Romania · Grade 12 · Practice Sheet 5

1. 1.

   A body starts at 20 m/s and accelerates at 2.9 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   A device runs at 161 V drawing 9.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Solve using the quadratic formula: x² − 2x − 8 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A triangle has sides a = 11 cm and b = 6 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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5. 5.

   Find the force needed to accelerate a 14 kg mass at 6.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A cone has base radius 6 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A population of 4,800 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 77 N moves an object 4 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Two masses 4,900 kg and 730 kg are 18 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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10. 10.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 1 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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12. 12.

    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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13. 13.

    A force of 57 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A 14 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    A wave has frequency 205 Hz and wavelength 3.39 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A triangle has sides a = 14 cm and b = 8 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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17. 17.

    In a triangle, a = 7, b = 17 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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18. 18.

    Find the force needed to accelerate a 12 kg mass at 1.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    In a triangle, a = 18, b = 15 and the included angle C = 50°. 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.

    A body starts at 5 m/s and accelerates at 1 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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