Math Lessons 1-16

measurement error

(meausred value-exact value)(100) / (exact value)

Solve: -5√2 x 2√5

-10√10

Solve: (-35√10)/ 5√2

-7√5

Simplify: -11√2 + 7√3 + 5√2 - 2√3 + 5√2

-√2 + 5√3

ABC electronics has put plasma TVs on 40% sale for the new year. Kevin has a coupoun which gets him an additional 20% off on the sale price. If the original price of the TV is 2500, at what price can Kevin buy the TV at the new year sale?

1200

A town named Appleville was established in the year 1960 with an initial population of 75. If the population of Appleville is doubling every 10 years, what is the projected population in the year 2040?

19200

When a positive integer y is divided by 7, the remainder is 4. What is the remainder when y+5 is divided by 7?

2

When a number n is divided by 8 the remainder is 7, what is the remainder if n is divided by 4?

3

A school has 125 seventh graders. Among them, 67 students are in tech ed and 38 are in art classes. Among the students who are in the tech ed class 10, are in the art class as well. How many seventh graders in the school are not in either tech ed or art classes?

30

What is the eleventh term of the geometric sequence: 3, 6, 12, 24 ....?

3072

Siri invested money on a stock, whose value decreased by 25% in the first month. What should be the percentage change in the second month for the stock to go back to its original value?

33.33%

What is the sum of the first nine terms of the geometric sequence: 20, 10, 5 .......?

40

The average income of 5 members in a family is $36,500. The average income of a neighboring family with 2 members is $52,000. What is the average income of both families combined?

40,928.57

The sum of the first two terms of a geometric progression is 36 and the product of the first and third terms is 9 times the second term. Find the sum of the first 8 terms.

40.5

(625)^1/4

5

If 3^4 + 3^4 + 3^4 = 3^n, what is the value of n?

5

What is the sum of the first 100 counting numbers?

5050

Solve: 4√2 x 7√2

56

Find the 20th term given that the third term is 9 and the 8th term is 24

60

What is the median of the set of all factors of 48?

7

The repairman estimated that it would cost $180 to repair my car. In fact, after repairs, I was charged $195. What was the percentage error in the estimate?

7.7%

Find the LCM of 84 and 120

840

rate

A ratio that compares two quantities measured in different units

Population growth or decline

P_f= P_i × r^n with n=(t_f - t_i)/t_r)

Median

The middle point after arranging all data points in either ascending or descending order

Sum of Infinite geometric sequence when x is -1<x<1

a [1/(1-r)]

ratio

a fraction that compares two quantities, which are measured in the same units

Sum of the first n terms of a geometric sequence

a1(1-r^n)/1-r

percent of a percent

n=(x/100)(y/100)(z)

Mean

obtained bydividing the sumof all data points with the total number of data points

Sum of the first n terms of an arithmetic sequence

sum= n((a1+an)/2)

Mode

the most frequently occurring data point

mutually exclusive or disjoint

when two sets do not have any shared elements

Anita can make "a" number of widgets in b days. How many widgets can she make in c days?

x = (a/b)c

When a number y is divided by x the quotient is 3 and the remainder is 5, what is y in terms of x?

y=3x+5

If a positive integer y is divided by x, the quotient if 5 and the remainder is 2. Express y in terms of x.

y=5x+2

Express 42 in the prime factorization form

(2)(3)(7)

Express 156 in the prime factorization form.

(2^2)(3)(13)

Express 36 in prime factorization form

(2^2)(3^3)

Set A as 3 elements, whose average is m and set B has 5 elements, whose average is n. What is the average of elements in set A and set B combined?

(3m+5n)/8

Weighted average

(am+bn+cp)/(m+n+p), where a, b, and c are mean values of sets a, b, and c, and where m, n, p are number of data points in the respecitve set

percentage error

(approximate value - exact value)(100) / (exact value)

For the numbers 13, 16, 12, 11, 8, 14, 12, and 18, which of the following is true? (a) median>mean>mode (b) mean>mode>median (c) mean>median>mode

(c) mean>median>mode

Percent change

(new value-original value)(100) / (original value)

If n=(a^x)(b^y)(c^z), where a, b, and c are prime numbers, then the number of factors of n is equal to....

(x+1)(y+1)(z+1)

The lowest temperature yesterday was -27 degrees Fahrenheit. If the lowest temperature the day before was -12 degrees Fahrenheit, what was the percentage change in the temperature?

-125%

The third term of a geometric sequence is -20 and the sixth term is -160. What is the tenth term of the sequence?

-2560

Andrew invested money on a stock, whose value decreased by 30% in the first month. In the next month, the value of the stock increased by 30%. What is the net percentage change in the value of the stock in the two month period?

-9%

Sam invented a new anti-bacterial medicine, which he named as Samicin. When treated with Samicin, the bacteria have a half-lifetime of 4 hours. By what fraction the bacterial count, in the blood sample of a patient, goes down in 24 hours, after being treated with Samicin?

1/64

A mixed sequence is described by subtracting four from one term and then multiplying the resulting term with negative one to get the next term. If this pattern is repeated starting with the first term as 7, what is the sum of the first fifty terms?

10

If the average of 6, x, 13, and y is 10, what is the average of x and y?

10.5

Find the sum of the first 100 positive odd integers.

10000

Find the GCF of 84 and 120

12

Find the number of factors in 72

12

How many positive integers less than 25 are divisible by 3 or 4?

12

Sean and his friend Kiran started a computer software services company nine years ago. After the first year, in the next eight years the company's annual revenue tripled every two years. The revenue in the first year was $1,000,000. If the company's revenue growth continues at this rate, in how many years from now will the company's revenue cross te $700,000,000 mark?

13

An arithmetic sequence has a common difference equal to 10 and its 6th term is equal to 52. Find its 15th term.

142

The first term of an arithmetic sequence is equal to 6 and the common difference is equal to 3. Find the value of the 50th term.

153

In math both Anu and Renu have the same average scores at the end of the year. Anu's quarterly scores are 93, 100, x, and 99. Renu's quarterly scores are 98, 85, 93, and y. What is the difference between scores y and x?

16

What is the sum of the first eight terms of the geometric sequence: 5, 15, 45 ....?

16400

Solve: 7√3 + 5√12

17√3

Find the number of factors in 700

18

If the GCF and LCM of n and 45 are 9 and 90, respectively, what is n?

18

In her vegetable garden, Sara has 20 tomato plants. The number of tomatoes on each plant is 9, 2, 5, 4, 12, 7, 8, 11, 9, 3, 7, 4, 12, 5, 4, 10, 9, 6, 9, 4. Find the standard deviation.

2.983

In a class, 1/3 of the people opted for a foreign language as an elective. Among those wjo opted for teh foreign language, 2/5 opted for Spanish. What fraction of the class opted for Spanish?

2/15

Mary baked a cake and ate 2/5 of it. Her brother ate 1/3 of the remaining cake. Her mother ate the rest. What fraction of the cake was eaten by Mary's mother?

2/5

Find how many factors 240 has.

20

The population of Potatoville is decreasing by 2% every year. If the population is 2,400 this year, what will be the population four years from now?

2213

Find the difference between consecutive terms (d) in an arithmetic sequence given that the first term is 10 and the 20th term is 466.

24

Sara had an equal number of quarters, dimes, and nickels. If she paid $3.20 to buy a gallon of milk using 1/3 quarters, 1/4 of dimes, and 1/2 of nickels, how many quarters did she originally have?

24

Simplify: 6√48

24√3

Frank is driving at an average speed of 45 mph. How many miles did he drive in 35 minutes?

26.25

Solve 27^1/3

3

In a fruit basket, the ratio of apples to bananas is 3/5, the ratio if cantaloupes to bananas is 1/7, and the ratio of cantaloupes to dragon fruits is 1/3. What is the ratio of apples to dragon fruits in the basket?

7/5

The fourth term of a geometric sequence is 27 and the seventh term is 1. What is the first term?

729

Solve (64)^1/2

8

What is 28% of 60% of 50?

8.4

What is 27^(4/3)

81

Solve: √2 x 4√2 x 11√2

88√2

Simplify: 7√5 + 5√7 + 3√5 - 2√7 - √5

9√5 + 3√7

prime factorization

Expressing a number as a product of only prime numbers in the form of n=(2^x)(3^y)(5^z)....

fraction of a fraction

a/b of c/d = (a/b)(c/d)

Expressing a fraction as a product of two or more fractions

a/c = (a/b)(b/c), a/d = (a/b)(b/c)(c/d), a/e = (a/b)(b/c)(c/d)(d/e)

complement of a set

all elements that are in the universal set S, but not in set A

proportionality

an equality of fraction or ratios. Can be written as a:b = c:d or a/b = c/d

Formula for the nth term of an arithmetic sequence

an= a1 + (n-1)d

Finding the nth term of a geometric sequence

an= a₁ * r ⁿ⁻¹

union (U) of sets

contains all elements from both sets

intersection (∩) of sets

contains all elements that are in both sets