For 17 years-old young
1st Bimester - ANALYTIC GEOMETRY - The line
- The point A(2, 3) dists Ö5 of a Q point in the bissectrix of the odd quadrants. Obtain the coordinates of Q.
- Achieve the medium point between A(-1, 4) and B(3, 6).
- Obtain the angular coefficient m of the points P(-2, 4) and Q(5, 1) and attain the general equation of the right line that contains these points.
- Knowing the reduced equation y=5x-3, obtain the points of intersection with the axles Ox and Oy.
- Calculate the angular coefficient of the lines with equations 3x-2y+5=0 and 6x-4y-3=0, and find the distance between them.
2nd Bimester - ANALYTIC GEOMETRY - Circles and conics
- Write the reduced equation of the circle that has ray r=3 and center C(2, -1).
- Obtain the center and the ray of the circle of general equation x2+y2-10x+2y+10=0.
- Verify the relative position between the line r:x+2y-3=0 and the circle l:x2+y2+4x-8y+11=0.
- Achieve the equation of the parabole that has focus F(1, 3) and diretrix y-5=0.
- For the ellipse of equation x2/9+y2/16=1, obtain the focus, the focal distance and the excentricity.
3rd Bimester - COMPLEXES NUMBERS
- Solve the equation x2-6x+10=0.
- Obtain the division of the number z1=3-2i by the number z2=1+5i.
- Write the trigonometric form of the number z=2-2Ö3i.
- Compute (1-i)11.
- Obtain the cubic roots of the number i.
4th Bimester - POLYNOMIAL EQUATIONS, STATISTICS AND DERIVED
- Verify, with the Briot-Ruffini algorithm, if P(x)=x4-2x3-x2+x+1 is divisible by d(x)=(x-1)(x+2).
- Solve the equation x4-2x3+5x2-8x+4=0, knowing that the number 2i is one root.
- Obtain the mean and the median of the numbers 1, 3, 5, 7, 8, 9, 10, 13, 16, 18 and 20.
- Achieve the standard deviation of the values of the table (height of children in a classroom).
Height (cm) Frequence
120 - 125 10
125 - 130 18
130 - 135 11
135 - 140 1
- Derive the polynomy P(x)=3x4+2x3-3x2+7x-5.
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