Ukraine · Grade 10 · Practice Sheet 46

1. 1.

   Find the momentum of a 11 kg object moving at 20 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   ₴2,600 is invested at 8% simple interest per year for 4 years. Find the interest earned.

   Formula:Simple Interest

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

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3. 3.

   A triangle has sides a = 20 cm and b = 20 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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4. 4.

   A force of 42 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A bag has 17 equally likely marbles, of which 11 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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6. 6.

   A triangle has sides a = 16 cm and b = 11 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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7. 7.

   A bag has 19 equally likely marbles, of which 15 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.

   A force of 78 N acts on an area of 0.6 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the force needed to accelerate a 51 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A bag has 18 equally likely marbles, of which 17 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.

    A wave has frequency 811 Hz and wavelength 2.65 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A bag has 19 equally likely marbles, of which 15 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 population of 6,200 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A cone has base radius 12 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    An object has mass 325.6 g and volume 37 cm³. Find its density.

    Formula:Density

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

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16. 16.

    A current of 8 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    An object with initial velocity 13 m/s accelerates at 3.4 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A value changes from 86 to 82. 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 12 m/s and accelerates at 4.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A force of 108 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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