Ukraine · Grade 11 · Practice Sheet 10

1. 1.

   Find the momentum of a 23 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   An object has mass 17 g and volume 17 cm³. Find its density.

   Formula:Density

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

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3. 3.

   An object with initial velocity 14 m/s accelerates at 1.4 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Find the force needed to accelerate a 29 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Solve using the quadratic formula: x² + 4x − 12 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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6. 6.

   A current of 1.4 A flows through a 16 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 8 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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8. 8.

   Find the force needed to accelerate a 9 kg mass at 5.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A triangle has sides a = 13 cm and b = 7 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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10. 10.

    A force of 51 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the gravitational potential energy of a 35 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 94 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A right-angled triangle has legs of 19 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    In a triangle, a = 14, b = 15 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 device runs at 174 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the momentum of a 46 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A cone has base radius 10 cm and height 10 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.

    Find the momentum of a 22 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A population of 3,400 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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20. 20.

    ₴2,800 is invested at 8% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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