1. In the base-5 number system, what is the sum of 303 and 2222?
2. Kim’s current monthly rent is $800. She is moving to another apartment complex, where the monthly rent will be $1,100. What is the percent increase in her monthly rent amount?
3. Which of the following statements is true?
A) The set of whole numbers is a subset of the set of natural numbers.
B) The set of integers is a subset of the set of natural numbers.
C) The set of integers is a subset of the set of rational numbers.
D) The set of rational numbers is a subset of the set of integers.
4. Mandy can buy 4 containers of yogurt and 3 boxes of crackers for $9.55. She can buy 2 containers of yogurt and 2 boxes of crackers for $5.90. How much does one box of crackers cost?
5. What is the derivative of f(x)=9x^2?
6. Which of the following functions converges?
7. McKenzie shades 1/5 of a piece of paper. Then, she shades an additional area 1/5 the size of what she just shaded. Next, she shades another area 1/5 as large as the previous one. As she continues the process to infinity, what is the limit of the shaded fraction of the paper?
8. A ball has a diameter of 7 inches. Which of the following best represents the volume?
A) 165.7 in^3
B) 179.6 in^3
C) 184.5 in^3
D) 192.3 in^3
9. A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. How many square inches of wrapping paper are needed to wrap the box?
10. Aidan has a plastic container in the shape of a square pyramid. He wants to fill the container with chocolate candies. If the base has a side length of 6 inches and the height of the container is 9 inches, how many cubic inches of space may be filled with candies?
CSET Foundation-Level Mathematics Test Answers
1. Answer: D
The sum is written as:
The sum of 2 and 3 equals 5, which must be represented as a 10. In the base-5 number system, a number cannot contain any 5’s. The 1 of each 10 is carried to the next column to the left.
2. Answer: D
The percent increase is represented as (1100-800)/800, which equals 0.375 or 37.5%.
3. Answer: C
The set of integers is contained within the set of rational numbers, and is hence, a subset. A rational number may be written as the ratio, a/b, where a and b are integers and b ≠ 0.
4. Answer: C
The situation may be modeled by the system
4x+3y = 9.55
2x+2y = 5.90
Multiplying the bottom equation by −2 gives
4x+3y = 9.55
-4x-4y = -11.80
Addition of the two equations gives -y = -2.25 or y = 2.25. Thus, one box of crackers costs $2.25.
5. Answer: C
The derivative of an equation of the form y = ax^n is equal to (n*a)x^(n-1). So the derivative of y = 9x^2 is equal to (2*9)x^(2-1) or 18x
6. Answer: C
The limit of the expression 4x/x, is 4, so the limit of the entire function is 1,004. The function converges.
7. Answer: B
The sequence 1/5,1/25,1/125,1/625,…, may be used to represent the situation. Substituting the initial value of 1/5 and common ratio of 1/5 into the formula S = a/(1-r) gives = (1/5)/(1-1/5) , which simplifies to S = (1/5)/(4/5) or S = 1/4.
8. Answer: B
The volume of a sphere may be calculated using the formula V = (4/3)*pi*r^3, where r represents the radius. Substituting 3.5 for r gives V = (4/3)*pi*(3.5)^3, which simplifies to V≈179.6.
9. Answer: C
The surface area of a rectangular prism may be calculated using the formula SA = 2lw+2wh+2hl. Substituting the dimensions of 14 inches, 6 inches, and 8 inches gives SA = 2(14)(6)+2(6)(8)+2(8)(14). Thus, the surface area is 488 square inches.
10. Answer: C
The volume of a pyramid may be calculated using the formula V=1/3 Bh, where B represents the area of the base and h represents the height. Since the base is a square, the area of the base is equal to 6^2, or 36 square inches. Substituting 36 for B and 9 for h gives V = (1/3)(36)(9), which simplifies to V = 108.