Vietnam · Grade 10 · Practice Sheet 18

1. 1.

   A wave has frequency 462 Hz and wavelength 0.89 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the gravitational potential energy of a 9 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A value changes from 199 to 57. 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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4. 4.

   A device runs at 233 V drawing 7.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   In a triangle, a = 6, b = 17 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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6. 6.

   A body starts at 12 m/s and accelerates at 3.8 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A bag has 21 equally likely marbles, of which 18 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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8. 8.

   Find the force needed to accelerate a 40 kg mass at 5.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A population of 2,700 grows 3% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

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

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Find the momentum of a 13 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Solve for x: 2x + 6 = 14.

    Formula:Solving a Linear Equation

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

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14. 14.

    In a triangle, a = 6, b = 12 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    A force of 199 N acts on an area of 0.6 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the force needed to accelerate a 49 kg mass at 6.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    An object with initial velocity 10 m/s accelerates at 4.4 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    Find the force needed to accelerate a 23 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Solve for x: 6x + 4 = 34.

    Formula:Solving a Linear Equation

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

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20. 20.

    A body starts at 6 m/s and accelerates at 2.5 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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