Japan · Grade 12 · Practice Sheet 31

1. 1.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 8 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 force of 20 N acts on an area of 2.4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A 38 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A device runs at 167 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A triangle has sides a = 15 cm and b = 6 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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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.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 2 and common difference d = 4.

   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 6.1 A flows through a 50 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Solve using the quadratic formula: x² + 8x + 12 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    Find the population standard deviation of: 20, 8, 5, 9, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the momentum of a 1 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A device runs at 129 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 48 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A wave has frequency 128 Hz and wavelength 2.44 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Two masses 4,700 kg and 240 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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16. 16.

    A population of 7,600 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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17. 17.

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

    Formula:Quadratic Formula

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

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18. 18.

    ¥1,200 is invested at 8% compound interest per annum for 4 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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19. 19.

    Find the force needed to accelerate a 26 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the population standard deviation of: 12, 15, 20, 19, 13 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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