Poland · Klasa 10 · Practice Sheet 40

1. 1.

   A body starts at 7 m/s and accelerates at 1.1 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 4 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A force of 194 N acts on an area of 5.7 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   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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5. 5.

   A cone has base radius 9 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 momentum of a 53 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   An object with initial velocity 10 m/s accelerates at 1.8 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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8. 8.

   zł 2,300 is invested at 3% compound interest per annum for 5 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.

   A current of 3.1 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    zł 3,900 is invested at 5% 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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11. 11.

    A bag has 24 equally likely marbles, of which 12 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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12. 12.

    A wave has frequency 381 Hz and wavelength 3.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    In a triangle, a = 17, b = 14 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Solve for x: 5x + 17 = 37.

    Formula:Solving a Linear Equation

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

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15. 15.

    In a triangle, a = 6, b = 13 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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16. 16.

    A cylinder has radius 8 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A force of 148 N acts on an area of 3.5 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A wave has frequency 78 Hz and wavelength 4.94 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A 39 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A wave has frequency 244 Hz and wavelength 3.79 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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