Ukraine · Grade 10 · Practice Sheet 13

1. 1.

   A 21 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A cylinder has radius 12 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   In a triangle, a = 13, b = 6 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A force of 174 N acts on an area of 4.7 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A population of 7,300 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the gravitational potential energy of a 42 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   Find the force needed to accelerate a 44 kg mass at 1.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Solve using the quadratic formula: x² + 5x + 4 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   A cylinder has radius 4 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A device runs at 226 V drawing 2.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the gravitational potential energy of a 11 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 19 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    ₴1,800 is invested at 5% compound interest per annum for 5 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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14. 14.

    A population of 2,600 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 8 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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16. 16.

    A 9 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A body starts at 13 m/s and accelerates at 4.9 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A wave has frequency 528 Hz and wavelength 1.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    A 9 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Solve for x: 6x + 18 = 60.

    Formula:Solving a Linear Equation

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

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