Transcript Algebra & Eqns

Grade 9 Math Review
Algebra
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Simplifying (collecting like terms)
Expanding (distributive property)
Properties of polynomials (terms)
Solving equations (simple, fractions)
Writing word and algebraic equations
Exponent Laws
Examples…
Question 1: Evaluate (-3)4
Answer: 81
Question 2: Write as a single power.
23 x 22 x 24
Answer:
2
9
Examples…
Question 3: Classify each polynomial
by the number of terms and degree.
a) x2 + 3x
b) 6a2b – 4b5 + a3b3
Answer a): Binomial of degree 2 (or 2nd degree)
Answer b): Trinomial of degree 6 (or 6th degree)
Examples…
Question 4: Simplify 7k + 5m – k – 6m
Answer: 6k - m
Question 5: Simplify
-3(2x – 6) – (8 – 6x)
Answer:
= -6x + 18 - 8 + 6x
= 10
Examples…
Question 6: Solve 2y – 7 = 13
Answer: 2y – 7 = 13
2y = 20
2y – 7 + 7 = 13 + 7
2y = 20
2
y = 10
y 8 y  4
Question 7: Solve

3
2
Answer: 6 y – 8 = y + 4 6
3
2
2
2(y-8) = 3(y+4)
2y – 16 = 3y + 12
-y = 28
-1
-1
y = -28
Examples…
Question 8: A triangle has angle
measures that are related as follows:
• the largest angle is eight times the
smallest angle
• the middle angle is triple the smallest
angle
Determine the measure of each angle.
Answer #8
Let s = the measure of the smallest angle
s + 3s + 8s =
180
12s =
180
12
s=
12
15
Therefore, the smallest angle is 15, the
middle angle is 45 , and the largest angle
is 120 .
Equations of Lines
• 2 key forms (standard and slope-yintercept form)
• Special cases of lines (horizontal,
vertical, parallel, perpendicular)
• Linear Systems (# of solutions)
Examples…
Question 9: Identify the slope and the
y-intercept of the line y = -3x + 2.
Answer: m = -3
b = 2
Question 10: Determine the slope and yintercept of the line 3x + 5y + 15 = 0.
Answer: Rearrange into y = mx + b first!
5y = -3x – 15
5 = 5
5
y = -3/5x – 3
Therefore, m=-3/5 and
b = -3
Examples…
Question 11: Determine the equation
of the line with slope 0.5 and passing
through the point (1,-4).
Answer: Step 1) Substitute m, x, and y
into y = mx + b and solve for b
y = mx + b
-4 = 0.5(1) + b
Step 2) Create your
equation using m and b:
-4 = 0.5 + b
-4 – 0.5 = 0.5 – 0.5 + b
-4.5 = b OR b = -4.5
y = 0.5x – 4.5
Examples…
Question 12: Determine the equation
for the line passing through (-2,5)
and (3,-5).
Answer:
Step 1) Calculate slope using the two points
Step 2) Use x and y from one point and
substitute into y = mx + b to solve for b
Step 3) Create your equation with m and b
Examples…
Question 13: Cindy is at a baseball game
with her younger brother, Mike. She has
$18 to spend on hamburgers and pop.
Hamburgers cost $3 each and pop cost
$2 each.
a) If Cindy buys only hamburgers, how many
can she buy?
b) Determine an equation to model the cost
scenario.
Answer a): She can buy 6 hamburgers.
Answer b):
C = 3h + 2p
Examples…
Question 14: Determine the number
of solutions to the linear system
y = 3x – 7
y = -3x + 5
Answer a): There is exactly one solution
to this linear system
Examples…
Question 15: Determine the equation
of the line parallel to 3x – 4y = 12 and
with an x-intercept of 6.
Answer: y = ¾x – 4.5