Switzerland · Grade 11 · Practice Sheet 45

1. 1.

   Solve using the quadratic formula: x² + 5x + 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the force needed to accelerate a 40 kg mass at 6.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the population standard deviation of: 17, 14, 9, 13, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   Find the force needed to accelerate a 48 kg mass at 7.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the sum of the first 3 terms of a geometric series with first term a = 4 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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6. 6.

   A body starts at 19 m/s and accelerates at 5.6 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   Find the force needed to accelerate a 38 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   CHF 2,900 is invested at 3% 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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9. 9.

   Find the force needed to accelerate a 25 kg mass at 2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the momentum of a 22 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A wave has frequency 139 Hz and wavelength 3.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A triangle has sides a = 20 cm and b = 12 cm with an included angle C = 30°. 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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13. 13.

    CHF 1,400 is invested at 3% 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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14. 14.

    A cylinder has radius 11 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the population standard deviation of: 4, 16, 7, 18, 7 (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 momentum of a 50 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A wave has frequency 410 Hz and wavelength 4.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    An object has mass 57.6 g and volume 32 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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19. 19.

    In a triangle, a = 17, b = 10 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A device runs at 27 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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