Qatar · Grade 12 · Practice Sheet 27

1. 1.

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

   Formula:Quadratic Formula

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

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2. 2.

   A device runs at 105 V drawing 3.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A force of 226 N acts on an area of 2.5 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A body starts at 9 m/s and accelerates at 4.6 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A cone has base radius 2 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Find the gravitational potential energy of a 47 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the force needed to accelerate a 7 kg mass at 6.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A population of 2,100 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A force of 393 N acts on an area of 9.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    QAR 1,200 is invested at 6% 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 90 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

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

    Formula:Quadratic Formula

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

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13. 13.

    Find the population standard deviation of: 7, 19, 10, 16, 4 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A device runs at 110 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 1 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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16. 16.

    An object with initial velocity 10 m/s accelerates at 2.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A triangle has sides a = 15 cm and b = 19 cm with an included angle C = 90°. 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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18. 18.

    A force of 347 N acts on an area of 0.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 242 Hz and wavelength 4.51 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the force needed to accelerate a 16 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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