Jordan · Grade 12 · Practice Sheet 2

1. 1.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 8 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A 7 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Two masses 7,000 kg and 860 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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4. 4.

   Find the gravitational potential energy of a 28 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A 28 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A body starts at 2 m/s and accelerates at 2.8 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Two masses 7,000 kg and 390 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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8. 8.

   A wave has frequency 485 Hz and wavelength 1.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the force needed to accelerate a 10 kg mass at 5.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A wave has frequency 859 Hz and wavelength 1.28 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    JD 600 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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12. 12.

    In a triangle, a = 16, b = 10 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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13. 13.

    A force of 142 N acts on an area of 8.5 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    Find the population standard deviation of: 4, 17, 7, 6, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A body starts at 19 m/s and accelerates at 3.3 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Solve using the quadratic formula: x² + 6x + 5 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    A force of 21 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A force of 270 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 267 Hz and wavelength 0.22 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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