Egypt · Grade 12 · Practice Sheet 47

1. 1.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 4 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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2. 2.

   A force of 362 N acts on an area of 9.8 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   In a triangle, a = 15, b = 16 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A body starts at 17 m/s and accelerates at 2.9 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Find the momentum of a 33 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A 31 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   Find the force needed to accelerate a 28 kg mass at 2.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A force of 56 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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9. 9.

   A current of 2.9 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Solve using the quadratic formula: x² − 8x + 15 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    Two masses 5,700 kg and 420 kg are 14 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.

    Find the population standard deviation of: 6, 7, 16, 15, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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13. 13.

    Find the force needed to accelerate a 45 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    In a triangle, a = 15, 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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15. 15.

    E£ 3,800 is invested at 3% 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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16. 16.

    A triangle has sides a = 11 cm and b = 13 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.

    A 6 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    A force of 9 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    E£ 700 is invested at 5% 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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20. 20.

    Find the force needed to accelerate a 21 kg mass at 1.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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