Vietnam · Grade 10 · Practice Sheet 27

1. 1.

   Solve for x: 3x + 7 = 25.

   Formula:Solving a Linear Equation

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

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2. 2.

   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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3. 3.

   A value changes from 51 to 222. 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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4. 4.

   VND 2,400 is invested at 6% compound interest per annum for 3 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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5. 5.

   A cone has base radius 3 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A wave has frequency 764 Hz and wavelength 0.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the force needed to accelerate a 47 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A population of 7,600 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A force of 104 N acts on an area of 0.8 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A force of 24 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A current of 5.9 A flows through a 46 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A force of 130 N acts on an area of 3.7 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A cone has base radius 8 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A value changes from 30 to 37. 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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15. 15.

    A body starts at 4 m/s and accelerates at 2.7 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the force needed to accelerate a 38 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Solve for x: 9x + 17 = 53.

    Formula:Solving a Linear Equation

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

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18. 18.

    A value changes from 112 to 211. 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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19. 19.

    In a triangle, a = 14, b = 8 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    Find the gravitational potential energy of a 40 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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