Poland · Klasa 12 · Practice Sheet 37

1. 1.

   An object with initial velocity 7 m/s accelerates at 4 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   In a triangle, a = 15, b = 16 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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3. 3.

   Two masses 1,100 kg and 660 kg are 4 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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4. 4.

   zł 800 is invested at 5% compound interest per annum for 5 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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5. 5.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A 11 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   A force of 291 N acts on an area of 6.4 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A body starts at 5 m/s and accelerates at 2.3 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A body starts at 6 m/s and accelerates at 5.1 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A population of 4,400 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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12. 12.

    A triangle has sides a = 8 cm and b = 14 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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13. 13.

    In a triangle, a = 17, b = 13 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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14. 14.

    Find the gravitational potential energy of a 5 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Two masses 7,900 kg and 830 kg are 4 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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16. 16.

    A force of 439 N acts on an area of 5.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 22 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    In a triangle, a = 9, b = 15 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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19. 19.

    Two masses 3,400 kg and 630 kg are 13 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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20. 20.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 7 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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