Make your own quiz Manage my Quizzes Plans / Features Guides and Help Contact Privacy & Security

AGN108: Introductory Mathematics and Statistics for Agriculture (Quiz 1)

Department of Agric Engineering, UCC

This Quiz is a learning tool for the Introductory Mathematics and Statistics for Agriculture course. Select ONE correct answer for each of the 15 multiple choice questions in the Quiz.

After you have selected an answer option for a Question, click on the "Next" button to reveal the correct answer with its accompanying explanation. Thank you & Happy Learning!

Dr Ernest Ekow Abano, MGSAE, MASABE

Department of Agric Engineering, UCC

This Quiz is a learning tool for the Introductory Mathematics and Statistics for Agriculture course. Select ONE correct answer for each of the 15 multiple choice questions in the Quiz.

After you have selected an answer option for a Question, click on the "Next" button to reveal the correct answer with its accompanying explanation. Thank you & Happy Learning!

Dr Ernest Ekow Abano, MGSAE, MASABE

Which of the following is/are true about differentiation?

I. It is measured by the rate of change of curves

II. The rate of change is measured by the slope of the straight line

III. The rate of change is measured by a tangent line

A. I and II

B. I only

C. II and III

D. II only

E. III only

CORRECT ANSWER & EXPLANATION

The only true statement is I.

The II statement is false because the rate of change is measured by the slope of the tangent line and not the slope of just any straight line.

This makes the III statement false as well.

Hence, the correct answer is B

CORRECT ANSWER & EXPLANATION

The only true statement is I.

The II statement is false because the rate of change is measured by the slope of the tangent line and not the slope of just any straight line.

This makes the III statement false as well.

Hence, the correct answer is B

The data below shows the marks obtained by a class of Level 100 students, after a test;

5, 3, 6, 9, 3, 4, 2, 8, 7, 6, 5, 1, 3, 9, 4, 3, 8, 10, 11

Use the data above to Find the mean

A. 2.5

B. 3.0

C. 4.4

D. 5.0

E. 5.6

CORRECT ANSWER & EXPLANATION

The formula to compute the basic mean or average is:

And there are 19 numbers in the list

The correct option is therefore E

CORRECT ANSWER & EXPLANATION

The formula to compute the basic mean or average is:

And there are 19 numbers in the list

The correct option is therefore E

The data below shows the marks obtained by a class of Level 100 students, after a test;

5, 3, 6, 9, 3, 4, 2, 8, 7, 6, 5, 1, 3, 9, 4, 3, 8, 10, 11

Use the data above to Determine the median

A. 2.5

B. 3.0

C. 4.4

D. 5.0

E. 5.6

CORRECT ANSWER & EXPLANATION

The median is the middle value when the numbers are arranged in either ascending or descending order.

1,2,3,3,3,3,4,4,5,5,6,6,7,8,8,9,9,10,11

Since there are 19 numbers, count nine numbers from either end of the list (a total of 18 numbers).

This leaves the middle value as 5 and therefore the correct answer is D

CORRECT ANSWER & EXPLANATION

The median is the middle value when the numbers are arranged in either ascending or descending order.

1,2,3,3,3,3,4,4,5,5,6,6,7,8,8,9,9,10,11

Since there are 19 numbers, count nine numbers from either end of the list (a total of 18 numbers).

This leaves the middle value as 5 and therefore the correct answer is D

The average of a list of 10 numbers is 15. If one of the numbers is removed, the average of the remaining numbers is 14. What is the missing number that was removed?

A. 10

B. 20

C. 21

D. 22

E. 24

CORRECT ANSWER & EXPLANATION

The question is about the application of averages to find missing numbers.

The sum of the numbers is 150.

When a number was removed from the list of 10 numbers, the equation now becomes

Here the sum is: 126 (That is 9 x 14)

Therefore the number removed is the difference between the sums

i.e. 150 - 126 = 24

The correct answer is therefore E

CORRECT ANSWER & EXPLANATION

The question is about the application of averages to find missing numbers.

The sum of the numbers is 150.

When a number was removed from the list of 10 numbers, the equation now becomes

Here the sum is: 126 (That is 9 x 14)

Therefore the number removed is the difference between the sums

i.e. 150 - 126 = 24

The correct answer is therefore E

A manufacturer has found that marginal cost is 3q² - 60q + 400 Ghana Cedis per unit when q units have been produced. The total cost of producing the first 2 units is GH¢ 900. What is the total cost of producing the first 5 units in GH¢?

A. 1375

B. 1587

C. 2663

D. 2875

E. 3087

CORRECT ANSWER & EXPLANATION

Marginal cost is the rate of change in the total cost arising from quantity produced per unit. Therefore, the equation given represents the differential of producing different quantities of the goods. Hence,

Implying that to get the total cost function of producing each item, one needs to integrate the marginal cost function. Therefore,

Where C is the constant of integration.

Given that when Q is 900, q is 2. Substituting this function into the total cost function,=>

The total cost of producing 5 units is therefore

The correct answer is therefore B

CORRECT ANSWER & EXPLANATION

Implying that to get the total cost function of producing each item, one needs to integrate the marginal cost function. Therefore,

Where C is the constant of integration.

Given that when Q is 900, q is 2. Substituting this function into the total cost function,=>

The total cost of producing 5 units is therefore

The correct answer is therefore B

The graph above shows how the Jackson family continues to grow between 1991 and 1998 by indicating the total number of children in the family at the end of each year. The Jackson's have one set of twins who were born to Mrs Jackson one year in July. During what year were the twins born?

A. 1998

B. 1997

C. 1996

D. 1994

E. 1993

CORRECT ANSWER & EXPLANATION

The principle of statistics to use in answering this question, is the principle of cumulative frequency and observation of the bars in the chart.

The Number of people in a family is accumulated as the years go by.

From the chart, in 1992, one child was born.

No child was born in 1993, that is why the bar in 1993 is constant.

But in 1994, another child was born into the family.

By extension of the principle, one can see that it was in 1997 that two people were born into the family.

And since it’s impossible to give two separate births in a year by humans, it presupposes twins were born into the Jackson family in 1997, making B the correct answer

CORRECT ANSWER & EXPLANATION

The principle of statistics to use in answering this question, is the principle of cumulative frequency and observation of the bars in the chart.

The Number of people in a family is accumulated as the years go by.

From the chart, in 1992, one child was born.

No child was born in 1993, that is why the bar in 1993 is constant.

But in 1994, another child was born into the family.

By extension of the principle, one can see that it was in 1997 that two people were born into the family.

And since it’s impossible to give two separate births in a year by humans, it presupposes twins were born into the Jackson family in 1997, making B the correct answer

The sample mean of x and y is k, which of the following is the mean of x, y, and z?

CORRECT ANSWER & EXPLANATION

This question is about the mean or average of algebraic expressions. Algebraic expressions can be averaged in the same way as any other values of figures.

The mean of x, y, and z is:

But x + y = 2k, implying that,

The correct answer is therefore A.

CORRECT ANSWER & EXPLANATION

This question is about the mean or average of algebraic expressions. Algebraic expressions can be averaged in the same way as any other values of figures.

The mean of x, y, and z is:

But x + y = 2k, implying that,

The correct answer is therefore A.

The owner of a shoe boutique wants to know which size of shoes to stock to cover all sizes recently sold on campus. Which of the shoe sizes should he or she stock in large quantities?

A. Mean of the sizes

B. Median of the sizes

C. Range of the sizes

D. Variance of the sizes

E. Mode of the sizes

CORRECT ANSWER & EXPLANATION

The question is asking for the possible sizes of shoes, from the maximum through to the minimum .

The correct option here is C, which is the range of the Shoe Sizes

CORRECT ANSWER & EXPLANATION

The question is asking for the possible sizes of shoes, from the maximum through to the minimum .

The correct option here is C, which is the range of the Shoe Sizes

The sum of two numbers that differ by 1 is in terms of t, what is the value of the greater number of the two numbers?

CORRECT ANSWER & EXPLANATION

Let x and y be the two numbers and assume that x is greater than y.

→ x - y = 1 or y = x - 1

Given that the sum of the two number is t implies that

x + y = t and

x = t - y but

y = x - 1

meaning

x = t - (x - 1)

x = t - x + 1

x + x = t + 1

2x = t + 1

Therefore the correct answer is C.

CORRECT ANSWER & EXPLANATION

Let x and y be the two numbers and assume that x is greater than y.

→ x - y = 1 or y = x - 1

Given that the sum of the two number is t implies that

x + y = t and

x = t - y but

y = x - 1

meaning

x = t - (x - 1)

x = t - x + 1

x + x = t + 1

2x = t + 1

Therefore the correct answer is C.

The sum of four consecutive odd integers w, x, y, and z is 24.

What is the median of the set

A. 3

B. 5

C. 7

D. 9

E. 24

CORRECT ANSWER & EXPLANATION

Odd integers are numbers that are not divisible by 2. In other words they are not multiples of two.

The consecutive odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19…

So we look for four consecutive numbers that sum up to 24 to represent w, x, y, and z.

They are 3,5,7, and 9.

→ The set

becomes

The middle number of the set is 7. Option C is the answer

CORRECT ANSWER & EXPLANATION

Odd integers are numbers that are not divisible by 2. In other words they are not multiples of two.

The consecutive odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19…

So we look for four consecutive numbers that sum up to 24 to represent w, x, y, and z.

They are 3,5,7, and 9.

→ The set

becomes

The middle number of the set is 7. Option C is the answer

The average of x and y is 5 and the average of x, y, and z is 8. What is the value of z?

A. 19

B. 14

C. 13

D. 11

E. 3

CORRECT ANSWER & EXPLANATION

By the principle of averages:

Substituting the value of x+y=10 into the other equation, we have:

⇒ 10 + z = 24

z = 24 - 10 = 14

The correct answer is B

CORRECT ANSWER & EXPLANATION

By the principle of averages:

Substituting the value of x+y=10 into the other equation, we have:

⇒ 10 + z = 24

z = 24 - 10 = 14

The correct answer is B

According to the graph above, between which two consecutive years was the greatest change in the price of cashew nut?

A. 1981 and 1982

B. 1982 and 1983

C. 1983 and 1984

D. 1984 and 1985

E. 1985 and 1986

CORRECT ANSWER & EXPLANATION

The question is asking for the highest price change regardless of whether it is a decrease or an increase.

Simply study the graph and subtract the prices between two consecutive years (i.e 1982 and 1983; 1984 and 1985; and 1985 and 1986 etc..)

The price change between 1982 and 1983 is [4.25 - 3.50] = 0.75

The price change between 1984 and 1985 is [4.75 - 3.75] = 1.0

The price change between 1985 and 1986 is [4.50 - 3.75] = 0.75

The highest price change occurs between 1984 and 1985.

The correct answer is D

CORRECT ANSWER & EXPLANATION

The question is asking for the highest price change regardless of whether it is a decrease or an increase.

Simply study the graph and subtract the prices between two consecutive years (i.e 1982 and 1983; 1984 and 1985; and 1985 and 1986 etc..)

The price change between 1982 and 1983 is [4.25 - 3.50] = 0.75

The price change between 1984 and 1985 is [4.75 - 3.75] = 1.0

The price change between 1985 and 1986 is [4.50 - 3.75] = 0.75

The highest price change occurs between 1984 and 1985.

The correct answer is D

The results of a survey of 16 students at University of Cape Coast are given in the grid above. It shows the distance, to the nearest miles, that students at various grade level walk to lecture halls.

How many students travel more than 5 miles to lectures?

A. 4

B. 6

C. 7

D. 8

E. 9

CORRECT ANSWER & EXPLANATION

Count the number of data points after 5 miles on the distance axis.

You will count 3 data point on 6 miles, 3 data point on 7 miles and 2 data points on 8 miles.

Summing the data points (3 + 3 + 2) = 8

Therefore, the correct answer is D

CORRECT ANSWER & EXPLANATION

Count the number of data points after 5 miles on the distance axis.

You will count 3 data point on 6 miles, 3 data point on 7 miles and 2 data points on 8 miles.

Summing the data points (3 + 3 + 2) = 8

Therefore, the correct answer is D

What is/are the grade(s) of students who travel less than three miles to lecture halls?

A. Below 12th grade

B. Below 11th grade

C. Above 9th grade

D. Between 10th and 1th grade

E. None of the above

CORRECT ANSWER AND EXPLANATION

Observe the grades on the Grade axis for students who travel for 1 or 2 miles to the lecture hall.

You will notice that the grades that fall into this category are the 9th, 10th and 11th Grades.

None of the answer options from A to D match this.

The correct answer is therefore E

CORRECT ANSWER AND EXPLANATION

Observe the grades on the Grade axis for students who travel for 1 or 2 miles to the lecture hall.

You will notice that the grades that fall into this category are the 9th, 10th and 11th Grades.

None of the answer options from A to D match this.

The correct answer is therefore E

Which of the following is true about the students who travel 7 or more miles to lecture hall?

A. Half are 9th graders

B. Half are 10th graders

C. All of them are 11th graders

D. 40 % of them are 12th graders

E. None of the above

CORRECT ANSWER & EXPLANATION

Count the number of data points or students who travel 7 miles or more to lecture hall.

You will find five (5) data points or students.

Out of the five students, 2 are 12th graders, 1 is an 11th grader, and 2 are 9th graders.

2 out of 5 is the same as 40%.

Therefore, 40% are 12th graders

20% are 11th graders and

40% are 9th graders.

Hence the correct answer is D.

CORRECT ANSWER & EXPLANATION

Count the number of data points or students who travel 7 miles or more to lecture hall.

You will find five (5) data points or students.

Out of the five students, 2 are 12th graders, 1 is an 11th grader, and 2 are 9th graders.

2 out of 5 is the same as 40%.

Therefore, 40% are 12th graders

20% are 11th graders and

40% are 9th graders.

Hence the correct answer is D.

{"name":"AGN108: Introductory Mathematics and Statistics for Agriculture (Quiz 1)", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"AGN108: Introductory Mathematics and Statistics for Agriculture (Quiz 1)","img":"https://cdn.poll-maker.com/8-401231/mas.jpg?sz=1200-000000100053"}