Finland · Grade 11 · Practice Sheet 42

1. 1.

   Find the force needed to accelerate a 17 kg mass at 1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A device runs at 37 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A body starts at 17 m/s and accelerates at 5.7 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   An object has mass 8 g and volume 5 cm³. Find its density.

   Formula:Density

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

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5. 5.

   Find the population standard deviation of: 19, 3, 9, 18, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   A force of 108 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A population of 5,600 grows 10% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A right-angled triangle has legs of 15 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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9. 9.

   A wave has frequency 672 Hz and wavelength 3.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A cone has base radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    An object has mass 100.8 g and volume 48 cm³. Find its density.

    Formula:Density

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

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12. 12.

    Solve using the quadratic formula: x² + 2x − 15 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the gravitational potential energy of a 23 kg object raised 12 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A device runs at 219 V drawing 8.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A wave has frequency 419 Hz and wavelength 3.74 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    In a triangle, a = 5, b = 6 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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18. 18.

    Solve using the quadratic formula: x² − 1x − 20 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 2 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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20. 20.

    A 18 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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