Percents
Write 7.53% in decimal form.
7.53% → 0.0753
Is 2y+10+3x-3 a polynomial? Why or why not?
No. Polynomials must be simplified and variables cannot be divided (negative exponents mean division as do variables in the denominator).
Identify the base and the exponent of this expression: 25?
2 is the base.
5 is the exponent.
Does the model represent equivalent fractions? (Refer to picture)
a) 6/12
b) 4/8
They both cover half of the circle. They are equivalent fractions.
Name a characteristic of a histogram.
(answers may vary)
a) The bars have no gaps in between.
b) The bars are of equal width that correspond to the equal class intervals.
c) The height of each bar corresponds to the frequency of the class it represents.
15% of what gives us 150?
0.15x = 150
(0.15x)/0.15= 150/0.15
x = 1000
So, 15% of 1000 is 150
Cherice believes that the polynomial below is a cubic binomial. Vicky says that it's a linear monomial. Who do you agree with and why?
a3 + 4
Cherice is correct. Cubic describes the degree (three) and binomial describes the number of terms (two).
Bonus half: Write a polynomial expression that would make Vicky correct.
Write these two expressions using expanded multiplication notation: x5 and 32
x5 = x * x * x * x * x
32 = 3 * 3
Create an equivalent fraction by filling in the model. (Refer to picture)
multiply both numerator and denominator by 5; we get the fraction 35/20 equivalent to 7/4
List all the possible steps to find the median of a data set.
1) Rearrange the data set from least to greatest order.
2) If there's only one number in the middle of the set, that is the median
3) If there are two numbers falling in the middle of the set, you find the average/mean of those two points (add the numbers and divide by how many numbers we added).
What is 33.5% of 3/5 of $1,000?
0.335 * (3/5) * (1000) = $201
What is the degree of this term: x2y3?
2 + 3 = 5
A degree is the sum of all exponents on its variables of term. In a degree of a polynomial, you find the term with the largest sum of exponents (aka a degree). That is why you add the 2 and 3 exponents even if the variables are different.
Simplify the following:
a) x3 * x5
b) (72x4y)5
a) x8
b) 710x20y5
Write two fractions that would simplify to 2/3.
(answers may vary)
Example answer: 20/30 (multiplied 2 and 3 by 10) and 10/15 (multiplied 2 and 3 by 5)
Match the following:
a) Mean 1) 75th percentile
b) Mode 2) the middle value
c) Median 3) biggest # - smallest #
d) Range 4) min and max
e) 3rd quartile 5) add and divide; average
f) whiskers 6) most frequent
g) 1st quartile 7) 25th percentile
a5
b6
c2
d3
e1
f4
g7
You are at a restaurant and your bill is $80.50. You want to tip 20%. How much will your bill be?
$80.50 * 0.18 = approximately $16.10 (tip amount)
$80.50 + $16.10 = $96.60 (total bill)
Write this polynomial in standard form: 5n(n2 +1 - 7n) - (n3 + 8)
1) Distribute: 5n3 + 5n - 35n2 - n3 - 8
2) Simplify: 4n3 + 5n - 35n2 - 8
3) Rearrange: 4n3 - 35n2 + 5n - 8
Rewrite the following radicals in fractional exponent form.
a) sqrt(4)
b) 4sqrt(45)
a) 41/2
b) 45/4
Damian says you cannot create equivalent fractions for the number 6 because it is not a fraction. Do you agree with them? Show or explain your reasoning.
Damian is wrong.
6/1 (improper fraction). An example of its equivalent fraction could be 12/2 by multiplying both 6 and 1 by the number 2.
Note: An improper fraction is a fraction in which the numerator is greater than or equal to the denominator.
Graham has taken 5 exams in Math Lab so far. His grades are the following: 85, 97, 79, 90, and 93. He has one more exam left to take. He wants to get at least a 90 in class. What grade should he get on the last exam to get a 90 in class?
(85 + 97 + 79 + 90 + 93 + x) / 6 = 90
(85 + 97 + 79 + 90 + 93 + x) = 90 * 6
444 + x = 540
x = 540 - 444
x = 96
So, Graham needs to get a 96 on his last exam to get a 90 in Math Lab.
You have two coupons for a pizza from Dominos. One is a $5 off coupon, and the other is a 10% off coupon. Which should you apply first to save the greatest amount of money?
DOUBLE PRIZE option: Explain your answer through calculation or verbally (how the coupons work).
10% off first, then $5 off coupon
Double Prize answer:
If we do $5 coupon first, then the 10% discount is taken off our $5, essentially making it a $4.50 coupon instead. Let's say the initial cost is $20.
a) 10% off, then $5 off
0.9($20) = $18.00
$18.00 – $5.00 = $13.00 total cost
b) $5 off, then 10% off
$20.00 – $5.00 = $15.00
0.9($15) = $13.50 total cost
Create a trinomial that has degree 10 that uses at least 3 different variables.
(answers may vary)
Example: x5y2z3 + x2 + y
Simplify this radical: sqrt(25p10q2)
DOUBLE PRIZE option: simplify cuberoot(27x3y8)
5p5q
DOUBLE PRIZE answer:
cuberoot(33x3y6y2) = 3xy2cuberoot(y2)
Zizi says 3/4 and 4/3 are equivalent fractions because they use the same numbers. Do you agree with her? Show or explain your reasoning.
Zizi is incorrect. Both of these fractions are in their simplest forms, and they're not equal in value. 3/4 = 0.75 where as 4/3 = 1.3 repeating.
Charlotte had a yard sale and recorded how many items she sold in various price ranges. (refer to image)
a) Create a histogram to display the data.
b) Describe the distribution and what it means in context.
a) (refer to image)
b) The distribution is negatively skewed, meaning the majority of items she sold were cheaper. The more expensive the item, the fewer she sold.