substitution or elimination and inequalities
Simplifying Exponents
Polynomials
Quadratics
Probability and Data Analysis
100
Solve by substitution:
Express your answer as an ordered pair.
x + y = -1
x= y + 7
(3,-4)
100
Simplify.
100
Factor
5(m-1)-7m(m-1)
(m − 1)(5 − 7m)
100
Find the zeros and the axis of symmetry of the parabola.
zeros: −2, −6; x = −4Explanation:
The zeros are −6 and −2.
To find the axis of symmetry find the average of the zeros.
x = 
= −4
100
The probability of a spinner landing on green is 25%. What are the odds of the spinner NOT landing on green?
Odds against 75:25 or 3:1
The odds of the spinner NOT landing on green are 3:1
200
Solve by Elimination:
Express your answer as an ordered pair.
3x -2y = 21
-4x -5y = -5
(5,-3)
200
Write the expression using only positive exponents. Assume no denominator equals zero.
625z8/81y32
200
Factor the polynomial by grouping.
3x3 + 6x2 − 2x − 4
(x + 2)(3x2 − 2)Explanation:
3x3 + 6x2 − 2x − 4
Group terms that have a common
number or variable as a factor.
= (3x3 + 6x2) − (2x + 4)
Factor out the GCF of each group.
= 3x2(x + 2) − 2(x + 2)
x + 2 is a common factor.
= 3x2(x + 2) − 2(x + 2)
Factor out x + 2.
= (x + 2)(3x2 − 2)
200
Solve the quadratic equation x2 − 4x = 21 by factoring.
x = 7; x = −3
Explanation:
x2 - 4x = 21
x2 - 4x - 21 =0 Write the equation in standard form.
(x - 7)(x + 3) =0 Factor the trinomial.
x - 7 = 0 or x + 3 =0. Use the Zero Product Property.
x =7 or x =-3 Solve each equation.
The solutions are 7 and -3.
200
Decide if the following is a combination or permutation. Then give the number of possible outcomes.
To decide which team will lead the class discussion, a teacher writes the names of 5 students on slips of paper and puts them in a hat. Then she draws 2 names. How many teams of two are possible?
Combination.
10 possible teams of 2.
C = 5!/2!(5-2)! = 5!/2!3! = 10
300
Solve the given system using elimination.
p = -5
q = -1
300
Subtract
(9c5 − c4 )−(c5 + 3c4 − 1)
8c5 − 4c4 + 1
300
Factor 3x2 + 2x − 8
(x + 2)(3x − 4)
300
Use the Zero Product Property to solve the equation
(x – 4)(x + 5) = –18.
The solutions are −2 and 1
Explanation:
(x − 4)(x + 5) = −18
FOIL. x2 + x − 20 =−18
Write the equation in standard form
x2 + x − 2 =0
Factor the trinomial
x − 1)(x + 2) = 0
Use the Zero Product Property.
x − 1 =0. or. x + 2 =0
Solve each equation
x =1 or x =−2
The solutions are 1 and −2.
300
Constellations are made up of more than one star. The table shows the number of stars that make up various constellations. Find the mean, median, mode, and range of the data set
mean = 34.8; median = 34;
mode = 28; range = 19
400
Solve by using substitution. Express your answer as an ordered pair.
(2,-3)
400
Write the product in scientific notation.
(7.15×104)(2.8×10−3)
400
Determine whether 4x2 + 6x + 9 is a perfect square. If so, factor it. If not, explain why.
No, 4x2 + 6x + 9 is not a perfect square.
4x2 and 9 are perfect squares, but 6x is not equal to 2(2x)(3).
So 4x2 + 6x + 9 is not a perfect square.
Explanation:
4x2 + 6x + 9
a = 2x, b = 3
= (2x)2 + 2(2x ⋅ 3) + 32
Write the trinomial as a2 + 2ab + b2.
Since 2(2x ⋅ 3) ≠ 6x, 4x2 + 6x + 9 is not a perfect-square trinomial.
400
Solve the equation x2 − 6x − 2 = 0 by completing the square.
Explanation:
400
At a race track, the average speed of the race cars is measured every lap. The box-and-whisker plot represents the average speed of a certain car for several laps. What is the median?
131
500
Is (-4,6) a solution to the given system. Show your work
y ≤ 3 - x
y > x + 4
YES:
(-4,6)
y ≤ -x +3
6 ≤ 4+3
6 ≤ 7
y > x+4
6 > -4 + 4
6 > 0
500
Simplify. Write the expression using only positive exponents.
Assume no denominator equals zero.
500
Factor the polynomial 7xy + 14x − 35y − 70 completely
7(x − 5)(y + 2)
Explanation:
7xy + 14x − 35y − 70
= 7(xy + 2x − 5y − 10)
Factor 7 from the polynomial.
= 7[x(y + 2) − 5(y + 2)]
−5(y + 2) = − 5y − 10
= 7(x − 5)(y + 2)
Factor (y + 2) from both terms.
500
The height in feet of a baseball can be modeled by the function y = −16t2 + 64t, where t is the time in seconds after the ball is hit. Find the baseball's maximum height and the time it takes to reach this height. Then find how long the baseball is in the air.
64 ft; 2 s; 4 s
Explanation:
y = −16t2 + 64t
Step 1 Find the axis of symmetry.
The axis of symmetry is x = 2.
Step 2 Find the vertex.
y = −16(2)2 + 64(2)
y = −64 + 128
y = 64
The vertex is (2, 64).
The baseball's maximum height is 64 ft and it takes 2 s to reach this height.
The baseball takes the same time to fall back to the ground. Therefore it is in the air for 4 s.
500
The scores of 9 students in a test are 6, 10, 7, 11, 13, 17, 14, 19, and 10. Find the mean, median, mode, and range of the data set. Round to the nearest hundredth if necessary.
mean: 11.89; median: 11; mode: 10; range: 13