Czechia · Grade 10 · Practice Sheet 46

1. 1.

   A cone has base radius 11 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A bag has 12 equally likely marbles, of which 2 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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3. 3.

   An object has mass 77.9 g and volume 41 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Find the force needed to accelerate a 40 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object has mass 52.2 g and volume 9 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the momentum of a 43 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   An object has mass 391 g and volume 46 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A cylinder has radius 3 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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10. 10.

    Kč 900 is invested at 4% compound interest per annum for 4 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.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 11 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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12. 12.

    A body starts at 19 m/s and accelerates at 3.7 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the gravitational potential energy of a 16 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A bag has 11 equally likely marbles, of which 1 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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15. 15.

    A right-angled triangle has legs of 18 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A wave has frequency 538 Hz and wavelength 0.32 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Solve for x: 2x + 17 = 39.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 2 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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19. 19.

    An object with initial velocity 6 m/s accelerates at 4.6 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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20. 20.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 5 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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