Qatar · Grade 12 · Practice Sheet 30

1. 1.

   In a triangle, a = 16, b = 10 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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2. 2.

   A wave has frequency 855 Hz and wavelength 3.11 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A force of 417 N acts on an area of 5.3 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   QAR 2,400 is invested at 4% 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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5. 5.

   A device runs at 49 V drawing 4.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   An object with initial velocity 7 m/s accelerates at 4 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   A wave has frequency 531 Hz and wavelength 2.17 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   In a triangle, a = 7, b = 6 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Two masses 4,000 kg and 550 kg are 10 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 force of 269 N acts on an area of 1.4 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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12. 12.

    Find the population standard deviation of: 7, 10, 8, 15, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A force of 114 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A population of 3,400 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A body starts at 1 m/s and accelerates at 3.4 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A population of 4,400 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    Find the sum of the first 6 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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18. 18.

    A force of 57 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A current of 1 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A wave has frequency 603 Hz and wavelength 4.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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