Poland · Klasa 10 · Practice Sheet 2

1. 1.

   Find the force needed to accelerate a 26 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Solve for x: 3x + 4 = 10.

   Formula:Solving a Linear Equation

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

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3. 3.

   A triangle has sides a = 13 cm and b = 20 cm with an included angle C = 30°. 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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4. 4.

   An object with initial velocity 12 m/s accelerates at 4 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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5. 5.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 8 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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6. 6.

   Find the force needed to accelerate a 60 kg mass at 5.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   An object with initial velocity 13 m/s accelerates at 2.5 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A force of 92 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A force of 243 N acts on an area of 8.5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A population of 1,900 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    A value changes from 106 to 163. 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.

    Solve for x: 4x + 4 = 48.

    Formula:Solving a Linear Equation

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

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14. 14.

    zł 2,300 is invested at 8% compound interest per annum for 4 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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15. 15.

    A device runs at 41 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the momentum of a 43 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A cone has base radius 8 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A triangle has sides a = 8 cm and b = 19 cm with an included angle C = 45°. 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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19. 19.

    zł 3,300 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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20. 20.

    A cylinder has radius 13 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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