🥀 • Module 11 : Ratios, Functions & Transformations Flashcards
This lesson covers ratios, rates (speed, density), quadratics, functions (domain, range, composite, inverse), and transformations (reflection, rotation, enlargement). As well as probability with tree and Venn diagrams.
How do you simplify a ratio?
Divide both sides of the ratio by their highest common factor.
What does “sharing in a ratio” mean?
Distribute a quantity in parts proportional to the given ratio.
If a car travels 120km in 2 hours, what is its speed?
Speed = Distance/Time
120/2=60km/h
What is the formula for density?
Density = Mass/Volume
How do you factorize a quadratic equation?
Find two numbers that multiply to the constant and add up to the coefficient of x.
Example : x² + 5x + 6=0,
The two numbers that multiply to 6 and add up to 5 are 2 and 3, so the factorized form is
(x+2)(x+3)=0
What is the domain of a function?
The set of all possible input values (x-values).
What is the range of a function?
The set of all possible output values (y-values) produced by the function.
What is a composite function?
A function formed by applying one function to the result of another function.
Example : If f(x)=2x and g(x)=x+3,
Then the composite function f(g(x))=2(x+3)= 2x+6
How do you describe the reflection change from the points (3,4) on the x-axis of a coordinated plane?
The shape would reflect to the points (3, -4).
What is a rotation transformation?
A rotation turns a shape around a fixed point by a certain angle, in a certain direction.
Example : Rotating point (2,3) by 90 degrees clockwise around the origin gives (3,-2).
How do you perform a translation?
A translation moves every point of a shape by the same distance in the same direction.
Example : Translating point (2,3) by (4,-1) gives (6,2).
Because 2+4=6, 3+-1=2.
What is an enlargement?
An enlargement changes the size of a shape, keeping the same proportions and center of enlargement.
Example : Enlarging point (2, 3) by a scale factor of 2 gives (4, 6).
Because 2x2=4, 3x2=6.
What is the probability of an event not occurring?
It is 1 minus the probability of the event occurring.
Example : If the probability of raining today is 0.3, then the probability of no rain is 1 - 0.3 =0.7
What is a tree diagram used for in probability?
A tree diagram helps visualize and calculate the probability of different outcomes in a sequence of events.
Example : If the probability of a coin landing heads in 1/2, and the probability of rolling a 3 on a dice is 1/6, the probability of both events occurring is (1/2)x(1/6)=1/12.
How do you rotate a shape on a coordinate plane?
Rotate each point by the given angle around the center of rotation using the rules:
90° Clockwise: (x, y) → (y, -x)
90° Counterclockwise: (x, y) → (-y, x)
180° Rotation: (x, y) → (-x, -y)
