Russia · Grade 10 · Practice Sheet 17

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 10 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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2. 2.

   An object has mass 34.8 g and volume 6 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A force of 109 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   In a triangle, a = 16, b = 11 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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5. 5.

   A wave has frequency 33 Hz and wavelength 1.51 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Find the force needed to accelerate a 58 kg mass at 2.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   ₽1,000 is invested at 8% 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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8. 8.

   A right-angled triangle has legs of 10 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   Find the force needed to accelerate a 58 kg mass at 4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 4 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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11. 11.

    A cone has base radius 4 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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12. 12.

    A force of 357 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A cone has base radius 2 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A force of 124 N acts on an area of 1.3 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    ₽1,000 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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16. 16.

    A force of 55 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the gravitational potential energy of a 7 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A force of 57 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 10 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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