Czechia · Grade 11 · Practice Sheet 8

1. 1.

   A right-angled triangle has legs of 10 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   In a triangle, a = 13, b = 6 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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3. 3.

   A body starts at 9 m/s and accelerates at 4.1 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   An object has mass 212.8 g and volume 28 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A 27 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   Find the force needed to accelerate a 34 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A population of 1,800 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A force of 165 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the force needed to accelerate a 47 kg mass at 6.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 378 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A 18 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A population of 1,100 grows 5% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 28 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A body starts at 15 m/s and accelerates at 5.8 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A wave has frequency 95 Hz and wavelength 1.04 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Kč 1,300 is invested at 8% 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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17. 17.

    In a triangle, a = 7, b = 9 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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18. 18.

    A population of 4,900 grows 2% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    Find the force needed to accelerate a 21 kg mass at 4.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 25 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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