AQA UNIT 2 – Higher level PRIME FACTORS C
B
WORKING WITH SYMBOLS
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 Find the least common multiple (LCM) of two or more numbers Find the highest common factor (HCF) of two or more numbers
D
Expand brackets such as 4( x
C
Expand and simplify an expression such as
3) Factorise an expression such as 6x 8 3(3x 7) 2(3x 1)
B
Expand and simplify two brackets such as ( x 3)( x
5)
Expand and simplify two brackets such as (3x 1)(2 x 3) Simplify fractions such as
x 3
x 5
and
2 ( x 1) 2 x 1
SEQUENCES D C
Write the terms of a sequence or a series of diagrams given the nth term Write the nth term of a linear sequence or a series of diagrams
GRAPHS OF LINEAR FUNCTIONS D
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 crosses the line y C
B
FRACTIONS AND DECIMALS D
C
3x 5
4
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) 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 B
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 fractions and decimals Add and subtract mixed numbers Multiply and divide fractions and mixed numbers Find the reciprocal of a number Convert fractions to decimals Solve more complex ratio and proportion problems 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 Understand the effect of multiplying and dividing by numbers between 0 and 1 Convert recurring decimals to fractions
AQA UNIT 2 – Higher level EQUATIONS AND INEQUALITIES D
Solve an equation such as 3x
INDICES AND STANDARD INDEX FORM
2 6 x or 4(2 x 1)
20
D
A
Use the terms square, positive square root, negative square root, cube and cube root Recall integer squares from 2x2 to 15x15 and the corresponding square roots Recall the cubes of 2, 3, 4, 5 and 10 and the corresponding cube roots Use index notation and index laws for positive powers 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 Use index notation and index laws for fractional powers such
A*
as 16 2 and 16 0.5 Use index notation and index laws for fractional powers such
Represent and interpret inequalities on a number line C
Solve equations such as 4 x 5
3( x 4) or x
2
x 8
9 or
2x 1 1 6
Solve an inequality such as 2x 7 9 Find the integer solutions of an equality such as B
8 ‹ 2n 5
2x 1 x 3 5 6 3 2 Solve an inequality such as 2 x 2 4 x Represent inequalities, such as x y ‹ 7 , as a region on a Solve an equation such as
graph
1
PERCENTAGES D
C B
Compare harder percentages, fractions and decimals Work out more difficult percentages of a given quantity Increase or decrease by a given percentage Express one quantity as a percentage of another Work out a percentage increase or decrease Understand how to use successive percentages Work out reverse percentage problems REAL LIFE GRAPHS
D
C B
C B
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 Find the average speed in km/h from a distance-time graph with time in minutes Discuss and interpret graphs modelling real situations
as 8
2
3
and 8
2
3
FORMULAE D
Substitute numbers into formulae such as C
C
Derive complex expressions and formulae Distinguish between expression, an equation, an identity and a formula Rearrange linear formulae such as p 3q 5
B A
A 1 9
Rearrange formulae involving brackets, indices, fractions and square roots Rearrange formulae where the variable appears twice SURDS
A A*
Rationalise the denominator of a surd Simplify surds, such as “write 3
2
5 in the form a b 5 ”
AQA UNIT 2 – Higher level QUADRATIC EQUATIONS AND ALGEBRAIC PROOF C B A
Solve problems using step by step deductions Factorise an expression such as x 2 5x 14 or x 2 9 Solve an equation such as x 2 5x 14 0 Factorise an expression such as 3x 2 7 x 2 or 3x 2 27 Simplify an expression such as
x2
3x 2 by factorising x 1 7 x 2 0 by factorising 2
Solve an equation such as 3x 2 Derive a proof using reasoning and logic A*
Solve an equation such as
3
4
2 x 2 x 1 Solve an equation such as x 2 8x 11 0 by completing the square
SIMULTANEOUS EQUATIONS B
Solve a pair of simultaneous equations such as x 3y
3x 2 y A
5
Solve a pair of simultaneous equations such as y
y
x
2
9 and
4x 5 and