Germany · Klasse 10 · Practice Sheet 23

1. 1.

   A wave has frequency 681 Hz and wavelength 1.3 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 10 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A population of 8,500 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Find the force needed to accelerate a 28 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Solve using the quadratic formula: x² + 0x − 9 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   €900 is invested at 6% compound interest per annum for 3 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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7. 7.

   A force of 9 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A cone has base radius 4 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   An object with initial velocity 4 m/s accelerates at 4.3 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    A right-angled triangle has legs of 3 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A 19 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A wave has frequency 660 Hz and wavelength 3.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Solve for x: 9x + 7 = 115.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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14. 14.

    A population of 9,000 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A wave has frequency 638 Hz and wavelength 2.76 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Find the force needed to accelerate a 47 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cylinder has radius 6 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    Solve for x: 6x + 12 = 24.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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19. 19.

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

    Formula:Quadratic Formula

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

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20. 20.

    A 13 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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