Mexico · Grado 10 · Practice Sheet 24

1. 1.

   A force of 148 N acts on an area of 9.4 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A right-angled triangle has legs of 17 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the force needed to accelerate a 44 kg mass at 2.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A cone has base radius 9 cm and height 18 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 momentum of a 23 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   An object has mass 220.4 g and volume 38 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A cylinder has radius 2 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   A population of 4,000 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A device runs at 136 V drawing 4.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A triangle has sides a = 18 cm and b = 20 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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11. 11.

    A 8 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    An object with initial velocity 0 m/s accelerates at 2.3 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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13. 13.

    Find the force needed to accelerate a 44 kg mass at 3.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    $2,000 is invested at 8% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    Solve for x: 8x + 8 = 104.

    Formula:Solving a Linear Equation

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

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16. 16.

    A cylinder has radius 11 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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17. 17.

    A triangle has sides a = 12 cm and b = 10 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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18. 18.

    Find the force needed to accelerate a 34 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A value changes from 60 to 128. 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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20. 20.

    Find the momentum of a 54 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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