Czechia · Grade 10 · Practice Sheet 14

1. 1.

   A right-angled triangle has legs of 11 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   An object has mass 109.2 g and volume 14 cm³. Find its density.

   Formula:Density

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

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3. 3.

   An object with initial velocity 12 m/s accelerates at 2.3 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   Find the force needed to accelerate a 15 kg mass at 7.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A population of 7,300 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Kč 500 is invested at 7.5% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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7. 7.

   A cone has base radius 3 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   In a triangle, a = 10, b = 5 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   A force of 100 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the force needed to accelerate a 50 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A right-angled triangle has legs of 16 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A cylinder has radius 13 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A current of 6 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the force needed to accelerate a 41 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 19 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A device runs at 122 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A 13 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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18. 18.

    An object has mass 214.5 g and volume 39 cm³. Find its density.

    Formula:Density

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

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19. 19.

    A value changes from 101 to 130. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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20. 20.

    A wave has frequency 177 Hz and wavelength 0.29 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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