Hong Kong · Grade 10 · Practice Sheet 38

1. 1.

   A population of 1,200 grows 8% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   Find the gravitational potential energy of a 48 kg object raised 5 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A population of 2,800 grows 2% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   An object with initial velocity 3 m/s accelerates at 3.9 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A force of 77 N acts on an area of 0.7 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A population of 2,100 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   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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8. 8.

   An object with initial velocity 8 m/s accelerates at 4.3 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   Find the force needed to accelerate a 25 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A wave has frequency 217 Hz and wavelength 4.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 4 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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12. 12.

    HK$ 2,200 is invested at 8% compound interest per annum for 2 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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13. 13.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Solve using the quadratic formula: x² + 2x − 8 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    In a triangle, a = 17, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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16. 16.

    A body starts at 1 m/s and accelerates at 1.9 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A current of 6.3 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the momentum of a 7 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    An object has mass 142.1 g and volume 49 cm³. Find its density.

    Formula:Density

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

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20. 20.

    Find the gravitational potential energy of a 26 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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