Ecuador · Grado 10 · Practice Sheet 39

1. 1.

   A wave has frequency 445 Hz and wavelength 4.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A population of 4,400 grows 10% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A current of 5.4 A flows through a 24 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A device runs at 135 V drawing 8.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the force needed to accelerate a 49 kg mass at 8.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A triangle has sides a = 14 cm and b = 19 cm with an included angle C = 30°. 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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7. 7.

   Find the momentum of a 24 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A cylinder has radius 7 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A right-angled triangle has legs of 7 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A triangle has sides a = 16 cm and b = 20 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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12. 12.

    A force of 228 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A body starts at 17 m/s and accelerates at 2.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    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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15. 15.

    Find the gravitational potential energy of a 8 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A force of 127 N acts on an area of 2.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A triangle has sides a = 5 cm and b = 12 cm with an included angle C = 30°. 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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18. 18.

    A population of 4,500 grows 10% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    In a triangle, a = 9, b = 5 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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20. 20.

    Find the gravitational potential energy of a 20 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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