Israel · Grade 12 · Practice Sheet 47

1. 1.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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2. 2.

   A wave has frequency 729 Hz and wavelength 4.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A current of 2.1 A flows through a 54 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 4 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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5. 5.

   A population of 3,200 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A cone has base radius 12 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A force of 41 N moves an object 6 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A current of 7.7 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Two masses 4,500 kg and 870 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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10. 10.

    A device runs at 169 V drawing 9.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the population standard deviation of: 6, 11, 19, 18, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A device runs at 215 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A 27 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    Find the momentum of a 13 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the force needed to accelerate a 12 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    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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19. 19.

    ₪3,100 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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20. 20.

    Solve using the quadratic formula: x² − 5x + 4 = 0.

    Formula:Quadratic Formula

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

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