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videos gratefully source from Infinity+One (full playlist here)
1a. Equations of straight lines
1a. Equations of straight lines
you can either use:
y = mx +c
or y - y1 = m(x-x1)
1b. Parallel lines
1b. Parallel lines
For parallel lines, the gradient remains the same but the y-intercept changes.
You can use either y=mx+c or y - y1 = m(x-x1)
2. Expanding Brackets
2. Expanding Brackets
Single brackets
Quadratics
Square Brackets
3a. Quadratics - Factorising by hand
3a. Quadratics - Factorising by hand
Khan Academy - factorsing quadratics
JED Maths - factorsing quadratics
3b. Quadratics - Solving
3b. Quadratics - Solving
Graphics Calculator to solve
Quadratic Formula to solve
4. Solving intersecting points of a line and parabola/circle
4. Solving intersecting points of a line and parabola/circle
Now we are ready to start solving intersection points between curves and straight lines.
Whenever a circle, parabola, or hyperbola come into contact with a straght line, you will need to solve a quadratic to find the points of interesection. It is a good idea to use the discriminant to find how many solutions exist before you try to find solutions.
How to find the discrimiant
Intersection points of a parabola nad line
Another line and circle example.
5. Lines and Hyperbolas
5. Lines and Hyperbolas
Example with two solutions
y=2/(x-1) and y = 2x+1
6. Aiming for Excellence - Finding different "k" values
6. Aiming for Excellence - Finding different "k" values
If you're aiming for excellence, you generally need to find an unknown that satisifes one or more conditions.
It could look somthing like:
take two curves: y = x + k and y = x^2
What value(s) of k give only one solution?
7. Bonus - the golden ratio
7. Bonus - the golden ratio
The golden ration can be found such that φ - 1 = 1/φ which gives the result that φ≈1.618. This magical number appears all over nature. Try and solve the above to determine the golden ratio (hint: you'll need to use the quadratic formula.)
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