C1 C2 M1 Revision
Core 1
Linear Graphs and Equations
For any straight line, the gradient (M) is: dy/dx or difference in y/difference in x which is (y2-y1)/(x2-x1)
Equation of a line: y=mx+c which is used when the gradient and intercept is known or y-y1=m(x-x1) when the gradient and the co-ordinates (x1,y1) of a single point that the line passes through is known. You'll need to learn this equation.
[The equation of the line can be kept in this form unless stated in the exam. (reduces error chance) Also, usually there is a working mark, so state the fact that the gradient is difference in y/difference in x]
The mid-point of two graphs is found by (x1+x2)/2 , (y1+y2)/2 in the form (x,y)
Lines with the same gradient are parallel, while lines with gradients that are negative reciprocals of each other is perpendicular to it. (perpendicular means at a right angle to)
[they usually want you to state that 'the perpendicular line's gradient is the negative reciprocal', so stick it in. It is also usefull to draw out diagrams if they ask about right angle triangles, (usually something to do with negative reciprocals rather than pythagoras.)]
In 2D Lines that are not parallel must intesect, the point of intersection can be found by simultaneous equations by: • equating coefficients of the two lines • substituing one equationinto the other • equating both equations for y.
Surds
surd form is exact. they involve irrational roots, which are roots that cannot be expressed as fractions as they are irrational for example: √5' (for clarification purposes ' marks the end of the root) • √a' x √b' = √a x b' = √ab' • √a' / √b' = √a/b' • √a+b' ≠ √a'+√b'
It is often more useful when denominator of a fraction is rationalised. This is done by multiplying the top and bottom by the conjugate, as the product of two conjugates is always rationalised because (a+b)(a-b)=(a^2)-(b^2) and a surd^2 is always rational. (^2 means squared)
Quadratic Graphs and
Linear Graphs and Equations
For any straight line, the gradient (M) is: dy/dx or difference in y/difference in x which is (y2-y1)/(x2-x1)
Equation of a line: y=mx+c which is used when the gradient and intercept is known or y-y1=m(x-x1) when the gradient and the co-ordinates (x1,y1) of a single point that the line passes through is known. You'll need to learn this equation.
[The equation of the line can be kept in this form unless stated in the exam. (reduces error chance) Also, usually there is a working mark, so state the fact that the gradient is difference in y/difference in x]
The mid-point of two graphs is found by (x1+x2)/2 , (y1+y2)/2 in the form (x,y)
Lines with the same gradient are parallel, while lines with gradients that are negative reciprocals of each other is perpendicular to it. (perpendicular means at a right angle to)
[they usually want you to state that 'the perpendicular line's gradient is the negative reciprocal', so stick it in. It is also usefull to draw out diagrams if they ask about right angle triangles, (usually something to do with negative reciprocals rather than pythagoras.)]
In 2D Lines that are not parallel must intesect, the point of intersection can be found by simultaneous equations by: • equating coefficients of the two lines • substituing one equationinto the other • equating both equations for y.
Surds
surd form is exact. they involve irrational roots, which are roots that cannot be expressed as fractions as they are irrational for example: √5' (for clarification purposes ' marks the end of the root) • √a' x √b' = √a x b' = √ab' • √a' / √b' = √a/b' • √a+b' ≠ √a'+√b'
It is often more useful when denominator of a fraction is rationalised. This is done by multiplying the top and bottom by the conjugate, as the product of two conjugates is always rationalised because (a+b)(a-b)=(a^2)-(b^2) and a surd^2 is always rational. (^2 means squared)
Quadratic Graphs and