Czechia · Grade 12 · Practice Sheet 25

1. 1.

   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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2. 2.

   A device runs at 127 V drawing 0.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A wave has frequency 281 Hz and wavelength 2.77 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 9 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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5. 5.

   A population of 8,700 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   In a triangle, a = 13, b = 17 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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7. 7.

   Find the force needed to accelerate a 45 kg mass at 4.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A triangle has sides a = 14 cm and b = 14 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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9. 9.

   Find the force needed to accelerate a 37 kg mass at 2.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Kč 3,700 is invested at 4% 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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11. 11.

    Find the momentum of a 59 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A wave has frequency 154 Hz and wavelength 0.62 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Solve using the quadratic formula: x² − 4x + 3 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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14. 14.

    Two masses 4,300 kg and 730 kg are 20 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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15. 15.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A cone has base radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    In a triangle, a = 13, b = 11 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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18. 18.

    Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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19. 19.

    A triangle has sides a = 9 cm and b = 14 cm with an included angle C = 90°. 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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20. 20.

    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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