AQA A LEVEL MATHS BOOK 2 EXAM
QUESTIONS AND ANSWERS 2026
How can you test n for primality? - ANSWERSDivide by all of the primes less than the
square root of n?
What is the easiest way to prove that a statement is not always true? - ANSWERSFind
a counter example that disproves the statement.
How does proof by contradiction start? - ANSWERSFrom the opposite of the statement
you are trying to prove, and show that this results in an impossible conclusion.
(Assume that ...)
What does co-prime mean? - ANSWERSTwo integers whose only shared positive
common factor is 1.
What does arbitrary number mean? - ANSWERSA value selected randomly, by
personal whim, or without a specific reason, rule, or system.
What is a composite number? - ANSWERSA positive integer greater than 1 that has
more than two factors.
What does a mapping describe? - ANSWERSA relationship between a set of input (x)
and output (y) values.
How can you test if a mapping is a function? - ANSWERSIf each input value maps to
exactly one output value. (Vertical line test)
What notation can be used to define a function? - ANSWERSf(x) = x^2 + 2
f:x -> x^2 + 2
When is a function one-to-one? - ANSWERSIf each input value (x) maps to exactly one
output (y) value.
(Horizontal line test)
When is a function many-to-one? - ANSWERSIf more than one input value (x) maps to
the same output value (y).
(Horizontal line test)
, What is the notation for when x is an element of the set of natural numbers? -
ANSWERSx exists in N
What is the notation for when x is an element of the set of integers? - ANSWERSx
exists in Z
What is the notation for when x is an element of the set of rational numbers? -
ANSWERSx exists in Q
What is the notation for when x is an element of the set of real numbers? - ANSWERSx
exists in R
What is the domain of a function? - ANSWERSThe set of input values allowed.
What is the range of a function? - ANSWERSThe set of output values produced for a
given domain.
What does an inverse function do? - ANSWERSIt reverses the effect of the original
function.
What steps must you take to find an inverse function? - ANSWERS- Swap x with y
- Rearrange to make x the subject
- Replace x with f^-1(x) and y with x
What is f^-1 f(x) equal to? - ANSWERSf^-1 f(x) = ff^-1(x) = x
What is a reflection of the line y=f(x) in the line y=x? - ANSWERSThe inverse function
The domain of f(x) is the same as the range of the inverse function.
What are the only functions that have inverse functions? - ANSWERSOne-to-one
When two vertical transformations or two horizontal transformations are combined, what
happens to the outcome? - ANSWERSChanging the order of them affects the outcome.
When one vertical transformation and one horizontal transformation are combined, what
happens to the outcome? - ANSWERSThe outcome does not depend on the order.
How can you sketch a modulus graph? - ANSWERSStart with the graph of y=f(x) and
reflect in the x-axis any parts that are below the x-axis.
What is [x-a] < b equivalent to? - ANSWERS-b < x-a < b
What is [x-a] > b equivalent to? - ANSWERSx-a > b or x-a < -b
QUESTIONS AND ANSWERS 2026
How can you test n for primality? - ANSWERSDivide by all of the primes less than the
square root of n?
What is the easiest way to prove that a statement is not always true? - ANSWERSFind
a counter example that disproves the statement.
How does proof by contradiction start? - ANSWERSFrom the opposite of the statement
you are trying to prove, and show that this results in an impossible conclusion.
(Assume that ...)
What does co-prime mean? - ANSWERSTwo integers whose only shared positive
common factor is 1.
What does arbitrary number mean? - ANSWERSA value selected randomly, by
personal whim, or without a specific reason, rule, or system.
What is a composite number? - ANSWERSA positive integer greater than 1 that has
more than two factors.
What does a mapping describe? - ANSWERSA relationship between a set of input (x)
and output (y) values.
How can you test if a mapping is a function? - ANSWERSIf each input value maps to
exactly one output value. (Vertical line test)
What notation can be used to define a function? - ANSWERSf(x) = x^2 + 2
f:x -> x^2 + 2
When is a function one-to-one? - ANSWERSIf each input value (x) maps to exactly one
output (y) value.
(Horizontal line test)
When is a function many-to-one? - ANSWERSIf more than one input value (x) maps to
the same output value (y).
(Horizontal line test)
, What is the notation for when x is an element of the set of natural numbers? -
ANSWERSx exists in N
What is the notation for when x is an element of the set of integers? - ANSWERSx
exists in Z
What is the notation for when x is an element of the set of rational numbers? -
ANSWERSx exists in Q
What is the notation for when x is an element of the set of real numbers? - ANSWERSx
exists in R
What is the domain of a function? - ANSWERSThe set of input values allowed.
What is the range of a function? - ANSWERSThe set of output values produced for a
given domain.
What does an inverse function do? - ANSWERSIt reverses the effect of the original
function.
What steps must you take to find an inverse function? - ANSWERS- Swap x with y
- Rearrange to make x the subject
- Replace x with f^-1(x) and y with x
What is f^-1 f(x) equal to? - ANSWERSf^-1 f(x) = ff^-1(x) = x
What is a reflection of the line y=f(x) in the line y=x? - ANSWERSThe inverse function
The domain of f(x) is the same as the range of the inverse function.
What are the only functions that have inverse functions? - ANSWERSOne-to-one
When two vertical transformations or two horizontal transformations are combined, what
happens to the outcome? - ANSWERSChanging the order of them affects the outcome.
When one vertical transformation and one horizontal transformation are combined, what
happens to the outcome? - ANSWERSThe outcome does not depend on the order.
How can you sketch a modulus graph? - ANSWERSStart with the graph of y=f(x) and
reflect in the x-axis any parts that are below the x-axis.
What is [x-a] < b equivalent to? - ANSWERS-b < x-a < b
What is [x-a] > b equivalent to? - ANSWERSx-a > b or x-a < -b
