Sweden · Grade 10 · Practice Sheet 9

1. 1.

   A wave has frequency 577 Hz and wavelength 2.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   In a triangle, a = 15, b = 5 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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3. 3.

   Solve for x: 4x + 3 = 27.

   Formula:Solving a Linear Equation

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

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4. 4.

   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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5. 5.

   An object with initial velocity 1 m/s accelerates at 4.2 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A force of 278 N acts on an area of 2.7 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   kr 2,800 is invested at 10% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   A triangle has sides a = 7 cm and b = 6 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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9. 9.

   In a triangle, a = 12, b = 13 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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10. 10.

    Find the force needed to accelerate a 49 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    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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12. 12.

    A body starts at 14 m/s and accelerates at 5.1 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A cone has base radius 3 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    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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15. 15.

    A force of 81 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A 3 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Find the momentum of a 25 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    An object has mass 411.6 g and volume 49 cm³. Find its density.

    Formula:Density

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

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19. 19.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    Find the gravitational potential energy of a 10 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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