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OCR A-Level Mathematics
1. Pure Mathematics
1.2 Algebra and Functions
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Cards (100)
What is a function defined as in mathematics?
A relation with unique outputs
Match the variable type with its role in a function:
Independent variable ↔️ Input value
Dependent variable ↔️ Output value
The general form of a linear function is
f
(
x
)
=
f(x) =
f
(
x
)
=
m
x
+
mx +
m
x
+
b
b
b
, where
m
m
m
is the slope and
b
b
b
is the y-intercept
Match the function type with its general form:
Linear ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
m
x
+
mx +
m
x
+
b
b
b
Quadratic ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
2
+
ax^{2} +
a
x
2
+
b
x
+
bx +
b
x
+
c
c
c
Exponential ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
a^{x}
a
x
If
f
(
x
)
=
f(x) =
f
(
x
)
=
x
2
+
x^{2} +
x
2
+
1
1
1
, then
f
(
2
)
=
f(2) =
f
(
2
)
=
5
5
5
True
What is the quadratic formula used to solve quadratic equations?
x
=
x =
x
=
−
b
±
b
2
−
4
a
c
2
a
\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}
2
a
−
b
±
b
2
−
4
a
c
Quadratic equations have the general form
ax^{2}
+ bx + c = 0</latex>.
True
Match the quadratic equation solving method with its description:
Factoring ↔️ Find factors to rewrite as
(
p
x
+
q
)
(
r
x
+
s
)
=
(px + q)(rx + s) =
(
p
x
+
q
)
(
r
x
+
s
)
=
0
0
0
Completing the Square ↔️ Rewrite as
(
x
+
h
)
2
=
(x + h)^{2} =
(
x
+
h
)
2
=
k
k
k
Quadratic Formula ↔️ Use
x
=
x =
x
=
−
b
±
b
2
−
4
a
c
2
a
\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}
2
a
−
b
±
b
2
−
4
a
c
What are the solutions to x^{2} - 4x + 3 = 0</latex> after applying the quadratic formula?
x
=
x =
x
=
3
3
3
and
x
=
x =
x
=
1
1
1
When is the quadratic formula most useful for solving quadratic equations?
For non-factorable equations
What are the key methods for factorizing polynomials?
Common factors, standard formulas, grouping terms
How do you factorize
x
2
−
5
x
+
x^{2} - 5x +
x
2
−
5
x
+
6
6
6
?
(x - 2)(x - 3)</latex>
What does combining like terms involve in simplifying algebraic expressions?
Adding or subtracting terms with the same variables and exponents
A function is a relation where each input corresponds to exactly one
output
.
True
Match the function type with its general form:
Linear ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
m
x
+
mx +
m
x
+
b
b
b
Quadratic ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
2
+
ax^{2} +
a
x
2
+
b
x
+
bx +
b
x
+
c
c
c
Exponential ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
a^{x}
a
x
The graph of a linear function is a
straight
Match the function type with its general form:
Linear ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
m
x
+
mx +
m
x
+
c
c
c
Quadratic ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
2
+
ax^{2} +
a
x
2
+
b
x
+
bx +
b
x
+
c
c
c
Exponential ↔️
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
a^{x}
a
x
What is the quadratic formula?
x
=
x =
x
=
−
b
±
b
2
−
4
a
c
2
a
\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}
2
a
−
b
±
b
2
−
4
a
c
Match the factorization method with its formula:
Difference of Squares ↔️
a
2
−
b
2
=
a^{2} - b^{2} =
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
(a + b)(a - b)
(
a
+
b
)
(
a
−
b
)
Perfect Squares ↔️
(
a
±
b
)
2
=
(a \pm b)^{2} =
(
a
±
b
)
2
=
a
2
±
2
a
b
+
a^{2} \pm 2ab +
a
2
±
2
ab
+
b
2
b^{2}
b
2
Common Factors ↔️
a
x
+
ax +
a
x
+
b
x
=
bx =
b
x
=
x
(
a
+
b
)
x(a + b)
x
(
a
+
b
)
What is the result of applying the distributive property to 2(x + 3)</latex>?
2
x
+
2x +
2
x
+
6
6
6
When applying the distributive property, you multiply the outside factor by each term inside the
parentheses
.
True
For
f
(
x
)
=
f(x) =
f
(
x
)
=
x
\sqrt{x}
x
, the domain is
x
≥
0
x \ge 0
x
≥
0
, which means
x
x
x
must be greater than or equal to zero
When composing functions, the output of
g
(
x
)
g(x)
g
(
x
)
becomes the input of
f
(
x
)
f(x)
f
(
x
)
True
What is the general form of a linear function?
f
(
x
)
=
f(x) =
f
(
x
)
=
m
x
+
mx +
m
x
+
b
b
b
Steps to solve a linear equation
a
x
+
ax +
a
x
+
b
=
b =
b
=
0
0
0
1️⃣ Subtract
b
b
b
from both sides
2️⃣ Divide by
a
a
a
To solve
a
x
=
ax =
a
x
=
−
b
- b
−
b
, divide both sides by a
In function notation, the value of the function
f
f
f
at
x
x
x
is written as f(x)
What are the three types of functions mentioned in the material?
Linear, quadratic, exponential
What is the condition for the base
a
a
a
in an exponential function
f
(
x
)
=
f(x) =
f
(
x
)
=
a
x
a^{x}
a
x
?
a
>
0
a > 0
a
>
0
and
a
≠
1
a \neq 1
a
=
1
In function notation, the dependent variable represents the
output
Match the method for solving quadratic equations with its description:
Factoring ↔️ Find factors that multiply to the equation
Completing the Square ↔️ Rewrite as
(
x
+
h
)
2
=
(x + h)^{2} =
(
x
+
h
)
2
=
k
k
k
Quadratic Formula ↔️ Use
x
=
x =
x
=
−
b
±
b
2
−
4
a
c
2
a
\frac{ - b \pm \sqrt{b^{2} - 4ac}}{2a}
2
a
−
b
±
b
2
−
4
a
c
To solve
a
x
+
ax +
a
x
+
b
=
b =
b
=
0
0
0
, first subtract b from both sides.
The factoring method is best used when factors are easily
visible
.
True
To solve
x
2
−
4
x
+
x^{2} - 4x +
x
2
−
4
x
+
3
=
3 =
3
=
0
0
0
using the quadratic formula, first identify
a
=
a =
a
=
1
1
1
,
b
=
b =
b
=
−
4
- 4
−
4
, and c = 3.
The quadratic equation
a
x
2
+
ax^{2} +
a
x
2
+
b
x
+
bx +
b
x
+
c
=
c =
c
=
0
0
0
can be solved using factoring, completing the square, or the quadratic formula.
The quadratic formula is always applicable, especially for non-factorable
equations
.
The formula for the difference of squares is
a
2
−
b
2
=
a^{2} - b^{2} =
a
2
−
b
2
=
(
a
+
b
)
(
a
−
b
)
(a + b)(a - b)
(
a
+
b
)
(
a
−
b
)
, which factors into two binomials.
To simplify algebraic expressions, you combine like terms, use the
distributive property
, and apply exponent rules.
True
What is the result of
(
x
2
)
3
(x^{2})^{3}
(
x
2
)
3
after applying exponent rules?
x
6
x^{6}
x
6
What does
f
(
x
)
f(x)
f
(
x
)
represent in function notation?
The output value
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