Queen Margaret Academy
Higher Maths
Traffic Light Summary
Unit 1
AA Higher Traffic Light Summary Sheets
Queen Margaret Academy
Higher Mathematics
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Know the gradient formula: m =
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Know the distance formula: d = √(
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Show that point are collinear:
- 3 Points are collinear if they have the same gradient and have a
common point.
Know gradient of a straight line equals tan of the angle between
line and positive direction of x-axis m tan
Know that lines that are parallel have the same gradient.
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Know that line with gradients m1 and m2 are perpendicular when m1 x m2
=m -1.
Know how to work out the midpoint of a line.
Know the equation of the line is y – b = m(x – a) and multiplied out can be
written in the form ax + by + c = 0.
Determine the equation of an altitude:
- Find the gradient of the line the altitude intersects.
- Use m1 x m2 = -1 to find the gradient of the altitude.
- Use gradient of altitude and a point on that line to state the
equation.
Determine the equation of a median:
- Find the midpoint of the line the median intersects.
- Use the midpoint and other point line passes through
to get the gradient.
- Use the midpoint or other point on the line along with
the gradient to state the equation of the median.
Determine the equation of the perpendicular bisector:
- Find the midpoint of the line the median intersects.
- Find the gradient of the line the perpendicular
bisector intersects.
- Use m1 x m2 = -1 to find the gradient of the
perpendicular bisector.
- Use m2 and midpoint and substitute into equation of a line.
Use simultaneous equations to find the coordinates where two lines
meet.
Tackle past paper questions on staright line.
AA Higher Traffic Light Summary Sheets
Green
Red
Learning Statement
Amber
Unit 1: Straight line
Queen Margaret Academy
Higher Mathematics
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Understand what the Domain and Range of a function are.
- Domain to do with the x-coordinates
- Range to do with y-coordinates.
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Recognise a composite function as h(x) = g(f(x)) and be able to find h(x)
when given g(x) and f(x).
e.g h(x) = f(g(x)), where f(x) = x2 + 3 and g(x) = x – 2
h(x) = f(g(x)) = f(x – 2) = (x – 2)2 + 3
Understand what the inverse function is (f(x)-1) and how to calculate it.
e.g. f(x) = 3x + 1, f(x)-1 =
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Given the graph of f(x) be able to draw:

f(x) + a ( Moves graph up by value of a)
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f(x) – a (moves graph down by value of a)
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-f(x) (reflects graph of x-axis)
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f(-x) ( reflects graphs on y-axis)
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f(x + a) (moves graph to the left by value of a)
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f(x – a) ( moves graph to the right by value of a)
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af(x) ( Stretches/Compresses graph on y-axis - multiplies y-coordinates
by value of a)

f(ax) (Stretches/Compresses graph on x-axis - divides x-coordinates by
value of a)
Know the general features of exponential and logarithmic functions.
- Exponential -> f(x) = ax
- Logarithmic -> f(x) = logax
Be able to graph the inverse of a function by reflection in the line y = x.
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Find the equation of an exponential function from two points on the
graph.
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Find the equation of a logarithmic function from a graph.
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Know the meaning of the word Amplitude and period.
AA Higher Traffic Light Summary Sheets
Green
Amber
Learning Statement
Red
Unit 1: Functions and Graphs
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Know the general features of the sin, cos and tan graphs.
y = sinx
y = cosx
y = tanx
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Know the general features of sine and cosine graphs, y = sin(ax + b), y =
cos(ax + b), y = asinbx, y = acosbx.
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Know that π radians = 180 degrees.
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Convert between degrees and radians.
- Common exact value radians e.g. 45o = , 30o = , 60o =
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- Degrees x π ÷ 180 = radians (must be to at least 2 decimal places)
Know and be able to use your exact values traingles.
Solve trig equations of the form:
2sinx – 1 = 0
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2sin4x + √ = 0
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tan2x = 3
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3sin2x – 4sinx + 1 = 0
- 2cos(x + 60) = √
Completing the square – write the equation in the form y = ax2 + bx + c in
the form y = a(x + b)2 + c:
 Put the equations equal to each other. Multiply out the bracket
on right hand side and equate coefficents with left hand side.
e.g. 2x2 – 8x + 9 = a(x + b)2 + c
2x2 – 8x + 9 = ax2 + 2abx +ab2 + c
ab2 + c = 9
(2)(-2)2 + c = 9
8+c=9
c=1
Tackle past paper questions on functions and graphs
a=2
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2ab = -8
2(2)b = -8
b = -2
AA Higher Traffic Light Summary Sheets
AA Higher Traffic Light Summary Sheets