Precalculus: Practice Questions with AnswersCurriculum: PrecalculusGrades: 11–12Questions: 12Mode: Practice These are the real questions from this STEPCAI practice lesson. Read each question, pick your answer, then open Show the answer to check yourself and read why it is right. On STEPCAI the same lesson runs interactively: you click an answer and get instant feedback, and a free account keeps your scores. 1. A function assigns to each input in its domain:- exactly one output
- no outputs
- at least one output
- two outputs
Show the answerAnswer: A. exactly one output
By definition, a function must produce exactly one output for every input in its domain. 2. What is the domain of f(x) = 1/(x-3)?- x >= 3
- All real numbers except x=3
- All real numbers
- All real numbers except x=0
Show the answerAnswer: B. All real numbers except x=3
The expression is undefined when the denominator equals zero, so x=3 must be excluded, and the domain is all other real numbers. 3. If f(x) = x+2 and g(x) = 3x, what is f(g(2))?- 12
- 6
- 8
- 10
Show the answerAnswer: C. 8
First evaluate the inner function g(2)=6, then plug that result into f to get f(6)=6+2=8. 4. Which best describes the inverse of a function f?- A function that undoes what f does, swapping inputs and outputs
- The same function reflected across the x-axis
- A function with the same domain and range as f but a different rule everywhere
- A function that doubles f's outputs
Show the answerAnswer: A. A function that undoes what f does, swapping inputs and outputs
The inverse function reverses the mapping of f, so if f takes a to b, the inverse takes b back to a. 5. On the unit circle, what is the ordered pair (cos, sin) at angle 0 radians?- (-1,0)
- (1,0)
- (0,0)
- (0,1)
Show the answerAnswer: B. (1,0)
At an angle of 0 radians the point lies on the positive x-axis at (1,0), so cos(0)=1 and sin(0)=0. 6. In a right triangle, sine of an acute angle equals:- hypotenuse over opposite
- opposite over hypotenuse
- opposite over adjacent
- adjacent over hypotenuse
Show the answerAnswer: B. opposite over hypotenuse
Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. 7. Which function represents exponential growth?- f(x)=2x
- f(x)=x^2
- f(x)=2^x
- f(x)=1/x
Show the answerAnswer: C. f(x)=2^x
In exponential growth the variable appears in the exponent, so as x increases the output multiplies repeatedly by the base, as in f(x)=2^x. 8. log base 10 of 100 equals:- 100
- 1
- 2
- 10
Show the answerAnswer: C. 2
log base 10 of 100 asks '10 to what power gives 100', and since 10^2=100, the answer is 2. 9. What is the degree of the polynomial 4x^3 - 2x + 5?- 3
- 5
- 1
- 2
Show the answerAnswer: A. 3
The degree of a polynomial is the highest exponent on the variable, and here the highest power of x is 3. 10. In the arithmetic sequence 5, 8, 11, 14, ..., what is the common difference?- 5
- 2
- 3
- 4
Show the answerAnswer: C. 3
Each term is found by adding 3 to the previous term (8-5=3, 11-8=3), so the common difference is 3. 11. What is the value of i^2, where i is the imaginary unit?- -1
- i
- 1
- -i
Show the answerAnswer: A. -1
The imaginary unit i is defined so that i^2 = -1. 12. A vector has both:- direction only
- magnitude only
- magnitude and direction
- neither magnitude nor direction
Show the answerAnswer: C. magnitude and direction
A vector is defined by two properties together: a magnitude (size or length) and a direction. More free high school sample lessonsSee all free sample lessons »
|