Download PLP-for-National-5

Surds and Indices
EF
  
I can simplify a surd
e.g. √48 = √16 × √3 = 4√3 and
75

75
5
5
I can express a surd with a
rational denominator
e.g.
2

2
3

3
3
3

I can factorise algebraic
expressions involving a
difference of two squares
e.g. x² – y² = (x + y)(x – y) and
4x² – 9y² = (2x – 3y)(2x + 3y)
I can factorise a trinomial
e.g. x² + x – 6 = (x + 3)(x – 2) and
2x2 – 5x – 3 = (2x + 1)(x – 3)
3x4 + 5x2 – 2 = (3x2 – 1)(x2 + 2)
2 3
3
I can simplify expressions using
the law of indices [see below]
I know to add indices when
multiplying and to subtract them
when dividing
5
  
I can complete the square of a
quadratic
x x
x
 6  x2
6
x
x
3
e.g.
Completing the Square
8
I know to multiply the indices
when taking one power to
another
e.g.
( x 4 ) 5  x 20
Algebraic Fractions
I know what a negative power
means and I can use the rules of
indices to simplify expressions
involving them.
I can change from scientific
notation to ordinary numbers
and vice versa eg 3200 = 32 x
103, 67 x 10-5 = 0000067
I can carry out calculations using
scientific notation
I can reduce a fraction to its
lowest terms
3
( x  2)
 ( x  2)
e.g.
2
( x  2)
I can add and subtract algebraic
fractions
e.g.
I can multiply algebraic
expressions involving brackets
e.g. x(x + 2y) = x² +2xy
I can multiply algebraic
expressions involving brackets
e.g. (3x + 5)(x – 1) = 3x² + 2x – 5
I can multiply algebraic
expressions involving brackets
e.g. (x + 2)(x² – 3x + 1) = x³ – x² – 5x
+2
I can factorise algebraic
expressions involving common
factors
e.g. x² + 3x = x(x + 3)
4 3 12
 
a b ab
  
I can round to a given number of
significant figures
Algebraic Expressions
4 3 4b  3a
 
a b
ab
I can multiply and divide
algebraic fractions
e.g.
Significant Figures
  
Gradient of a Straight Line
  
I can find the gradient of the
line joining two points using the
gradient formula
  
Properties of the Circle
I can find the length of an arc
of a circle
I can find the area of a sector
of a circle
I can calculate the angle at the
centre given the arc length or
area of a sector
  
Volumes of Solids
  
I can find the volume of a
sphere
I can find the volume of a cone
I can find the volume of a
cylinder
I can find the volume of a
composite shape involving
sphere, cone and cylinder
I can find an unknown dimension
in the above shapes when I know
its volume
Rel
Straight Line
  
I can find the equation of a
straight line given 2 points or 1
point and a gradient
I can identify the gradient and
y-intercept values from various
forms of the equation of a
straight line
I can use functional notations
Systems of Equations
  
I can construct an equation to
illustrate given information
I can solve simultaneous linear
equations in two
variables algebraically
I know how to find the point of
intersection of two lines
I can solve simultaneous linear
equations in two
variables by drawing the lines
Subject of the Formula
I can change the subject of a
formula
v = u + at for t
I can change the subject of a
formula involving squares and
square roots
Quadratic Functions
I know what the graph of a
quadratic of the form y = kx²
looks like
I know what the graph of a
quadratic of the form
y = (x + a)²+ b looks like
I can identify the nature of the
turning point of a quadratic from
its equation.
e.g. (x – 3)²+ 5 has a minimum
turning point
6 - (x + 4)² has a maximum
turning point
I can write down the turning
point of a quadratic from its
equation
e.g. (x – 3)²+ 5 has turning point
(3, 5)
6 - (x + 4)² has turning point
(-4, 6)
I know what is meant by the
term ‘roots of a quadratic’
I can solve a quadratic equation
graphically
i.e. where the graph crosses the
x - axis
I can solve a quadratic equation
by factorising
e.g. x²+ x – 6 = 0;
(x + 3)(x – 2) = 0; (x + 3) = 0 or
(x – 2) = 0; x = -3 or 2
I can solve a quadratic equation
by using the quadratic formula
x
 b  b 2  4ac
2a
I know the discriminant is
b 2  4ac
I can use the discriminant to
determine the nature of the
roots of a quadratic equation
I know if the roots of a
quadratic equation are rational
or irrational
I can use the discriminant to
find co-oefficients given the
nature of the roots
  
  
Pythagoras Theorem
  
I know and can use Pythagoras
Theorem
I can calculate the distance
between 2 points on a coordinate
grid
I can use Pythagoras Theorem in
3D problems
I can use the Converse of
Pythagoras to prove if a triangle
is right angled.
Properties of Shapes
  
I can apply properties of shapes
to quadrilaterals, triangles,
polygons and circles
I know that a tangent to a circle
makes a right angle at the point
of contact
I know that the angle in a semi
circle is a right angle
I know the relationship between
the centre and chords of a circle
I can use the above properties
to calculate unknown angles in a
circle
Graphs of Trigonometric
Function
I can recognise the basic graphs
of the Sine, Cosine and Tangent
functions
I understand what is meant by
the period of a function and can
find it from its graph or
equation
I can identify the equation of
trig graphs involving multiple
angles and varying maximum and
minimum values
e.g. y = 2 sin3x has max/min
value 2/-2 and period 120o
I can identify the equation of
trig graphs involving a vertical
translation
e.g. y = sin x + 2
I can identify the equation of
trig graphs involving phase
angles
e.g. y = sin(x – 30)o
I can sketch the graph of trig
functions involving multiple
angles and varying maximum and
minimum values
e.g. y = 2 sin3x has max/min
value 2/-2 and period 120o[3
cyles in 360o)
I can sketch the graph of a trig
function involving phase angles
y = cos(x + 45)o
Trigonometric Relationships
Similarity
I can prove if triangles are
mathematically similar if
equiangular or corresponding
sides in proportion
I can calculate the enlargement
or reduction scale factor
I can calculate a missing length
in mathematically similar shapes
I can calculate a missing area in
mathematically similar shapes
I can calculate a missing volume
in mathematically similar shapes
  
  
I can find the sine, cosine and
tangent of angles other than
acute angles
I can solve simple trig equations
e.g. 2 sin xº + 1 = 0
I can simplify expressions using
sin²A + cos²A and tan A = sin
A/cos A
I can calculate exact values
  
App
Trigonometry
  
I can find the area of a triangle
using A = ½ ab sin C
I can use the Cosine rule to find
the length of a side in a triangle
I can use the Cosine rule to find
the size of an angle in a triangle
I can use the Sine rule to find
the length of a side in a triangle
I can use the Sine rule to find
the size of an angle in a triangle
I can use bearings to find
distance or direction
I know when to use the Sine and
Cosine rules to solve problems in
an everyday context
Vectors
I can express one quantity as a
percentage of another
I can carry out calculations
involving percentages in
appropriate contexts:
appreciation/depreciation
I can carry out calculations
involving percentages in
appropriate contexts: compound
interest
I can use reverse percentages to
calculate an original quantity
  
I can simplify fractions and find
equivalent fractions
I can carry out calculations
involving addition and
subtraction of fractions
I can carry out calculations
involving multiplication and
division of fractions
I can carry calculations involving
a combination of operations with
fractions
  
A vector is a quantity with both
magnitude (size) and direction
I can calculate the length of a
vector
I can calculate a component
given two from A and B and
vector AB
I can add, subtract and find
scalar multiples of vectors
Percentages
Fractions
  
Use of simple statistics
I can calculate Mean, Median,
Mode and Range of a data set
I can find the median and
quartiles from a data set
I can construct and interpret
boxplots
I can calculate the interquartile
range of a data set
I can calculate the Standard
Deviation of a data set
I can compare data sets
comparing mean, median,
interquartile range and standard
deviation
I can construct and interpret a
scattergraph
I can determine the equation of
a best fitting straight line
  
General Maths Aims
  
Set working out carefully and
neatly
Listen to instructions given by
teacher
Check that answers are sensible
Show all working carefully
Take care with presentation of
work
Work quietly when required
Check for careless mistakes
Listen carefully to lessons
Curriculum for Excellence
Aims
I can respect the views of
others
I can make informed decisions
I can work in partnership or in
teams
I can lead a group
I can solve problems
I can use technology for learning
I con contribute to class lessons
I can link and apply different
kinds of learning to a new
situation
  
HOLY CROSS HIGH SCHOOL
MATHEMATICS
DEPARTMENT
PERSONAL LEARNING PLAN
National 5
PUPIL NAME………………………………………
CLASS………………………………………
Term 1:………………………………………….
Term 2:…………………………………………
Term 3:…………………………………………
Term 4:…………………………………………
At the beginning of each topic your teacher will
tell you what your aims are going to be and allow
you time to indicate these on the sheet.
When the topic is completed you will be given
time to say how YOU feel you have progressed
and to discuss it with your teacher and your
parents.
Each term you will ask your parents to sign the
front cover to show that you have discussed it
with them.
You have to rate your progress using the traffic
light system.