Algeria · Grade 12 · Practice Sheet 24

1. 1.

   A force of 10 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Solve using the quadratic formula: x² − 2x − 8 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   DA 2,200 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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4. 4.

   Find the gravitational potential energy of a 20 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 216 V drawing 1.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Two masses 6,700 kg and 410 kg are 15 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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7. 7.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 6 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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8. 8.

   A current of 6.4 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   A wave has frequency 632 Hz and wavelength 1.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A device runs at 81 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A wave has frequency 182 Hz and wavelength 1.36 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A force of 73 N moves an object 26 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A cone has base radius 8 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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14. 14.

    A wave has frequency 857 Hz and wavelength 2.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the force needed to accelerate a 26 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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17. 17.

    A wave has frequency 612 Hz and wavelength 4.35 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    In a triangle, a = 5, b = 8 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A population of 1,600 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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