WorksheetsFINAL EXAMINATION in GE 3 (Mathematics in the Modern World)
Total questions: 48
Worksheet time: 2hrs 36mins
What is mode?
The middle number in an ordered set of data.
The value that occurs the most often in a data set.
The sum of all the numbers in a data set divided by the size.
The sum of the between the greatest and the least elements, divided by two.
What is the most common used indicator of the degree of dispersion and is also the most dependable measure to estimate the variability in a total population?
Mean Deviation
Range
Standard Deviation
Variance
Which is NOT a characteristic of normal distribution?
Symmetrical
Bell-shaped
Random
Continuous
What is the purpose of z-scores?
To describe the exact location of a score within a distribution
To find the standard deviation of the distribution
To find the mean of the distribution
To describe the shape of the distribution
Which of the following is NOT a measure of dispersion?
standard deviation
percentile
range
variance
Kate took a sample of 50 pieces of data. She added up all of the pieces of data and then divided by 50. What measure of center is she working on?
Mean
Median
Mode
Range
What does the standard deviation represent?
How many different variations are in the data set.
How spread out each data value is from the mean.
How the population varies compared to the sample.
The range, but with a bunch of other stuff going on.
If a number is added to a set that is far away from the mean, how does this affect standard deviation?
The standard deviation will increase
The standard deviation will decrease
The standard deviation becomes zero
It has no effect
The mode score on the 6th grade math test was 94. Which of these interpretations must be correct?
94 was the highest score on the test.
No student scored below a 94.
More students received a 94 than any other score.
A score of 91 was slightly below average.
If a number is added to a set that is far away from the mean, how does this affect standard deviation?
The standard deviation will increase
The standard deviation will decrease
The standard deviation becomes zero
It has no effect
What is the range of 45, 56, 23, 74, and 63?
23
51
40
86
What is the average height of the following students whose height are 6.5, 5.3, 3.4, 4, and 5.5?
4.82
5.93
4.94
4.52
On an examination given to 8600 students, Hal’s score of 405 was higher that the scores of 2236 of the students who took the examination. What is the percentile for Hal’s score?
25th
27th
28th
26th
Roland received a score of 70 on a test for which the mean score was 65.5. Roland has learned that the z-score for his test is 0.6. What is the standard deviation for this set of test scores?
4.5
5.5
6.5
7.5
Given the sample data, what is its sample variance? 25, 16, 29, 13, 16, 12
629.15
2220
3958.33
4750
A data set has a mean of x̄=443 and a standard deviation of 8. What is the z-score of x=429?
z429=−0.78
z429=−1
z429=0.78
z429=1
Marco’s score in a 75-item test was the median score. Which of the following is true?
75% of his classmates got a score equal or below his score.
60% of his classmates got a score equal or below his score.
50% of his classmates got a score equal or below his score.
35% of his classmates got a score equal or below his score.
If the standard deviation of a data is 4.5 and if each value of the data is decreased by 5, what is the new standard deviation?
4.5
5.0
0
9.0
Which of the following pairs of variables has the highest possibility to be related?
lifestyle of a person ; lifespan of a person
number of fishes in the sea ; number of animals in the land
number of full moons in a month ; number of birth in a month
length of legs of a human ; number of achievements of a human
Use the box-and-whisker plot below to determine which statement is accurate?
One half of the cholesterol levels are between 180 and 197.5.
One half of the cholesterol levels are between 180 and 211.
About 75% of the adults have cholesterol levels less than 180.
About 25% of the adults have cholesterol levels of at most 211.
Which of the following pairs of variables has the highest possibility to be related?
lifestyle of a person ; lifespan of a person
number of fishes in the sea ; number of animals in the land
number of full moons in a month ; number of birth in a month
length of legs of a human ; number of achievements of a human
The Jackson triplets, Jenny, John, and James, are in different algebra classes at City High. On their final exams, Jenny scored 77 on a test with a mean of 69 and a standard deviation of 11; John scored 79 on a test with a mean of 73 and a standard deviation of 9; and James scored 75 on a test with a mean of 67 and a standard deviation of 10. Who had the best score?
James
Jenny
John
None of these
Jenny scored at the 99th percentile on a test. How should we interpret this information?
Jenny scored the highest on the test.
Jenny scored 99 percent on the test.
Jenny scored better than 99 percent of students who took the test.
Jenny belongs to the 99 percent of the students who score better on the test.
What measure of central tendency (mean, median or mode) would be best for the following set of data? 0, 89, 92, 97, 99, 100
Mode, because it is the one that shows up the most.
There is not a best measure of central tendency for this data.
Mean, because there is not an outlier. You should always use the mean.
Median, because there is an outlier. The outlier could be incorrect and would influence the mean too much.
Interest paid on the original principal plus the accumulated interest is referred as what?
Simple Interest
Compound Interest
Exact Interest
Ordinary Interest
The simple interest formula is I=Prt. What does the P represent the principle?
The amount the bank owes you for being a customer at their bank.
The amount of money borrowed or deposited.
The percent interest for his year.
The amount taxed.
The simple interest formula is I=Prt. What does the t represent?
Principle
Time, in years
Time, in hours
Interest
Dylan invested money from China Bank at 1.05% simple interest for 3 years. It was charged P 472.50 for interest. What is P472.50 in the given?
Principal
Future Value
Interest
Rate
Dylan invested money from China Bank at 1.05% simple interest for 3 years. It was charged P 472.50 for interest. What is 1.05% in the given?
Rate
Simple Interest
Interest
Percentage
Dylan invested money from China Bank at 1.05% simple interest for 3 years. It was charged P 472.50 for interest. What formula will be used to determine the amount of borrowed money?
I=Prt
I=F(1+j)n
P=I/rt
P=(1+r)tF
Why does compound interest generally yield a higher accumulated amount than simple interest for the same principal, rate, and time?
Because simple interest uses a higher interest rate than compound interest.
Because compound interest adds interest only at the end of the term.
Because it earns interest on both the principal and the previously earned interest.
Because simple interest subtracts interest from the principal each year.
Which of the following sentence is a statement?
How many odd integers are there between 40 and 120?
Be sure to round your answers to the nearest 100th.
If x is a number, then x^3 is even.
Natural numbers are better than whole numbers.
Which of the following describes rate (i)?
It is the amount paid or earned for the use of money.
It is charged by the lender, or rate of increase of the investment.
It is the amount of money borrowed or invested on the origin date.
It is computed on the principal and also on the accumulated past interests.
If you are calculating the simple interest and you are given the time in months. How can you find the time in years?
divide 12 by the months
divide the months by 12
multiply 12 times the months
change the months to a decimal
Suppose an amount of P4000 was deposited in a bank and it became P4085 after 3 months, what is the interest rate?
7.5%
8.0%
8.5%
9.0%
An amount of P1000 was deposited in an account earning 5% interest, compounded semiannually. How much is in the account at the end of 1 year?
P50.00
P50.63
P1050.00
P1050.63
What is the negation of the quantified statement below? Then determine the negation’s truth value.
Every boy likes math.; True
Some boys like math.; True
Some boys like math.; False
Every boy likes math.; False
An amount of P1000 was deposited in an account earning 5% interest, compounded semiannually. How much interest is in the account at the end of 1 year?
P50.00
P50.63
P1050.00
P1050.63
A bank is offering 2.5% simple interest on a savings account. If you deposit P5,000, how much interest will you earn in three years?
P5375
P375
P37500
P42500
A principal amount of P8,000 is invested at 6% annual interest. How much more will it earn under compound interest (compounded annually) than under simple interest after 3 years?
P8.64
P18.72
P28.64
P32.48
A couple plans to invest money for their child’s college education. What principal must be deposited by the parents when their child turns 7 in order to have P30,000 when the child reaches the age of 18? Assume the money earns 6% interest, compounded quarterly.
P15,581.72
P15,803.63
P18,072.29
P57,759.99
How can you make sure that compounding works out in your favor?
When growing your savings, time is your friend. The longer you can leave your money untouched, the greater it can grow, because compound interest grows exponentially over time.
Paying the minimum on your credit cards will cost you dearly because you’ll barely make a dent in the interest charges and your balance could actually grow.
In addition to affecting your monthly payment, keep your borrowing rates high because the interest rates on your loans determine how quickly your debt grows.
All of these.
Two students invested the same principal at 5% for 4 years. Student A used simple interest, while Student B used compound interest (annually). By analyzing the growth patterns, which statement best explains why Student B ends with a higher amount?
Simple interest decreases each year while compound interest remains constant.
Compound interest grows faster because each year’s interest is computed on an increasing base.
Compound interest uses a different formula that always doubles the money while simple interest does not double.
You are comparing two investment offers for ₱10,000 at 6% interest for 5 years. Investment X uses simple interest, while Investment Y compounds quarterly. Based on how interest accumulates, which factor most contributes to Investment Y having the higher future value?
The principal used for simple interest is smaller compared to the compound interest.
Quarterly compounding reduces the interest because the compounding periods are shorter.
Simple interest adds a penalty each quarter while the compound interest doubles every year.
Quarterly compounding increases the frequency of interest addition, raising the effective annual rate.
Two banks offer the same rate and time period. Bank A compounds annually, while Bank B compounds monthly. When analyzing their results, which conclusion is valid?
Annual compounding always gives more than monthly compounding than the simple interest.
Monthly compounding reduces the amount earned because interest is divided into smaller parts.
Monthly compounding yields a slightly higher amount because interest is added more frequently.
Both banks produce the same amount because the rate is the same thus yielding the same amount after the period.
A bank offers a savings account with 5% interest rate, compounding annually. Another bank offers savings account with 3% interest rate, compounding quarterly. Suppose you want to deposit an amount of ₱5000, which of the two would give you a higher amount after 1 year? Why?
The bank that offers 5% interest rate, because it compounds only once a year.
The bank that offers 3% interest rate, because it compounds four times a year.
The bank that offers 5% interest rate, because it offers higher interest than the other bank.
The bank that offers 3% interest rate, because it will give me an amount of ₱5250 as compared to the ₱5248 of the other bank.
Both Ryan and Tom open their accounts with an initial deposit of ₱3500. They are both planning a six-year investment and will withdraw their money after 6 years. Who will have a greater balance in six years? How much more will that person have? Ryan’s Saving Account: The interest rate is 4.75% and is compounded annually. Tom’s Savings Account: The simple interest rate is 5.75%.
Tom will have ₱83.77 more than Ryan.
Ryan will have ₱83.77 more than Tom.
Ryan will have ₱3416.23 more than Tom.
Tom will have ₱3416.23 more than Ryan.
Which of the following biconditional statements are TRUE? I. x² = 4 if and only if x = 2 II. |x – 5| < 0 if and only if x ≠ 5 III. x + 3 < 4 if and only if x + 3 < 0
II only
I and III
II and III
all three are equivalent
