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Math Diagnostic Quiz: Core Topics

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Algebra and data analysis

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Math Diagnostic Quiz: Core Topics
 

Math Diagnostic Quiz: Core TopicsOnline version

Algebra and data analysis

by Andrea Gastelum
1

In a parking lot, 35 vehicles total and 110 tires. How many cars and motorcycles are there if cars have 4 tires and motorcycles 2?

2

Simplify: (3x^3y^3)(2x^-1y^2)/(6x^8y^5).

3

If alternate interior angles are equal: (3x+10)° = ? (5x-20)°

4

For the quadratic sequence 2,6,12,20,30,..., find a,b,c in an^2+bn+c.

5

What is the 15th term of the sequence 2,6,12,20,30,...?

6

Mean of the data set 5,7,7,8,8,8,9,9,10,10 is 8.1. If 5 is removed, what is the new mean?

7

With 5 removed, what is the new median of the data 7,7,8,8,8,9,9,10,10?

8

Original dataset median is 8. What is the effect on the median if 5 is removed?

9

Original dataset mean and median (before removal) were 8.1 and 8. Which statement is true after removing 5?

10

What is the total number of wheels after removing the 5 from the dataset?

Feedback

Let c+m=35 and 4c+2m=110. Solve to get c=20, m=15.

Combine exponents: x^(3-1-8)=x^-6 and y^(3+2-5)=y^0.

Set the two alternate interior angles equal and solve for x.

t_n = n(n+1) matches a=1, b=1, c=0.

t_n = n^2+n; t_15 = 15^2+15 = 240.

New sum=76, n=9, mean≈76/9≈8.44.

Median of 9 values is the 5th value, which is 8.

Removing the smallest value does not change the middle value for this dataset.

Removing the lowest value raises the mean; the median remains 8.

Original sum 81; remove 5 reduces sum to 76; 9 values remain.

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