Jordan · Grade 12 · Practice Sheet 38

1. 1.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 9 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A wave has frequency 724 Hz and wavelength 2.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Two masses 8,600 kg and 330 kg are 9 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.

   A device runs at 98 V drawing 5.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A body starts at 15 m/s and accelerates at 2.8 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   Find the force needed to accelerate a 15 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 26 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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8. 8.

   In a triangle, a = 7, b = 9 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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9. 9.

   Find the force needed to accelerate a 47 kg mass at 1.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    JD 700 is invested at 4% 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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11. 11.

    A force of 460 N acts on an area of 3.1 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A population of 2,500 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A force of 288 N acts on an area of 3.8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A force of 7 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Find the sum of the first 4 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A device runs at 223 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 41 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A 32 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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19. 19.

    Find the gravitational potential energy of a 7 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    In a triangle, a = 11, b = 11 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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