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Unit 2 Higher Learning objectives
Learning objectives
Grade
Prime factors
find the least common multiple (LCM) of two simple numbers
find the highest common factor (HCF) of two simple numbers
write a number as a product of prime factors
C
find the least common multiple (LCM) of two or more numbers
find the highest common factor (HCF) of two or more numbers.
B
Fractions
find one quantity as a fraction of another
solve problems involving fractions
divide a quantity in a given ratio
solve simple ratio and proportion problems, such as finding the ratio of teachers to
students in a school
add and subtract decimals
multiply and divide decimals
D
add and subtract mixed numbers
multiply and divide fractions
find the reciprocal of a number
solve more complex ratio and proportion problems such as sharing money in the
ratio of people’s ages
solve ratio and proportion problems using the unitary method
round numbers to different degrees of accuracy, decimal places and significant
figures
recognise that recurring decimals are exact fractions and that some exact fractions
are recurring decimals
C
understand the effect of multiplying and dividing by numbers between 0 and 1
convert recurring decimals to fractions.
B
Indices and standard index form
use the terms square, positive square root, negative square root, cube and cube
root
recall integer squares from 2 x 2 to 15 x 15 and the corresponding square roots
recall the cubes of 2, 3, 4, 5 and 10
D
use index notation and index laws for positive powers
C
use index notation and index laws for negative powers
convert between ordinary and standard index form numbers
use standard index form for calculations involving multiplication and/or division
B
1
use index notation and index laws for fractional powers such as 16 2 and 16 0 .5
2
use index notation and index laws for fractional powers such as 8 3 and 8

2
3
A
A*
Surds
rationalise the denominator of a surd
simplify surds, such as write (3 -
5 )2 in the form a + b 5
A
A*
Sequences
write the terms of a sequence or a series of diagrams given the nth
term
D
write the nth term of a sequence or a series of diagrams.
C
Graphs of linear functions
draw the graph of a line, such as y = 3x - 5, without being given a table of values
solve problems such as finding where the line y = 3x - 5 crosses the line y = 4
D
find the gradients of straight-line graphs
find the midpoint of a line segment such as the line from A(1, 5) to B(3, 7)
C
find the gradient and equation of a line through two points such as (0, 3) and (5, 13)
find the equation of a line parallel to another line, such as y = 3x - 5, passing through
a given point, such as (1, 4).
B
Percentages
increase or decrease by a given percentage
express one quantity as a percentage of another
D
work out a percentage increase or decrease
C
understand how to use successive percentages
work out reverse percentage problems.
B
Working with symbols
expand brackets such as 4(x - 3)
factorise an expression such as 6x + 8
D
expand and simplify an expression such as 3(3x - 7) - 2(3x + 1)
C
expand and simplify two brackets such as (x - 3)(x + 5)
expand and simplify two brackets such as (3x + 1)(2x - 3)
B
simplify fractions such as
x
x
2( x  1) 2
+ and
3 5
x 1
Equations and inequalities
solve an equation such as 3x + 2 = 6 – x or 4(2x – 1) = 20
represent and interpret inequalities on a number line
solve an equation such as 4 x  5  3( x  4) or
2x  7
x x
  9 or
1
2 8
4
D
C
solve an inequality such as 2x - 7 < 9
find the integer solutions of an inequality such as -8 < 2n ≤ 5
2x  1 x  3 5


6
3
2
solve an inequality such as 3x + 2 ≤ 4 - x
represent linear inequalities in two variables, such as x + y < 7, as a region on a
graph.
solve an equation such as
B
Formulae
substitute numbers into formulae such as
( A  1)
C=
9
derive complex expressions and formulae
distinguish between an expression, an equation, an identity and a formula
D
rearrange linear formulae such as XXX
C
rearrange formulae involving brackets, indices, fractions and square roots
B
rearrange formulae where the variable appears twice.
A
Real life graphs
interpret real-life graphs
find simple average speed from distance–time graphs
recognise from a distance–time graph when the fastest average speed takes place
D
find the average speed in km/h from a distance–time graph with time in minutes
C
discuss and interpret graphs modelling real situations.
B
Quadratic graphs
solve a problem using step by step deductions
C
factorise an expression such as x2 - 5x + 14 or x2 - 9
solve an equation such as x2 - 5x + 14 = 0
B
factorise an expression such as 3x2 + 7x + 2 or 3x2 - 27
A
x  3x  2
2
simplify an expression such as
by factorising
x2  1
solve an equation such as 3x2 + 7x + 2 = 0 by factorising
derive a proof using reasoning and logic
3
4

2
x  2 x 1
solve an equation such as x2 - 8x + 11 = 0 by completing the square.
solve an equation such as
A*
Simultaneous equations
solve a pair of simultaneous equations such as x + 3y = 9 and 3x - 2y = 5
B
solve a pair of simultaneous equations such as y = 4x + 5 and y = x2
A
solve a pair of simultaneous equations such as x + 2y = 1 and x2 + y2 = 29
A*