Mongolia · Grade 10 · Practice Sheet 38

1. 1.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 7 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   ₮2,000 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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3. 3.

   A force of 450 N acts on an area of 3 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A cone has base radius 7 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 8 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.

   In a triangle, a = 18, b = 15 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A wave has frequency 484 Hz and wavelength 2.94 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the force needed to accelerate a 28 kg mass at 4.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A wave has frequency 335 Hz and wavelength 2.37 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 10 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A value changes from 114 to 185. 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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13. 13.

    Find the momentum of a 4 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A wave has frequency 365 Hz and wavelength 2.81 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 2 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A bag has 23 equally likely marbles, of which 8 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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17. 17.

    A wave has frequency 474 Hz and wavelength 3.8 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the gravitational potential energy of a 26 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A wave has frequency 586 Hz and wavelength 0.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    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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