Czechia · Grade 10 · Practice Sheet 41

1. 1.

   A wave has frequency 588 Hz and wavelength 1.57 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A bag has 23 equally likely marbles, of which 13 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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3. 3.

   A body starts at 4 m/s and accelerates at 4.6 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   In a triangle, a = 7, b = 13 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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5. 5.

   A current of 2.1 A flows through a 19 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A device runs at 192 V drawing 3.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A current of 5.1 A flows through a 25 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A 34 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A cylinder has radius 5 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A bag has 26 equally likely marbles, of which 25 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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11. 11.

    An object with initial velocity 11 m/s accelerates at 2.4 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A bag has 11 equally likely marbles, of which 1 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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13. 13.

    A cone has base radius 10 cm and height 22 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 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A triangle has sides a = 6 cm and b = 15 cm with an included angle C = 120°. 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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16. 16.

    A wave has frequency 412 Hz and wavelength 3.07 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A cone has base radius 9 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A value changes from 106 to 107. 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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19. 19.

    A body starts at 13 m/s and accelerates at 1.4 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Solve for x: 5x + 3 = 33.

    Formula:Solving a Linear Equation

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

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