Bahrain · Grade 12 · Practice Sheet 29

1. 1.

   A force of 374 N acts on an area of 9.4 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Solve using the quadratic formula: x² + 1x − 12 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   BD 1,000 is invested at 8% compound interest per annum for 2 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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4. 4.

   A 13 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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5. 5.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the force needed to accelerate a 35 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A body starts at 5 m/s and accelerates at 3.5 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A force of 90 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 10 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the sum of the first 7 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    Two masses 8,900 kg and 400 kg are 11 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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12. 12.

    Solve using the quadratic formula: x² − 3x + 2 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A wave has frequency 605 Hz and wavelength 4.48 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    In a triangle, a = 12, b = 18 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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15. 15.

    A force of 52 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A body starts at 5 m/s and accelerates at 5.1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A triangle has sides a = 15 cm and b = 17 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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19. 19.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 9 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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20. 20.

    Two masses 6,300 kg and 730 kg are 12 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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