Czechia · Grade 10 · Practice Sheet 8

1. 1.

   A bag has 26 equally likely marbles, of which 17 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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2. 2.

   A wave has frequency 420 Hz and wavelength 4.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 6 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   A value changes from 146 to 131. 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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5. 5.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 11 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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6. 6.

   A cone has base radius 2 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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7. 7.

   Kč 2,000 is invested at 8% 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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8. 8.

   A force of 119 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A device runs at 202 V drawing 5.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the momentum of a 27 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    A body starts at 8 m/s and accelerates at 4.6 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 4 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    A triangle has sides a = 12 cm and b = 17 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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14. 14.

    A cylinder has radius 10 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 12 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the force needed to accelerate a 20 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A population of 2,400 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    A 13 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    A value changes from 156 to 165. 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 13 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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