Japan · Grade 11 · Practice Sheet 33

1. 1.

   A cylinder has radius 9 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A force of 229 N acts on an area of 3.7 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A force of 54 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the momentum of a 31 kg object moving at 10 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   A triangle has sides a = 14 cm and b = 13 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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6. 6.

   A current of 1.7 A flows through a 21 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   In a triangle, a = 8, b = 5 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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8. 8.

   A triangle has sides a = 10 cm and b = 20 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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9. 9.

   A population of 2,100 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A force of 142 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A wave has frequency 464 Hz and wavelength 4.64 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A right-angled triangle has legs of 12 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A 30 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    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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15. 15.

    Find the force needed to accelerate a 19 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Two masses 7,300 kg and 250 kg are 6 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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17. 17.

    Find the force needed to accelerate a 11 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the population standard deviation of: 14, 11, 16, 11, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A force of 231 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A cylinder has radius 4 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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