Hong Kong · Grade 10 · Practice Sheet 37

1. 1.

   A cylinder has radius 2 cm and height 5 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 68 N acts on an area of 1 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A device runs at 198 V drawing 8.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A force of 173 N acts on an area of 9 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A triangle has sides a = 20 cm and b = 12 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 wave has frequency 209 Hz and wavelength 0.48 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the force needed to accelerate a 18 kg mass at 8.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Solve for x: 7x + 16 = 72.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   HK$ 600 is invested at 6% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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10. 10.

    A current of 3.8 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Solve for x: 5x + 11 = 56.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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12. 12.

    A value changes from 39 to 79. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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13. 13.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A current of 4.9 A flows through a 30 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A cylinder has radius 8 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    In a triangle, a = 8, b = 14 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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17. 17.

    A force of 90 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Find the gravitational potential energy of a 42 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A current of 5.2 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A triangle has sides a = 13 cm and b = 19 cm with an included angle C = 60°. 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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