You will need the following items:
Students may also use a calculator to complete this assessment.
Gather these materials before you begin.
Print out a copy of the PreCalculus Readiness Assessment. The printed part of the assessment is to be completed independently by the student and should take approximately 45 minutes. Be sure to keep track of the actual time your student spends on this part of the assessment. You may attempt to clarify the wording of a question if your student does not understand, but you should not answer specific questions asking how to solve a particular problem.
When your student has completed his work on paper, come back to the computer to complete the rest of the assessment.
Use this tool as an opportunity to help you determine your student’s understanding of the concepts.
For each problem, first check to see if the student answered it correctly. Then ask your student to explain to you how he arrived at each of his answers, or “teach back” the solution. Based on your student’s response, choose the statement(s) that most accurately describe how your student solved the problem. (IMPORTANT: Several of the questions require multiple responses. Be sure to mark ALL appropriate responses.)
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Your student’s performance indicates that he would be more successful in a lower level. Here are some additional steps you can take.
Your student’s performance indicates that he may be ready for PreCalculus. Here are some additional steps you should take.
Your student is ready for PreCalculus.
CORRECT ANSWER: 15 meters (m)
SAMPLE SOLUTION:
a^{2} + b^{2} =c^{3}
x^{2} + 8^{2} = 17^{2}
x^{2} + 64 = 289
x^{2} = 289 – 64
x^{2} = 225
x = 15
The missing side is 15 meters long.
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: 15 meters (m)
The student was expected to know and use the Pythagorean Theorem to find the missing side of the triangle.
a^{2} + b^{2} =c^{3}
x^{2} + 8^{2} = 17^{2}
x^{2} + 64 = 289
x^{2} = 289 – 64
x^{2} = 225
x = 15
The missing side is 15 meters long.
SKILL: Use the Pythagorean Theorem to find the missing side of a right triangle.
CORRECT ANSWER: 15 meters (m)
The student was expected to know and use the Pythagorean Theorem to find the missing side of the triangle.
a^{2} + b^{2} =c^{3}
x^{2} + 8^{2} = 17^{2}
x^{2} + 64 = 289
x^{2} = 289 – 64
x^{2} = 225
x = 15
The missing side is 15 meters long.
SKILL: Use the Pythagorean Theorem to find the missing side of a right triangle.
CORRECT ANSWER: x = -43
SAMPLE SOLUTIONS:
Solution A
Solution B
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: x = -43
The student was expected to use knowledge of proportions and solving equations to find the value of x. The sample solutions show two possible ways to solve this problem:
Solution A:
Solution B:
SKILLS: Use ratios to solve real-world problems; solve equations with variables on both sides.
CORRECT ANSWER: x = -43
The student was expected to use knowledge of proportions and solving equations to find the value of x. The sample solutions show two possible ways to solve this problem:
Solution A:
Solution B:
SKILLS: Use ratios to solve real-world problems; solve equations with variables on both sides.
CORRECT ANSWERS:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWERS:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify a rational expression.
CORRECT ANSWERS:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify a rational expression.
CORRECT ANSWER: 8qr – r
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: 8qr – r
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Add and subtract to simplify a rational expression.
CORRECT ANSWER: 8qr – r
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Add and subtract to simplify a rational expression.
CORRECT ANSWER:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify a complex fraction.
CORRECT ANSWER:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify a complex fraction.
CORRECT ANSWER:
SAMPLE SOLUTION:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
In order to solve this problem, the student needed to know the following concepts:
SKILL: Add fractions with polynomials in the denominator.
CORRECT ANSWER:
In order to solve this problem, the student needed to know the following concepts:
SKILL: Add fractions with polynomials in the denominator.
CORRECT ANSWER:
SAMPLE SOLUTIONS:
Solution A
Solution B
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
The student needed to understand how to perform operations with radicals. The sample solutions show two ways in which these concepts could be applied:
Solution A:
Here the radicals are combined first and then simplified.
Solution B:
Here the radicals are simplified first and then combined.
SKILL: Simplify expressions with radicals.
CORRECT ANSWER:
The student needed to understand how to perform operations with radicals. The sample solutions show two ways in which these concepts could be applied:
Solution A:
Here the radicals are combined first and then simplified.
Solution B:
Here the radicals are simplified first and then combined.
SKILL: Simplify expressions with radicals.
CORRECT ANSWER:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify an expression with a fractional exponent.
CORRECT ANSWER:
In order to solve this problem, the student needs to have mastered several concepts:
SKILL: Simplify an expression with a fractional exponent.
CORRECT ANSWER: 4
SAMPLE SOLUTIONS:
Solution A
Solution B
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: 4
SAMPLE SOLUTIONS:
Solution A
Solution B
SKILL: Simplify a division expression with irrational numbers.
CORRECT ANSWER: 4
SAMPLE SOLUTIONS:
Solution A
Solution B
SKILL: Simplify a division expression with irrational numbers.
CORRECT ANSWER: (x^{3} + 4b)(x^{3} – 4b)
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: (x^{3} + 4b)(x^{3} – 4b)
The student should have recognized the expression as the difference of two squares and factored it accordingly.
SKILL: Factor the difference of two squares.
CORRECT ANSWER: (x^{3} + 4b)(x^{3} – 4b)
The student should have recognized the expression as the difference of two squares and factored it accordingly.
SKILL: Factor the difference of two squares.
CORRECT ANSWER: -72
SAMPLE SOLUTION:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: -72
The student needed to know that i is an imaginary number representing the square root of -1. He then needed to apply this information to rename square roots of negative numbers and simplify expressions, as follows:
SKILL: Simplify expressions with imaginary numbers.
CORRECT ANSWER: -72
The student needed to know that i is an imaginary number representing the square root of -1. He then needed to apply this information to rename square roots of negative numbers and simplify expressions, as follows:
SKILL: Simplify expressions with imaginary numbers.
CORRECT ANSWER:
SAMPLE SOLUTION:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
The student was expected to know that he needed to multiply the denominator by the conjugate () in order to complete the square and obtain a whole-number denominator.
SKILL: Rationalize the denominator of a fraction.
CORRECT ANSWER:
The student was expected to know that he needed to multiply the denominator by the conjugate () in order to complete the square and obtain a whole-number denominator.
SKILL: Rationalize the denominator of a fraction.
CORRECT ANSWERS:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWERS:
The student was expected to notice that the equation could not be solved by factoring; therefore, he needed to know and use the quadratic formula to find the solution.
CORRECT ANSWERS:
The student was expected to notice that the equation could not be solved by factoring; therefore, he needed to know and use the quadratic formula to find the solution.
CORRECT ANSWER: E; x^{2} + y^{2} = 16
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER: E; x^{2} + y^{2} = 16
The student was expected to know the general equation for a circle: (x−h)^{2}+(y−k)^{2}= r^{2}
The student should also know the general equations for the other answer choices:
A. y = 3x This is the general equation of a line: y = mx + b
This equation can be rewritten as: y = 3x + 0
B. y^{2} = 4x^{2} – 12 This is the general equation of a hyperbola: x^{2}
CORRECT ANSWER: E; x^{2} + y^{2} = 16
The student was expected to know the general equation for a circle: (x−h)^{2}+(y−k)^{2}= r^{2}
The student should also know the general equations for the other answer choices:
A. y = 3x This is the general equation of a line: y = mx + b
This equation can be rewritten as: y = 3x + 0
B. y^{2} = 4x^{2} – 12 This is the general equation of a hyperbola: x^{2}
CORRECT ANSWER:
Ask the student to explain how he found the answer. Which of the following statements characterized his response? CLICK ALL THAT APPLY.
CORRECT ANSWER:
SKILL: Use unit multipliers (dimensional analysis) to convert units.
CORRECT ANSWER:
SKILL: Use unit multipliers (dimensional analysis) to convert units.
The next two questions are for the instructor. Click on the statement that best describes your student’s work during the written part of the assessment.
How long did it take the student to complete the assessment? Click on the best response.
A student who has mastered the prerequisite concepts should be able to complete the written assessment in about 45 minutes.
A student who has mastered the prerequisite concepts should be able to complete the written assessment in about 45 minutes.
How often did the student ask for help or hints as to how to solve a problem? (This is different than asking for clarification about how a question is worded.) Click on the best response.
A student who has mastered the prerequisite concepts should feel confident in his or her ability to solve the problems and should not need to ask for assistance.
A student who has mastered the prerequisite concepts should feel confident in his or her ability to solve the problems and should not need to ask for assistance.