- If the product
is written as an integer, then the number of digits in the integer product is
a. 12 b. 13 c. 14 d. 18 e. 19 - Given that M, A, T, and H are positive integers where
, 
, and 
. Arrange M, A, T, and H in order from least to greatest.
a. MATH b. AHMT c. HATM d. TMHA e. HTMA - Given
and 
the statement which is not always correct is
a. 
b. 
c. 
d. 
e. none of these - Emily’s monthly salary for part of the year was $2015. After she received a raise, her monthly salary for the remainder of the year was $2145. Her total earnings for the year, including a bonus of $2500, were $27,720. For how many months did she work at the lesser salary?
a. 3 b. 6 c. 8 d. 9 e. 4 - A lattice point in the plane is a point both of whose coordinates are integers. How many lattice points (including the endpoints) are there on the line segment joining the points (2, 0) and (16, 203)?
a. 15 b. 9 c. 8 d. 14 e. none of these - The quadratic equation
has nonzero coefficients c and d. The roots of the equation are also c and d. Find 
.
a. 4 b. 5 c. 3 d. 1 e. 0 - Mr. McMath has a penny, nickel, dime, quarter and a half-dollar. How many different sums of money can he form by choosing three of the coins?
a. 3 b. 5 c. 8 d. 9 e. 10 - If we define
for all integers m, and 
, then find the value of 
.
a. 5 b. 15 c. 105 d. 120 e. 240 - If a, b, and c are real zeros of the polynomial
find 
a. 
b. 
c. 
d. 
e. 
- Two polynomials in x are of degrees r and s, respectively. One of the polynomials is multiplied by the cube of the other. Which of the following could be the degree of the product?
a. 
b. 
c. 
d. 3rs e. none of these - If
, calculate the value of 
.
a. 
b. 
c. 
d. 
e. 
- Which of the following functions is neither odd nor even?
a. 
b. 
c. 
d. 
e. 
- Which point on the line
is nearest the circle 
a. 
b. 
c. 
d. 
e. 
- If
and 
, find the value of 
a. 91 b. 11 c. 136 d. 59 e. none of these - The sum of Jan and Ann’s age is 24 more than Joe’s age. The sum of Jan and Joe’s age is 10 more than Ann’s age. The sum of Joe and Ann’s age is 20 more than Jan’s age. Find the sum of Jan, Ann, and Joe’s age.
a. 18 b. 22 c. 27 d. 39 e. 54 - If
is the maximum point on the graph of 
then k equals
a. 13 b. 11 c. 
d. 
e. 15 - What is the area of the region bounded by the graph of
where 
is a positive integer?
a. 
b. 
c. 
d. 
e. none of these - A certain function F satisfies
for all real numbers x. The value of 
is
a. 3 b. 2 c. 1 d. 
e. not possible to determine - If
, then when simplified 
equals
a. 
b. 
c. 
d. 
e. none of these - If Andrew gets 73 on his next algebra test, his average will be 87. If he gets 97, his average will be 90. How many tests has Andrew already taken?
a. 7 b. 5 c. 6 d. 4 e. 8 - If
is a 
function and
is a point on its graph, which of the following statements is correct?
a. 
is a point on the graph of the inverse function 
b. 
is a point on the graph of the inverse function c. 
d. the graph of the inverse function will be symmetric about the y-axis.e. 
- Solve the inequality
, expressing your answer in interval notation.
a. 
b. 
c. 
d. 
e. 
- Operation
is defined as 
for all whole numbers a and b. Which of the following are properties of with respect to the set of whole numbers?
i. The operation is commutative.ii. The operation is associative.iii. There is an identity element. iv. Each element has an inverse. - A pair of fair dice is thrown. What is the probability that the two numbers that appear differ by exactly 2?
a. 
b. 
c. 
d. 
e. 
- Find
given that 
and 
.
a. 
b. 
c. 
d. 
e. 
- Determine
so that 
where 
is a polynomial of degree one.
a. 
b. 
c. 
d. 
e. 
- Exactly two of the divisors of
are between 60 and 80. Find the sum of these two divisors.
a. 142 b. 140 c. 128 d. 129 e. 126 - If a and b are the solutions of
, find the value of ab.
a. 
b. 
c. d. 
e. 
- If
, solve for x.
a. 
b. 
c. 
d. 
e. 
- If the average (arithmetic mean) of five consecutive integers is q, what is the difference between the greatest and least of the five integers?
a. 4 b. 3 c. 2q d. 4q e. none of these - To reproduce an old photograph, a photographer charges x dollars to make a negative
dollars for each of the first 10 prints, and 
dollars for each print in excess of 10 prints. If $54 is the total charge to make a negative and 20 prints from an old photograph, what is the value of x?
a. 3.5 b. 4 c. 4.5 d. 5 e. 6 - If
, then which of the following can be true?
a. 
b. 
c. 
d. 
e. 
- Three fractions are inserted between
and 
so that the five fractions form an arithmetic sequence. What is the sum of these three new fractions?
a. 
b. 
c. 
d. 
e. none of these - Let s and w represent positive integers. Find
a. 
b. 
c. 
d. 
e. 
- Suppose that
and 
Then 
is equal to
a. 45 b. 47 c. 49 d. 51 e. 8 - Given the sequence
a. 56 b. 29 c. 36 d. 39 e. none of these - Factor
into a product of binomials of the form 
What is the value of 
a. 8 b. 9 c. 10 d. 11 e. 12 - If
and 
, then 
is equal to
a. 
b. c. 
d. 
e. 
- While attempting to solve a quadratic equation, a student inadvertently interchanged the coefficient of
with the constant term causing the equation to change. He solved the new equation correctly. The two roots he got were 2 and 1, and 1 was a root of the original equation. What was the sum of the squares of the roots of the original equation?
a. 5 b. 
c. 
d. 
e. - If the graph of
is given as shown below,
which of the following is the graph of
?
| a. only i | b. only i, ii, and iii | c. only iii and iv |
| d. only i, iii, and iv | e. i, ii, iii, and iv |