In order to teach Foundational-Level Mathematics in the state of California, teacher candidates are required to take the CSET: Foundational-Level Mathematics exam which is actually Subtest I and Subtest II of the CSET: Mathematics exam. Each subtest must be registered for and taken individually. The computer-based subtests each include thirty-five multiple-choice questions and three constructed-response questions. You will have a total of two hours and thirty minutes for each subtest. A score of 220 is required to pass each subtest.

Subtest I (test code 211) consists of two content domains. The Number and Quantity domain is comprised of real and complex number systems and number theory. These questions verify your knowledge of the real number system and its subsets, your ability to perform operations, express real numbers in various forms, basic properties of natural numbers, the principle of mathematical induction to prove results in number theory, the Euclidean Algorithm, and the Fundamental Theorem of Arithmetic. The second content domain of subtest I is Algebra. The Algebra domain covers algebraic structures, polynomial equations and inequalities, functions, and linear algebra. A broad range of topics are included such as properties of real and complex numbers, factoring, manipulation of algebraic expressions, the Fundamental Theorem of Algebra, the Rational Root Theorem, the Conjugate Root Theorem, the Binomial Theorem, the Factor Theorem, the quadratic formula, polynomial inequalities, analyzing general properties of functions, applying arithmetic operations on functions, modeling, problem solving using nonlinear functions, vectors, matrices, analyzing properties of proportional relations, lines, linear equations, and graphs.

Subtest II (test code 212) also consists of two domains. The Geometry domain measures knowledge of Plane Euclidean Geometry, Coordinate Geometry, Three-Dimensional Geometry, and Transformational Geometry. The second domain, Probability and Statistics, involves permutations and combinations, finite probability, conditional probability and independence, computing and interpreting the probability of an outcome, the use of normal, binomial, and exponential distributions in solving and interpreting probability problems, and the calculation of expected values and using them in problem solving and evaluation. The Statistics questions include computing and interpreting means, medians, quartiles, range, interquartile range, and standard deviation of discrete and continuous distributions. You will need to bring your own graphing calculator for this subtest. A list of approved models is available on the testing website.

Mometrix, the world’s #1 test preparation company, has developed the CSET: Foundational-Level Mathematics practice test to assist you in passing this exam and beginning your career as a Foundational-Level Mathematics teacher. The practice test covers the same content as the actual test and includes answers and detailed explanations of those answers so that you can clearly understand which questions you missed and why you missed them. Success begins with the Mometrix CSET: Foundational-Level Mathematics practice test!

**1. In the base-5 number system, what is the sum of 303 and 2222?**

A) 2030

B) 2525

C) 3030

D) 3530

**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?**

A) 25.5%

B) 27%

C) 35%

D) 37.5%

**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?**

A) $1.75

B) $2.00

C) $2.25

D) $2.50

**5. What is the derivative of f(x)=9x^2?**

A) 3x

B) 9x

C) 18x

D) 18x^2

**6. Which of the following functions converges?**

A) f(x)=x^2/x

B) f(x)=2x

C) f(x)=4x/x+1000

D) f(x)=(3x^2+100)/x

**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?**

A) 1/5

B) 1/4

C) 1/3

D) 1/2

**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?**

A) 56

B) 244

C) 488

D) 672

**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?**

A) 98

B) 102

C) 108

D) 112

**CSET Foundation-Level Mathematics Test Answers**

**1. Answer: D**

The sum is written as:

2222

+ 303

3030

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.