Mexico · Grado 10 · Practice Sheet 7

1. 1.

   A wave has frequency 31 Hz and wavelength 4.02 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A value changes from 140 to 150. 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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3. 3.

   A force of 137 N acts on an area of 7.2 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A cylinder has radius 5 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   An object with initial velocity 11 m/s accelerates at 3.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A force of 67 N moves an object 22 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   An object has mass 98.8 g and volume 38 cm³. Find its density.

   Formula:Density

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

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8. 8.

   In a triangle, a = 8, b = 17 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   Solve for x: 2x + 8 = 32.

   Formula:Solving a Linear Equation

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

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10. 10.

    Solve using the quadratic formula: x² − 1x − 20 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    An object with initial velocity 11 m/s accelerates at 4.1 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the force needed to accelerate a 11 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    $3,500 is invested at 5% 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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14. 14.

    A body starts at 7 m/s and accelerates at 1.9 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    $4,200 is invested at 3% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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16. 16.

    A current of 3.7 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    In a triangle, a = 13, b = 8 and the included angle C = 110°. 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 19 terms of an arithmetic series with first term a = 3 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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19. 19.

    A force of 23 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A body starts at 1 m/s and accelerates at 1.6 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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