I can:
- multiply when I see brackets
- follow BEDMAS
We are learning to expand and simplify polynomial expressions
- write a bracket twice if it is squared
- collect like terms using the signs in front and only if their
variables are identical
1.
Expand and then simplify.
a.
(𝑥 + 4)(2𝑥 − 7)
b.
3(𝑥 − 4)(𝑥 + 2)
c.
4(𝑥 + 2)2 − 9
d.
(𝑥 − 2) − (3𝑥 + 4)2
We are learning to factor polynomial expressions using
I can:
methods of: common factoring, differences of squares, perfect - write a multiplication question (with brackets)
square, simple and complex trinomials
- find a common factor first (numbers that divide evenly or
letters that are everywhere)
2.
Factor.
a.
6𝑥 2 − 11𝑥
b.
𝑥 2 + 7𝑥 − 44
•
•
write down my common factor outside
write down what's left when I divide inside
- factor a simple trinomial (1x^2)
•
•
find two numbers that x to c and + to b
write my two special numbers in the brackets
- factor a complex trinomial (anything but 1)
c.
2
5𝑥 + 15𝑥 + 10
d.
6𝑥 2 + 13𝑥 − 5
e.
6𝑥 2 − 24
•
•
•
find two numbers that x to ac and + to b
•
•
see a subtract sign between TWO terms
•
factor as root + root and root - root
replace the x-term with my two special numbers
factor by grouping
- factor a difference of squares
recognize both terms as perfect squares because I
know their square roots
I can:
We are learning to solve quadratic equations
3.
Solve.
a.
(6𝑥 − 1)(3𝑥 + 5) = 0
b.
𝑥 2 + 5𝑥 + 4 = 0
c.
4𝑥 2 + 3𝑥 = 3𝑥 2 − 2𝑥 − 4
d.
6𝑥 2 + 7𝑥 − 11 = 2𝑥 + 4
- set my equation equal to zero
- factor; everything is in brackets OR formula; ax^2+bx+c
- set each bracket to zero if I chose to factor
To be able to use function notation accurately
4. Consider the relation 𝑓(𝑥) = 3(𝑥 − 2)2 + 8.
a. Calculate f(2) and f(6)
b. Write a mapping statement and use it to
describe the transformations that have
been applied.
c.
I can:

calculate f(x) by replacing all of the xs
with a value

write a mapping statement to transform
points

insides are for xs (brackets lie)

outsides are for ys

describe transformations

negatives mean reflections

multiplications mean
stretches/compressions

additions mean shifts

identify domain as xs that are part of
the relation

write notation D:{x|xER, any restriction}

identify range as ys that are part of the
relation

write notation R:{y|yER, any restriction}

identify a function as having no
cheating xs (ys can have as many
partners as they like)
State the domain and range.
5. Consider the relation {(3,5), (2,5), (3,9)}
a. State the domain and range.
b. Is this a function?
To be able to sketch parabolas
1. Sketch the parabolas:
a. 𝑓(𝑥) = 3𝑥 2 + 12𝑥 − 4
b. 𝑔(𝑥) = −2(𝑥 + 5)2 -6
c.
ℎ(𝑥) = 4(𝑥 + 3)(𝑥 − 7)
I can:

use two brackets to find two xintercepts

find the x of my vertex halfway between
my x-intercepts

find the y of my vertex as f(xvertex)

use the odd as to step from the vertex
OR
I can:

use one bracket to find my one vertex

use odd as to step from my vertex
OR
I can:

use -b/2a (from no brackets) to find the
x of the vertex and sub it in to find y

use odd as to step from my vertex
To be able to write equations for parabolas in vertex and factored
forms
I can:
2. Write the equation of a parabola with x-intercepts at -6 and 10. The parabola passes through (4,9).

use two x-intercepts to fill
in my two brackets

use one other point as x
and y and some algebra
to find a

use one vertex to fill in
one bracket

use one other point as x
and y and some algebra
to find a
OR
3. Write the equation of a parabola that passes through (7,11).
This parabola has a vertex of (4, -10).
To be able to find xs, ys and the vertex, given a
quadratic function in any of the three forms
1. The height of a ball is given by the function
ℎ(𝑡) = −4.9𝑡 2 + 19.6𝑡 + 24.5.
a. How high was the ball initially?
b. When did the ball hit the ground?
c.
What was the maximum height of
the ball?
I can:

find x-intercepts by setting y=0 and solving
(factor or formula or algebra)

find y-intercept by setting x=0 and using
BEDMAS

find any xs given a y (sometimes it's
hidded) by setting it to zero then factoring
or formula or using algebra

find any y given x using BEDMAS

find the vertex because it's halfway
between xs or it's -b/2a
We are learning to solve RATs
2. Solve the triangle below.
x
70
1.8m
I can
- use 180 - - to find the third
angle
- use PYTHAGOREAN
THEOREM to find the third side
 long side add or short
side subtract
- label my sides H then O then
A after selecting my THETA to
find a second side or second
angle
- Pick a formula (SOH CAH
TOA) that I have two numbers
for
 there is usually a side I
don't care about
- Sub in my values so I only
have one variable and then
solve
 angles require 2nd, sides
to do not
We are learning to solve non-RATS
3. Solve the triangle below.
6cm
x
50
8cm
I can:
- use 180 - - to find the third
angle
- use sine law when I have a full
pair (still need 2nd Function to
get an angle)
 find the third angle first
when possible
- use cosine law when I do not
have a full pair
 use c^2= for sides
 use cosC = for angles
To be able to sketch the graph of a periodic function to solve problems
4.
Sketch graphs of each of the following:
a. 𝑓(𝑥) = 6 sin(5(𝑥 − 20)) + 10
I can identify the period as:

the pattern in a periodic function

when the graph starts to repeat

360/the horizontal stretch or
compression (multiplication inside)
in the equation

the time it takes to go once around

twice as much time as it takes to go
from max to min
I can find the amplitude because:
b.

it's the height it goes up or down
from the axis of the curve (max +
min)/2

it's the size of the wave on my
graph

it's the vertical stretch
(multiplication outside) in my
equation
𝑓(𝑥) = 10 sin(2𝑥) − 5
I can find the start of the period (phase shift)
because:
c.
𝑓(𝑥) = −50 sin(180(𝑥 − 3)) + 100

it is where the pattern starts/stops

it's the horizontal shift (addition
inside) in the equation
I can find the axis of the curve because:

it's the midline on a graph

it's the (max + min) / 2

it's the vertical shift (addition
outside) in the equation
I can skect the y-axis using the amplitude and
the axis of the curve (outsides are ys)
5.
Write the equation of the sine function the represents a Ferris I can sketch the x-axis using the start of a
wheel with a radius of 50m on a 2m platform that goes around period, it's length and then middle, middle,
middle (insides are xs and they lie)
10 times an hour.
I can sub in ys to get xs (ALGEBRA)

using my x and my curve I can find
more xs.
We are learning to use mapping notation
1.
Write a mapping statement for 𝑦 = 3 sin(2𝑥) + 5.
a.
Describe the transformations that have been applied.
b.
State the domain and the range,
I can use numbers in the brackets (liars)
on my x and numbers outside brackets
on y
I can

see reflections as negatives

stretches as multiplications

shifts as additions
We are learning to simplify exponential
expressions using the exponent laws
2.
I can:

add the exponents when asked to multiply
(exponent law 1)
Simplify each of the following.

75 72
72
subtract exponents when asked to divide
(exponent law 2)

multiply exponents when asked to raise a
power to a power

write anything raised to zero as 1

write negative exponents as positive if i flip
the base

write fraction exponents as radicals
(−9)4 ((−9)2 )10
1 3
3 2
(24 ) (24 )
5−6 (5−1 )2
5−3
We are learning to solve exponential equations
3.
Solve.
a.
b.
100 = 2 × 2𝑥
36 = 6 × 6
I can:

simplify the equation by combining like bases
through the laws

drop the bases and set the exponents equal

use trial and error when all else fails!

do regular algebra to solve for the base
3𝑥
I can:
We are learning to solve problems using the graph
of an exponential function
4.
𝑥⁄10
sketch the graph of 𝑦 = 15(2)
it to approximate when y=1000
+ 15. Use

write an equation of the form y=ab^x where y is
future, a is starting, b is what happens each
period and x is number of periods

graph using a table of values by picking nice
values of x (make sure you consider the fraction)

find y given an x using BEDMAS

find x given a y using my graph