of a 22 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 31 Hz and wavelength 1.12 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   In a triangle, a = 15, b = 18 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Solve using the quadratic formula: x² + 2x − 24 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A current of 7.2 A flows through a 54 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A triangle has sides a = 20 cm and b = 19 cm with an included angle C = 120°. 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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9. 9.

   In a triangle, a = 15, b = 14 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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10. 10.

    A body starts at 9 m/s and accelerates at 2.4 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A wave has frequency 563 Hz and wavelength 4.68 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A body starts at 1 m/s and accelerates at 4.4 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the force needed to accelerate a 44 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the gravitational potential energy of a 11 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    $3,200 is invested at 3% 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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16. 16.

    In a triangle, a = 9, b = 10 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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17. 17.

    A device runs at 162 V drawing 9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the population standard deviation of: 18, 8, 16, 7, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A body starts at 9 m/s and accelerates at 5.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    An object with initial velocity 4 m/s accelerates at 1.5 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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