Algebra Facts Flashcards
What do we call this sequence and how do we get the next term? 1, 1, 2, 3, 5, 8, ….
Fibonacci sequence: Add the previous two terms
What’s a geometric sequence?
A sequence made by multiplying by the same value each time.
What’s an arithmetic sequence?
A sequence made by adding the same value each time
When finding the nth term of a quadratic sequence how do we find the coefficient of n²?
Halve the second difference
What type of sequence is 2, 6, 18, 54?
Geometric Sequence
What type of sequence is 8, 14, 20, 26?
Linear (Arithmetic) Sequence
How do you find the next term in a fibonacci sequence?
Add the previous two terms
What type of sequence is 2, 8, 18, 32?
Quadratic
What’s an identity?
An equation that is true no matter what values are chosen.
What type of algebra is a + b = 17
Formula
What type of algebra is 3a + 4b?
Expression
What type of algebra is x² + 3 = 19 ?
Equation
What does the symbol ≡ mean?
Identitically equal to
What does the symbol < mean?
Less than, but not equal to
What does the symbol > mean?
More than, but not equal to
What does the symbol ≤ mean?
Less than or equal to
What does the symbol ≥ mean?
More than or equal to
On an inequality diagram how do you include an integer?
Shade in the circle
What type of graph is y = x³?
Cubic
What type of graph is y = x²?
Quadratic
What type of graph is y = 2 to the power of x?
Exponential
What type of graph is y = 1/x?
Reciprocal
Where does the graph of y = a to the power x meet the y-axis?
(0,1)
Write down the equation of a circle centre (0, 0) and radius r.
x² +y² = r²
The transformation y = f(x) + a represents a translation of the graph y = f(x) in what direction?
Up by “a”
The transformation y = f(-x) represents a reflection of the graph y = f(x) in which axis?
y axis
The transformation y = f(x + a) represents a translation of the graph y = f(x)in what direction?
Left by “a”
y = -f(x) represents a reflection of the graph y = f(x) in which axis?
x-axis
The transformation y = f(x) - a represents a translation of the graph y = f(x) in what direction?
Down by “a”
The transformation y = f(x - a) represents a translation of the graph y = f(x)in what direction?
Right by “a”
y = f(-x) represents a reflection of the graph y = f(x) in which axis?
y-axis
In an error interval what two symbols are always used?
≤ then
If a number is rounded to 2 decimal places, its upper and lower bounds will have how many decimal places?
3
If a number is rounded to the nearest 1000, what is the largest numbers its upper and lower bounds will be a mutliple of?
500
85 ≤ x < 95 is an example of what?
Error Interval
Why is 350 ≤ x ≤ 450 not an error interval
The second symbol should be
Write down the coordinates of the minimum point of the graph y = (x+a)² + b
(-a, b)
Write down the quadratic formula
x = -b plus minus square root of (b squared minus 4ac) all divided by 2a
What is the maximum amount of solutions a quadratic equation can have?
2
What does ± mean in the quadratic formula?
There are two solutions, one from using + and one from using -
“x = -b plus minus square root of (b squared minus 4ac) all divided by 2a” is called what?
The Quadratic Formulae
In the quadratic formula what is a
The coefficient of x²
How do you calculate gradient from a linear graph?
Change in y divided by change in x
In y = mx + c what does c represent?
y-intercept
In the equation of a straight line y = mx + c, what does m represent?
Gradient
Is the line y = 5 horizontal or vertical?
Horizontal
What are perpendicular lines?
Lines that are at right angles (90 degrees) to each other.
What axis is the line x = 0?
The y-axis
What do we know about two linear graphs that have the same gradient and different y intercepts
They are parallel
What is the gradient of a straight line perpendicular to the straight line with gradient negative two thirds?
3/2
