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Intermediate 2 Unit 1
Learning Intention
Calculations involving percentages
carry out calculations involving percentages in
appropriate contexts: appreciation/depreciation
Volumes of solids
find the volumes of spheres, cones and prisms
round calculations to a required number of
significant figures
Linear relationships
find the gradient of a straight line between two
points (x1, y1) and (x2, y2)
know that in the equation y = ax + b of a straight
line, ‘a’ represents the gradient and ‘b’ represents
the intercept on the y-axis and use this to sketch
the line without drawing accurately
determine the equation of a straight line in the
form y = ax + b from its graph
Understood Not
References
Understood
Chapter 2
Pages 7 – 18
Revision Ex 1
Page 78
Level A/B
Ex 3 Page 11
Ex 5 Page 14
Ex 6 page 15
Qu 6 - 10
Chapter 3
Pages 19 – 31
Revision Ex 2
Page 80
Level A/B
Ex 4 Page 25
Qu 8 – 10
Ex 5 page 28
Qu 3 – 12
Chapter 1
Pages 1 – 6
Chapter 3
Ex 3 Page 37
Revision Ex 3
Page 83
Level A/B
Qu 8 – 10
Chapter 3
Ex4 Page 43
Level A/B
Qu 10 – 11
Ex 5 Page 45
Chapter 4
Ex 4 Page 43
Level A/B
Qu 10 – 11
Learning Intention
Algebraic operations
multiply algebraic expressions involving brackets
Factorise algebraic expressions:
common factor
difference of two squares (with numerical coefficients >1)
factorise trinomial expressions
Properties of the circle
find the length of an arc of a circle
find the area of a sector of a circle
use the properties of circles:
relationship between tangent and radius
angle in a semi-circle
the interdependence of the centre, bisector of
a chord and a perpendicular to a chord [A/B]
Understood Not
References
Understood
Chapter 5
Ex 1 Page 48
Ex 2 Page 50
Revision Ex 4
Page 86
Level A/B
Ex 1 Page 48
Qu 7 – 8
Ex 2 Page 50
Qu 4 - 5
Ex 3 Page 53
Ex 4 Page 53
Ex 5 Page 54
Ex 6 Page 56
Ex 8 Page 57
Level A/B
Ex 5 Page 54
Qu 4
Ex 7 Page 57
Chapter 6
Ex 1 Page 60
Level A/B
Ex 1 Page 60
Qu 9
Ex 3 Page 64
Revision Ex 5
Page 89
Ex 2 Page 62
Level A/B
Ex 2 Page 62
Qu 8 – 9
Ex 3 Page 64
Ex 8 Page 73
Ex 7 Page 71
Level A/B
Qu 8 -11
Level A/B
Ex 5 Page 68
Intermediate 2 Unit 2
Learning Intention
The statistical content of Mathematics 2 (Int 1) is
underlined and should be integrated into the
teaching of this unit. This content is required for
progression purposes and will be assessed only as
part of the overall statistical content.
Trigonometry
find the sine, cosine and tangent of angles other
than acute angles
find the area of a scalene triangle using
area = ½ bc sin A
solve scalene triangles by using the Sine
Rule/Cosine Rule
use the Cosine Rule to find an angle of a
triangle, given all three sides [A/B]
Simultaneous linear equations
construct formulae to describe a linear
relationship
know the significance of the point of intersection
of two graphs: solve simultaneous linear
equations in two variables graphically
solve simultaneous linear equations in two
variables algebraically
Understood Not
References
Understood
Chapter 8
Ex 2 Page 97
Revision Ex 1
Page 186
Ex 3 Page 99
Ex4 Page 100
Level A/B
Ex 4 Page 100
Qu 8
Ex 5 Page 102
Ex 6 Page 103
Ex 8 Page 106
Ex 11 Page 110
Ex 12 Page 112
Level A/B
Ex 7 Page 104
Ex 9 Page 107
Ex 10 Page 108
Ex 14 Page 117
Level A/B
Ex 13 Page 114
Ex 14 Page 117
Chapter 9
Ex 3 Page 125
Level A/B
Ex 3 Page 125
Qu 4 – 5
Revision Ex 2
Page 188
Ex 1 Page 121
Ex 2 Page 122
Level A/B
Ex2 Page 122
Qu 6 – 8
Ex 4 Page 127
Ex 5 Page 130
Level A/B
Ex 4 Page 127
Qu 8 - 9
Ex 5 Page 130
Qu 7 - 8
Learning Intention
Graphs, charts and tables
extract and interpret data from bar graphs, line
graphs, pie charts and stem-and-leaf diagrams
construct bar graphs, line graphs and stem-and leaf diagrams
construct and interpret a scattergraph
add a cumulative frequency column to an
ungrouped frequency table
find the median and quartiles from a data set or
ungrouped frequency table
construct and interpret boxplots and dotplots
construct a piechart
Use of simple statistics
calculate the mean, mode and range of a data set
or an ungrouped frequency table
Calculate the semi-interquartile range from a data
set or ungrouped frequency table
Calculate the standard deviation of a data set
determine the equation of a best-fitting straight
line on a scattergraph and use it to estimate a
y-value given the x-value
know that probability is a measure of chance
between 0 and 1
find probability defined as:
No. of favourable outcomes
No. of possible outcomes
where all the outcomes are equally likely
Understood Not
References
Understood
Chapter 10
Starting Points
Page 134
Revision Ex 3
Page 190
Starting Points
Page 134
Starting Points
Page 134
Ex 4 Page 143
Level A/B
Ex 5 Page 145
Ex 6 Page 147
Ex 7 Page 151
Ex 8 Page 152
Level A/B
Ex 9 Page 155
Ex 2 Page 140
Ex 3 Page 141
Chapter 11
Starting Points
Page 158
Ex 1 Page 162
Revision Ex 4
Page 194
Ex 2 Page 163
Ex 3 Page 166
Ex 4 Page 169
Ex 5 Page 171
Ex 6 Page 172
Ex 7 Page 175
Ex 8 Page 177
Ex 8 Page 177
Ex 9 Page 179
Ex 10 Page 181
Intermediate 2 Unit 3
Learning Intention
Algebraic operations
reduce an algebraic fraction to its simplest form
apply the four rules to algebraic fractions
change the subject of formulae
simplify surds
express with a rational denominator [A/B]
simplify expressions using the laws of indices
Quadratic functions
recognise quadratics of the form y = kx2 and
y = (x + a)2 + b; a, b, k Z from their graphs
identify the nature and coordinates of the turning
point and the equation of the axis of symmetry of
a quadratic of the form y = k(x + a)2 + b; a, b Z,
k = 1
know the meaning of the term ‘roots of a
quadratic equation’
solve quadratic equations graphically
solve quadratic equations by factorisation and by
using the quadratic formula
Understood Not
References
Understood
Chapter 13
Ex 1 Page 198
Ex 2 Page 200
Ex 3 Page 200
Level A/B
Ex 3 Page 200
Qu 6 - 8
Ex 4 Page 202
Level A/B
Ex 5 Page 204
Ex 6 Page 205
Ex 7 Page 206
Ex 8 Page 207
Ex 9 Page 208
Level A/B
Ex 10 Page 209
Ex 11 Page 209
Ex 12 Page 210
Ex 13 Page 211
Level A/B
Ex 13 Page 211
Qu 4 – 5
Ex 14 Page 212
Chapter 14
Ex 2 Page 218
Ex 3 Page 221
Level A/B
Ex 4 Page 223
Revision Ex 2
Page 257
Ex 5 Page 225
Level A/B
Ex 6 Page 226
Ex 7 Page 227
Ex 8 Page 228
Ex 9 Page 229
Ex 10 Page 232
Level A/B
Ex 9 Page 229
Qu 5 - 6
Learning Intention
Further trigonometry
recognise the graphs of sine, cosine and tangent
functions
sketch and identify trigonometric functions
involving a multiple angle
involving a phase angle [A/B]
solve simple trigonometric equations in degrees
define the period of a trigonometric function
either from its graph or from its equation
simplify expressions using
sin2 A + cos2 A = 1
and
tan A = sin A
cosA
[A/B]
Understood Not
References
Understood
Chapter 15
Starting Points
Page 234
Ex 4 Page 203
Revision Ex 3
Page 260
Ex 2 Page 238
Ex 3 Page 241
Ex 4 Page 243
Level A/B
Ex 5 Page 245
Ex 6 Page 249
Ex 2 Page 238
Ex 3 Page 241
Ex 4 Page 243
Level A/B
Ex 7 Page 252
John Paul Academy
Mathematics Department
Pupils Course Content Booklet
Intermediate 2 Mathematics
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