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Hints, Tips and Tricks.

ALGEBRA

 

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v     “To calculate the GRADIENT of a straight line graph, you need to draw in a sort of (backwards) L shape

to help work out the (change in y) and the (change in x). Then you divide.”

Example : P(2,3) Q(6,11)

Gradient = change in y  =  11-3  =  8  =  2

                   change in x       6-2        4

[ RP – Y9 – Alsop ]

 

v     “In the equation y=mx+c, the constant [c] is the y-axis intercept value (x=0) so you can see where the graph crosses the y-axis.”

Example : y=4x+3 would cross the y-axis at (0,3)

[ MM – Y9 – Croxteth ]

 

v     “With LINEAR equations [y=mx+c], the number [m] in front of the x tells you the GRADIENT of the straight line graph.”

Example : y=3x + 2 has a gradient of 3

[ LH  - Y9 – Croxteth ]

 

v     “If Linear Equations have the same gradient [m], they will have parallel straight line graphs.”

Example :  y=2x  will be parallel to  y=2x+1 and y=2x-3  etc.

[ JM – Y9 – Croxteth ]

 

v     “If 2 straight line graphs (linear) have different gradients, they will cross (intersection point) somewhere.”

Example : y=3x+1 will intersect y= -2x+6 at (1,4)

[ JH – Y9 – Croxteth ]

 

v     “For 2 graphs, you can find out the co-ordinates (x,y) of an intersection point by solving the 2 simultaneous equations”

Example :                               x+y=19

x-y=5.

Add to ELIMINATE y. Then 2x=24, x=12, so y=7 Intersection at (12,7)

[ RK – Y10 – De La Salle ]

 

v     “When you are FACTORISING a QUADRATIC equation, make sure it is like this  x2+bx+c,

then the number [c] on the end tells you what the two number factors will multiply to make (check + and -).”

Example : x2+5x-36   Try (+9)x(-4) = -36 , (+6)x(-6)=-36 , (+12)x(-3)=-36 etc

[ AH – Y9 – Anfield ]

 

v     “When you are trying to check the factors of a quadratic equation, the middle number [b] (co-efficient of x) tells you

what the two number factors will total (be careful with the + and -).”

Example : x2+5x-36 = (x+9)(x-4)  Check (+9)x(-4) = -36 and (+9 – 4) = +5   yes !

[ JR – Y9 – Anfield ]

 

                                                                              

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