2 I can graph a line 3 ways: Table of values x- and y-intercepts y-intercept and slopeEx. 1) y=-3x+2
3 I can graph a line 3 ways: Table of values x- and y-intercepts y-intercept and slopeEx. 2) 4x-3y=12
4 I can graph a line 3 ways: Table of values x- and y-intercepts y-intercept and slopeEx. 3) y=(2/3)x-5
5 I can translate a word problem into algebra What important, defining information are you missing? THIS WILL HELP YOU DEFINE YOUR VARIABLESHint: The question at the end will direct you to at least one of the variablesEXAMPLE: Karl owns a small airplane. He pays $50/h for flying time and $300/month for hangar fees at the local airport. If Karl rented the same type of airplane at a flying club, it would cost him $100/h. When will the monthly cost of owning and renting be the same?
6 I can solve a linear system by graphing Karl’s situation:y1=50x+300y2=100x
7 I can determine if a point is the solution to the system …using substitution!We found the POI for Karl was (6, 600) on the graph.How do we test our answer?Plug it into both equations!y1=50x+300y2=100x
8 I can determine the number of solutions by looking at the equations in the system Different slopeNo solutionsSame slope,different y-interceptsInfinite solutionssame y-intercept
9 I can solve a linear system by substitution 2𝑥−𝑦=2 and 3𝑥−3𝑦=−3CHECK YOUR ANSWER!
10 I can solve a linear system by elimination 2𝑥−𝑦=2 and 3𝑥−3𝑦=−3CHECK YOUR ANSWER!
11 I can solve problems using linear systems A weekend at a lodge costs $360 and includes 2 nights’ accommodation and 2 meals a day. A week costs $1200 and includes 7 nights’ accommodation and 10 meals. What is the cost of one night and one meal? How much would it cost for five nights and 4 meals?CHECK YOUR ANSWER!
13 I can calculate the length of a line segment, given its endpoints Distance formula:𝑑= 𝑥 2 − 𝑥 𝑦 2 − 𝑦 1 2Find the distance between (-7, 1) and (5, -2)
14 I can find the midpoint of a line segment Midpoint formula:𝑀=( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )Ex 1. Find the midpoint between (-4, 6) and (8, -2)
15 I can find the midpoint of a line segment Midpoint formula:𝑀=( 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 )Ex 2. Find the other endpoint of a line segment if one endpoint is (-4, -2) and the midpoint of the line segment is (2, 6).
16 I can solve problems involving midpoints, medians, and perpendicular bisectors Median: a line that joins a vertex of a triangle to the midpoint of the opposite side.Perpendicular Bisector: of a line segment is the line that is perpendicular to the line segment and passes through the midpoint of the line segment.
17 I can solve problems involving midpoints, medians, and perpendicular bisectors CONT’D STEPS TO FIND EQN OF MEDIAN:Calculate the midpoint of the line opposite the vertex of interestCalculate the slope of the line connecting the vertex of interest to that midpoint (ie. The median)Sub the slope into the eqn for a line: y=mx+bPlug in (x, y) (either the midpoint or the vertex of interest)Solve for bState equation with slope (m) and y-intercept (b)Find the equation of the median line from vertex C in triangle ABC if the coordinates of the vertices are A(-3, 3), B(2, -5), and C(5, 2)
18 I can solve problems involving midpoints, medians, and perpendicular bisectors CONT’D STEPS TO FIND EQN OF PERPENDICULAR BISECTOR:Calculate the midpoint of the line segmentCalculate the slope of the line segmentThe slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment it is bisectingPlug the slope and the midpoint into y=mx+bSolve for bState equation with slope (m) and y-intercept (b)Find the equation of the perpendicular bisector of the line segment from A(1, 1) to B(5, 3)
19 I can classify triangles given the coordinates of the vertices The vertices of triangle ABC are A(5, 5), B(-3, -1), and C(1, -3). Determine what kind of triangle it is.
20 I can classify triangles given the coordinates of the vertices The vertices of triangle ABC areA(5, 5), B(-3, -1), and C(1, -3).Determine what kind of triangle it is.
21 I can verify properties of geometric figures algebraically The vertices of triangle ABC are A(5, 5), B(-3, -1), and C(1, -3). Show that the median from vertex C is half as long as the hypotenuse.
22 I can verify properties of geometric figures algebraically CONT’D Classify the shape with vertices at A(-4, 2), B(2, -5), C(7, -3) and D(1, 5)
23 I can verify properties of geometric figures algebraically CONT’D PQRS is a rhombus with vertices at P(3, 3), Q(0, 1), R(3, -1), and S(6, 1).Verify that its diagonals bisect each other at right angles.
24 I can determine the shortest distance from a point to a line …the shortest distance from a point to a line is always the PERPENDICULAR PATH from the point to the line.
25 I can determine the equation of a circle centered at the origin, given the circle’s radius 𝑥 2 + 𝑦 2 = 𝑟 2State the equation of the circle:(a) centre origin, radius of 8(b) centre origin, radius of 1 3
26 I can determine the radius of a circle centered at the origin, given the circle’s equation Length of a circle’s radius:𝑟= 𝑥 2 + 𝑦 2A circle has the equation 𝑥 2 + 𝑦 2 =144. Where is its centre? What is its radius?
27 I can sketch a circle, given its equation A circle has the equation 𝑥 2 + 𝑦 2 =36. Sketch its graph.
28 I can determine the equation of a circle, given a point through which it passes Find the equation of the circle passing through (-5, 12)
29 STUDY Shapes and their names and properties Important terms (midpoint, median, perpendicular bisector)Formulas
36 I can factor 𝑎𝑥 2 +𝑏𝑥+𝑐, 𝑎≠120 𝑥 2 +6𝑥−24𝑥 2 −16𝑥+15
37 I can solve a quadratic equation by factoring 𝑥 2 +9𝑥+14=06 𝑥 2 −𝑥=15
38 I can identify the key features of a graph of a parabola
39 I can graph a parabola (determine the zeros and vertex ) from 𝑦=𝑎 𝑥 2 +𝑏𝑥+𝑐 𝑦=− 𝑥 2 +6𝑥−9
40 I can find the equation of a quadratic given its zeros and another point on the parabola A parabola has zeros at (-2, 0) and (4, 0), and passes through (2, 16). Find its equation.
41 I can solve problems involving quadratics When Kermit the Frog makes a giant leap from one lily pad to another, he follows a parabolic path. Kermit is in the air for 6 seconds before he makes a safe landing. Kermit knows that after 2 seconds, he is 72 cm high. How high is Kermit at his greatest height?
42 I can solve problems involving quadratics A design engineer uses the equation ℎ=− 𝑑 to model an archway for the entrance to a fair, where h is the height in metres above the ground, and d is the horizontal distance from the centre of the arch.How wide and tall is the arch?For what values of d is the relation valid? Why?If a width of 2.5 m is needed per line-up at the entrance, how many line-ups can there be?
Your consent to our cookies if you continue to use this website.