Mexico · Grado 10 · Practice Sheet 13

1. 1.

   A force of 24 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 2 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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3. 3.

   An object has mass 268 g and volume 40 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A body starts at 11 m/s and accelerates at 3.8 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A population of 5,600 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   $3,400 is invested at 6% 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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7. 7.

   A population of 2,500 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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8. 8.

   An object with initial velocity 3 m/s accelerates at 1.3 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   A cylinder has radius 14 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A force of 122 N acts on an area of 7.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A triangle has sides a = 5 cm and b = 9 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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12. 12.

    Solve for x: 4x + 18 = 34.

    Formula:Solving a Linear Equation

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

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13. 13.

    A current of 1.9 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the force needed to accelerate a 33 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    An object with initial velocity 12 m/s accelerates at 3.4 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    $600 is invested at 5% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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18. 18.

    A cylinder has radius 2 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the gravitational potential energy of a 2 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A body starts at 7 m/s and accelerates at 1.9 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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