GCSEFurther MathsAQATopic Questions2. Algebra & FunctionsAlgebraic Proof

Algebraic Proof (AQA GCSE Further Maths)

Topic Questions

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1
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Show that    open parentheses 2 n space plus space 3 close parentheses cubed space plus space n cubed   is divisible by 9 for all integer values of n.

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2
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Prove that    open parentheses 3 x plus 5 close parentheses squared minus 5 x open parentheses x plus 10 close parentheses greater-than or slanted equal to 0   for all values of x.

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3
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–2 <space a space < 0 and –1 < b < 1

Tick the correct box for each statement.

[4]

  Always true Sometimes true Never true
a squared space less than space 0 square square square
– 1 space less than space b cubed space less than space 1 square square size 26px square
b over a space less than space 0 size 26px square size 26px square size 26px square
a space – space b space greater than space 0 size 26px square size 26px square size 26px square

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4
Sme Calculator4 marks

a comma space b and c are numbers such that

table row a less than 0 row b greater than 1 row cell negative 1 end cell less than cell c less than 1 end cell end table

Tick the correct box for each statement.

  Always true Sometimes true Never true
a cubed space less than space 0 begin mathsize 28px style square end style begin mathsize 28px style square end style begin mathsize 28px style square end style
b space less than space 10 a squared square square square
a b space greater than space 0 square square square
b minus space c space greater than space 1 square square square

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