Hungary · Grade 12 · Practice Sheet 41

1. 1.

   Solve using the quadratic formula: x² + 1x − 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   A current of 2.7 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the force needed to accelerate a 60 kg mass at 8.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Two masses 1,000 kg and 570 kg are 4 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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5. 5.

   Ft 3,400 is invested at 8% compound interest per annum for 5 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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6. 6.

   A wave has frequency 434 Hz and wavelength 2.05 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A device runs at 239 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the sum of the first 7 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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9. 9.

   A force of 93 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    An object with initial velocity 3 m/s accelerates at 4.9 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    Find the gravitational potential energy of a 10 kg object raised 36 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Ft 1,300 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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13. 13.

    Find the momentum of a 10 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A body starts at 19 m/s and accelerates at 1.5 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the population standard deviation of: 15, 16, 15, 14, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the sum of the first 4 terms of a geometric series with first term a = 7 and common ratio r = 2.

    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 328 Hz and wavelength 4.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the gravitational potential energy of a 4 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Two masses 4,000 kg and 120 kg are 13 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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20. 20.

    In a triangle, a = 11, b = 7 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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