United States · Grade 12 · Practice Sheet 7

1. 1.

   A body starts at 19 m/s and accelerates at 4.4 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Find the force needed to accelerate a 8 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the population standard deviation of: 14, 12, 2, 18, 15 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Solve using the quadratic formula: x² + 3x + 2 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the momentum of a 51 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A wave has frequency 432 Hz and wavelength 1.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the population standard deviation of: 11, 20, 15, 19, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A current of 2.8 A flows through a 35 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 + 0x − 25 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    $700 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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11. 11.

    A device runs at 182 V drawing 5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the momentum of a 44 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the population standard deviation of: 5, 4, 7, 8, 3 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A current of 7.6 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    An object with initial velocity 12 m/s accelerates at 4.9 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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17. 17.

    Find the momentum of a 48 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 62 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the sum of the first 11 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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20. 20.

    Find the sum of the first 3 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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