Vietnam · Grade 10 · Practice Sheet 7

1. 1.

   A wave has frequency 365 Hz and wavelength 2.69 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 9 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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3. 3.

   A population of 5,500 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A wave has frequency 631 Hz and wavelength 0.53 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Solve using the quadratic formula: x² − 3x − 18 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 5 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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7. 7.

   A value changes from 48 to 218. 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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8. 8.

   Solve for x: 6x + 18 = 42.

   Formula:Solving a Linear Equation

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

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9. 9.

   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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10. 10.

    Solve for x: 5x + 7 = 62.

    Formula:Solving a Linear Equation

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

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11. 11.

    In a triangle, a = 5, b = 5 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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12. 12.

    Find the force needed to accelerate a 46 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A triangle has sides a = 7 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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14. 14.

    VND 600 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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15. 15.

    A 34 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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16. 16.

    A force of 36 N acts on an area of 8.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A current of 4.6 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the momentum of a 9 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the force needed to accelerate a 12 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 36 N moves an object 11 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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