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Maths Unit 3

Solving equations with graphs: The solution is always where the two graphs cross ­ use it to solve
simultaneous equations

Quadratic formula:

ax^2+bx+c = 0

X= (-b +/- sqrt (b^2 - 4ac)) / 2a

E.g 3x^2 +7x =1

3x^2+ 7x ­ 1 = 0

A= 3 b=7…

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Practice drawing graphs and quadratic graphs
Use the quadratic formula
Find the second formula to go on the graph
e.g.

You have the graph y = 2x^2 + 3. Solve the equation 2x^2 ­ 3x = 4

1. 2x^2 -3x -4 = 0 (make the solution you are trying to…

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An equilateral triangle has 3 lines of symmetry and 3 rotational symmetry

Isosceles triangle has one line of symmetry and 1 rotational symmetry

Right angled triangle (unless it is a right angled isosceles triangle) has no lines of symmetry and 1
rotational symmetry

A square has 4 lines of symmetry…

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PROJECTION

Front elevation ­ side elevation and plan (see pg 124)

Volume

Lxwxh

Surface area of one end x length (for cylinders etc.)

Volume of sphere : 4/3 r3

Area of cone: 1/3 r2x h

Pyramid: 1/3 base area x h

Frustum of a cone: cone with top cut off…

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o The a locus of points that are equidistant from two different lines is an angle bisector




(a line)
o The locus of a point that are from two given points ­ a perpendicular bisector (a line)




Construction
o Constructing 60° angles ­ also needed for constructing equilateral triangles
Step…

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Step two: From the point with a compass draw an arc on either side of the
line ­ through the line
Step three: From each of the arcs through the line draw an arc above the line
Step four: From the centre of the arcs to the point draw the…

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In this equation the vector v was added to the vector u. When v was added it
was `stuck' on the end of vector u. From the `start' point (indicated) to the end
point (indicated as `stop') another vector (u+v) is drawn.




E.g. In this vector equation I am adding…

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The second arrow down (2u) is where vector u is multiplied by 2 (a scalar) ­ this
means that it keeps its direction but it doubles in length (so becomes 2u).
The third arrow down is where vector u is multiplied by 1/2 (a scalar), this means
that it becomes…

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b. E.g. Enlarge wxyz with the scale factor of -2, centred around the origin




c. For this example you need to calculate the distance from a point to the centre of
enlargement (x to 0,0) then times it by the scale factor and, continuing the line,
measure that distance from…

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A transformation, a reflection and a rotation would always give something congruent
An enlargement would always give something similar

Areas and volumes on enlargement

With a scale factor of n
o Sides are n times as long
o Areas are n^2 times as big
o Volumes are n^3 times as…

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