Singapore · Grade 11 · Practice Sheet 40

1. 1.

   Find the force needed to accelerate a 37 kg mass at 6.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A 25 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Two masses 3,800 kg and 540 kg are 5 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.

   A cone has base radius 12 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   A wave has frequency 663 Hz and wavelength 4.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Two masses 5,800 kg and 530 kg are 16 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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7. 7.

   A triangle has sides a = 15 cm and b = 19 cm with an included angle C = 45°. 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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8. 8.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 10 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   Find the population standard deviation of: 15, 20, 10, 17, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A body starts at 8 m/s and accelerates at 5.5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the force needed to accelerate a 46 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 1 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    A force of 103 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A current of 7.6 A flows through a 33 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A body starts at 13 m/s and accelerates at 3.6 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A triangle has sides a = 18 cm and b = 15 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 cone has base radius 12 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A body starts at 3 m/s and accelerates at 5.6 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A device runs at 30 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A right-angled triangle has legs of 4 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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