Singapore · Grade 12 · Practice Sheet 1

1. 1.

   Find the force needed to accelerate a 56 kg mass at 7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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3. 3.

   A wave has frequency 133 Hz and wavelength 2.52 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A triangle has sides a = 19 cm and b = 13 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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5. 5.

   $3,500 is invested at 4% compound interest per annum for 5 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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6. 6.

   Find the gravitational potential energy of a 5 kg object raised 12 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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8. 8.

   A force of 352 N acts on an area of 8.6 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A current of 1 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A force of 203 N acts on an area of 1.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    In a triangle, a = 12, b = 15 and the included angle C = 80°. 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.

    A 37 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A wave has frequency 617 Hz and wavelength 3.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A device runs at 140 V drawing 8.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A triangle has sides a = 14 cm and b = 8 cm with an included angle C = 90°. 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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16. 16.

    In a triangle, a = 13, b = 8 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.

    Two masses 4,200 kg and 360 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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18. 18.

    An object with initial velocity 5 m/s accelerates at 1.3 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    A force of 23 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the population standard deviation of: 19, 17, 4, 10, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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