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EDEXCEL A-Level Maths
Pure Maths Year 1
Chapter 1 Algebraic Expressions
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Created by
Sophia Lethbridge
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Cards (21)
What can you use the
laws of indices
for?
To simplify powers of the
same base
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What is the
product rule
of
indices
?
a<sup>
m
</sup> × a<sup>n</sup> = a<sup>m+n</sup>
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What is the
quotient rule
of
indices
?
a<sup>m</sup> ÷ a<sup>n</sup> = a<sup>
m-n
</sup>
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What is the
power of a power rule
of
indices
?
(
a<sup>m</sup>
)<sup>n</sup> = a<sup>
mn
</sup>
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What is the
product of powers rule
of
indices
?
(
ab
)<sup>n</sup> = a<sup>n</sup>b<sup>n</sup>
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What is the process for
expanding brackets
?
Multiply each term in one
expression
by each term in the other expression.
For
example
, (x+5)(4x-2y+3) expands to:
x(4x-2y+3) + 5(4x-2y+3)
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How many
terms
do you get when multiplying (x+5) by (4x-2y+3)?
6
terms
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What is the
result
of
expanding
(x+5)(4x-2y+3)?
4x²
- 2xy + 23x - 10y + 15
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What is
factorising
in algebra?
Writing expressions as a
product
of their factors.
It is the opposite of
expanding
brackets.
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What is the form of a
quadratic expression
?
ax²
+ bx + c where a, b, and c are real numbers and
a ≠ 0
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How do you
factorise
a
quadratic expression
?
Find two factors of ac that add up to
b
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What is the
difference of two squares formula
?
x²
-
y²
= (
x + y
)(
x - y
)
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What is the
notation
for
real numbers
?
All positive and negative numbers, or zero, including
fractions
and
surds
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What is the
value
of
a<sup>0</sup>
?
1
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What is a surd?
A surd is a multiple of
√n
where n is not a
square
number
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Give examples of
surds
.
√2
, √19, and 5√2
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What characterizes the
decimal expansion
of a
surd
?
It is
never-ending
and
never repeats
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What are
irrational numbers
?
Numbers that cannot be written in the form
a/b
where a and b are integers
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What are the rules for manipulating
surds
?
√ab
= √a × √b
√a/√b
= √a/b
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What is
rationalising the denominator
?
Rearranging a fraction with a
surd
in the denominator to make the denominator a rational number.
Common methods include:
Multiply by
√a
for 1/√a
Multiply by
a - √b
for 1/(a - √b)
Multiply by
a + √b
for 1/(a + √b)
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What are the key points about
indices
and
surds
?
Laws of indices
simplify powers of the same base.
Factorising is the opposite of expanding brackets.
Quadratic expressions
are of the form ax² + bx + c.
Difference of two squares
: x² - y² = (x + y)(x - y).
Laws of indices apply to
rational powers
.
Surds can be manipulated using specific rules.
Rationalising denominators
is useful for fractions with surds.
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