Ecuador · Grado 10 · Practice Sheet 47

1. 1.

   A population of 2,600 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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2. 2.

   Solve for x: 4x + 12 = 28.

   Formula:Solving a Linear Equation

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

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3. 3.

   A wave has frequency 461 Hz and wavelength 0.67 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A device runs at 159 V drawing 1.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A force of 102 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   $4,800 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 bag has 14 equally likely marbles, of which 5 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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8. 8.

   A force of 264 N acts on an area of 6.3 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A triangle has sides a = 8 cm and b = 14 cm with an included angle C = 60°. 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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10. 10.

    Solve using the quadratic formula: x² + 11x + 30 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A bag has 28 equally likely marbles, of which 26 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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12. 12.

    Solve for x: 4x + 9 = 33.

    Formula:Solving a Linear Equation

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

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13. 13.

    Solve using the quadratic formula: x² − 1x − 6 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A triangle has sides a = 13 cm and b = 6 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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15. 15.

    A device runs at 112 V drawing 0.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 6 cm and b = 6 cm with an included angle C = 120°. 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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17. 17.

    A force of 243 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A 31 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    Solve for x: 9x + 11 = 101.

    Formula:Solving a Linear Equation

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

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20. 20.

    An object with initial velocity 7 m/s accelerates at 1.5 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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