Hong Kong · Grade 10 · Practice Sheet 25

1. 1.

   A right-angled triangle has legs of 17 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A population of 7,900 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Solve for x: 5x + 20 = 65.

   Formula:Solving a Linear Equation

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

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4. 4.

   A triangle has sides a = 9 cm and b = 11 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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5. 5.

   A current of 3.9 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A wave has frequency 725 Hz and wavelength 0.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   An object has mass 67.5 g and volume 27 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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8. 8.

   Find the momentum of a 14 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A cylinder has radius 9 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Solve for x: 8x + 11 = 75.

    Formula:Solving a Linear Equation

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

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11. 11.

    A wave has frequency 480 Hz and wavelength 4.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 4 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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13. 13.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A population of 6,300 grows 8% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A 6 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A cylinder has radius 6 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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18. 18.

    A cone has base radius 3 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A wave has frequency 435 Hz and wavelength 0.43 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the momentum of a 18 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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