1. A short way of writing 4(4) (that is 4 times 4) is 42 . The exponent 2 shows that 4 occurs as a factor two times.
Thus, 42 = 4(4).
2. A short way of writing x(x)(x) is x3 . If x = 2, then x3 = 23 =2(2)(2) = 8.
3. The expression 3x2 means 3(x)(x). Notice that 3 occurs as a factor only one time, while x occurs as a factor two times. If x = 5, then 3x2 = 3(5)(5) = 75.
If y = 2, then y5 =
72 =
If w = 3, then w4 =
If d = 5, then d3 =
If w = 3, then 5w2 =
If x = 2 and y = 3, then x4y2 =
Read the following passage and answer questions 7, 8, 9, 10, 11 & 12.
Lesson 2
Directions - Study this lesson then answer the exam questions that follow.
1. If a girl earns x dollars a day, in 6 days she will earn 6 times x or 6x, dollars.
2. If a person loses 4 pounds per month for m months, then the total weight change will be -4m pounds.
3. If 20 dollars is the cost of 5 books, one book will cost 20/5, or 4 dollars. Likewise, if x dollars is the cost of v hats, then one hat costs x dollars divided by v, or v/x dollars.
4. If y is the number of years a woman has lived, how many months has she lived? Since there are 12 months in a year, the number of months in y years will be 12 times y or 12y.
A boy is y years old. His sister is five times as old. The sister's age is
If Cindy reads at a rate of w words per minute, then in 4 minutes she would read
Choose the correct way of writing this sentence: A number c multiplied by itself is less than 35.
Susan collects d dollars from each of 20 customers on her paper route. She will collect a total of
Each year for five years in a row on the same day, John measured the height of a tree. During this time, it grew x inches per year. How much did it grow?
An egg carton has r rows and x eggs in each row. If 8 eggs are broken, how many unbroken eggs are in the carton?
Read the following passage and answer questions 13, 14, 15, 16, 17 & 18
Lesson 3
Directions - Study this lesson then answer the exam questions that follow.
1. The symbol f(x) means "function of x". In this lesson, f(x) = 2x + 1.
2. When a value of x is given, that value is substituted into the expression for f(x). Then the expression is simplified if possible.
Examples:
If x = 3, then f(x) = 2(3) + 1
= 6 + 1
= 7
If x = 5, then f(x) = 2(5) + 1
= 10 + 1
= 11
If x = a, then f(x) = 2(a) + 1
= 2a + 1
f(x) = 2x + 1 and x = 6, then f(6) =
If f(x) = 2x + 1 and x = 10, then f(10) =
If f(x) = 2x + 1 and x = 2, then f(2) =
If f(x) = 2x + 1 and x = 0, then f(0) =
If f(x) = 2x + 1 and x = (3 - 1)2 , then f((3 - 1)2 ) =
If f(x) = 2x + 1 and x = g, then f(g) =
Read the following passage and answer questions 19, 20, 21, 22, 23 & 24.
Lesson 4
Directions - Study this lesson then answer the exam questions that follow.
1. There is a certain order of operations in mathematics. For example, in the expression 3 + 2(4) the product of 2(4) must be done first, then that product should be added to 3. Multiplication is done before either addition or subtraction. Thus, 3 + 2(4) = 2 + 8 = 10.
2. In the expression 14/2 - 1, the quotient 14/2 must be found first. Then the 1 is subtracted from that quotient. Division is done before either addition or subtraction. Thus, 14/2 - 1 = 7 - 1 = 6.
3. If x = 5 and y = 3, then what is the value of 2x2 - 4y? Recall from lesson 1 that 2x2 - 4y means 2*x*x - 4*y. Thus, 2x2 - 4y = 2*5*5 - 4*3 = 50 - 12 = 38.
Note: The general rule is first to multiply or divide and then add or subtract. However, if some terms are enclosed in parentheses, then we calculate within the parenthesis first.
Example:
(1 + 5)3 = 6*3 = 18
If x = 5, then 3(x + 1) =
If w = 3, then 2 + w2 =
52 - 3*4 =
6 + 20/2 - 1 =
4 - 1 + 3 =
If x = 4 and y = 7, then 3x2 + 2y =
Read the following passage and answer questions 25, 26, 27 & 28.
Lesson 5
Directions - Study this lesson then answer the exam questions that follow.
1. The value of n! can be represented by the following equation; Notice that the factors start with n and go all the way down to 1.
n! = n(n - 1)(n - 2) . . .(2)(1)
Examples:
3! = (3)(2)(1) = 6
5! = (5)(4)(3)(2)(1) = 120
2. Suppose Jim, John and Jerry run a race. One of them will win, one will come in second place and one will come in last. There are six possible ways in which the three runners could finish the race.
Solution: There are three persons that could finish first, two that could finish second and only one that could finish last. Therefore, (3)(2)(1) = 6 ways or without multiplying the answer could be written 3!
4! =
(3!)(3!) =
(8 - 5)! =
3(4!) =
Directions: Do not take the time to multiply out the answer. Use the factorial or exponent symbols to express your answer.
Twelve athletes run the 100m dash. If there are no ties, how many possible rank orders are there in which the 12 athletes could place?
Directions: Do not take the time to multiply out the answer. Use the factorial or exponent symbols to express your answer.
George knows that a 5 digit personal identification number is used as his password to log into the school computer network, but he cannot remember his number. If he uses a systematic trial and error method to find the correct number, what is the largest number of trials he might have to make?
What is the sum of -3 and +1?
A class of 25 students consists of x girls and y boys. What shows the relationship between x and y?
In which quadrant does the point (-1, -3) lie?
If x = 5 and y = 2, then x2y =
(+4) + (-3) + (+5) + (-8) + (-6) =
If -5 + w = 20, then w =
The area of a rectangle is 144 square inches. Its width is 9 inches. What is its length?
If x = 2 and f(x) = 3x - 1, then f(2) =
If x - (-3) = 10, then x =
Use the table above to answer this question:
If C = -2, then Z =