7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Mini Exam 6\",\"description\":\"Timed practice exam\",\"url\":\"https://www.theschoolofmathematics.com/quiz/ap-precalculus-mini-exam-6\",\"timeRequired\":\"PT25M\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Timed Mini Exams\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://www.theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://www.theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Mini Exam 6\",\"item\":\"https://www.theschoolofmathematics.com/quiz/ap-precalculus-mini-exam-6\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Mini Exam 6"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Timed practice exam

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Timed AP Precalculus Mini Exam 6

"},"excerpt":{"rendered":"

Timed practice exam

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":25,"niveau_difficulte":"$undefined","categorie":"Timed Mini Exams","nombre_questions":10,"score_minimum":80,"ordre_questions":"Aleatoire","questions":[{"id":"cmo50vxc60151jg68owtq4j6b","texte_question":"

In the $$xy$$-plane, the function $$f$$ is graphed and contains the point $$(4,3)$$. Which of the following points is on the graph of $$y=3f(x)-2$$?

","type_question":"QCM","explication":"

The point $$(4,3)$$ means $$f(4)=3$$

Use the transformation.

$$y=3f(x)-2$$

Substitute

$$x=4$$. $$y=3f(4)-2$$

$$y=3(3)-2$$ $$y=9-2$$

$$y=7$$ So the point is $$(4,7)$$

Final answer: $$(4,7)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$(4,3)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(4,7)$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(3,4)$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(6,3)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc60156jg68trakoruu","texte_question":"

Consider the piecewise function

$$P(t)=200-0.5t^2$$, $$0\\le t$$<$$10$$

$$P(t)=150-5t$$, $$10\\le t\\le12$$.

Which of the following statements is correct about the average rates of change of $$P$$?

","type_question":"QCM","explication":"

Compute average rate on $$0\\le t\\le5$$.

$$P(0)=200$$

$$P(5)=200-0.5(25)=187.5$$

$$\\frac{187.5-200}{5-0}=-2.5$$

Compute average rate on $$5\\le t\\le10$$.

$$P(10)=200-0.5(100)=150$$

$$\\frac{150-187.5}{10-5}=-7.5$$

Compare.

$$-2.5$$>$$-7.5$$

So, the rate on $$0\\le t\\le5$$ is greater.

Final answer: $$\\text{A}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"The average rate of change on $$0\\le t\\le5$$ is greater than on $$5\\le t\\le10$$.","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

The average rate of change on $$5\\le t\\le10$$ is greater than on $$0\\le t\\le5$$.

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

The average rate of change on $$10\\le t\\le11$$ is greater than on $$11\\le t\\le12$$.

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

The average rate of change on $$0\\le t\\le5$$ equals that on $$5\\le t\\le10$$.

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc6015bjg68z456xn33","texte_question":"$18","type_question":"QCM","explication":"

From the table.

$$A(10)=220$$

$$A(12)=260$$

$$A(15)=295$$

$$A(18)=280$$

The values increase then decrease.

So, the maximum is near $$x=15$$.

The maximum value is approximately $$295$$

Final answer: $$295$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$260$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$295$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$305$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$330$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc6015gjg68m7vyvvy7","texte_question":"

The function $$M$$ is defined by $$M(t)=ae^{-0.02t}+b$$, where $$a$$ and $$b$$ are positive constants. If $$M(0)=20$$ and $$\\lim_{t\\to\\infty}M(t)=4$$, for what value of $$t$$ is $$M(t)=10$$?

","type_question":"QCM","explication":"

Find $$b$$.

$$\\lim_{t\\to\\infty}M(t)=b$$

$$b=4$$

Use $$M(0)=20$$.

$$a+4=20$$

$$a=16$$

Write the function.

$$M(t)=16e^{-0.02t}+4$$

Set equal to $$10$$.

$$16e^{-0.02t}+4=10$$

$$16e^{-0.02t}=6$$

$$e^{-0.02t}=\\frac{3}{8}$$

Take natural log.

$$-0.02t=\\ln\\left(\\frac{3}{8}\\right)$$

$$t=\\frac{-\\ln\\left(\\frac{3}{8}\\right)}{0.02}$$

$$t\\approx48.96$$

Final answer: $$48.96$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$34.66$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$40.55$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$45.81$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$48.96$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc7015ljg68obmgh4kb","texte_question":"

Which of the following intervals represents all $$x$$ such that $$p(x)\\ge0$$ for $$p(x)=x(x-3)(x+1)$$?

","type_question":"QCM","explication":"

Find the zeros.

$$x=-1$$

$$x=0$$

$$x=3$$

Test the interval $$(-\\infty,-1)$$.

Using $$x=-2$$,

$$(-2)(-5)(-1)$$<$$0$$

Test the interval $$(-1,0)$$.

Using $$x=-\\frac{1}{2}$$,

$$\\left(-\\frac{1}{2}\\right)\\left(-\\frac{7}{2}\\right)\\left(\\frac{1}{2}\\right)$$>$$0$$

Test the interval $$(0,3)$$.

Using $$x=1$$, $$(1)(-2)(2)$$<$$0$$

Test the interval $$(3,\\infty)$$.

Using $$x=4$$, $$(4)(1)(5)$$>$$0$$

Include the zeros because $$p(x)\\ge0$$.

The solution set is $$[-1,0]\\cup[3,\\infty)$$

Final answer: $$[-1,0]\\cup[3,\\infty)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$[-1,3]$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(-\\infty,-1]\\cup[0,3]$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(-\\infty,-1]\\cup[3,\\infty)$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$[-1,0]\\cup[3,\\infty)$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc7015qjg68rev9eymn","texte_question":"

The function $$f$$ is given by $$f(x)=4\\cdot16^x$$. Which of the following is an equivalent form of $$f(x)$$?

","type_question":"QCM","explication":"

Rewrite $$16$$ as a power of $$2$$.

$$16=2^4$$

Substitute.

$$f(x)=4\\cdot(2^4)^x$$

Use the power rule.

$$f(x)=4\\cdot2^{4x}$$

Final answer: $$4\\cdot2^{4x}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$2\\cdot4^{2x}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4\\cdot2^{4x}$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$8\\cdot2^{2x}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4\\cdot4^x$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc7015vjg68yf5zf9pr","texte_question":"

The function $$f$$ is given by $$f(x)=-3x^5+2x^2-1$$. Which of the following describes the end behavior of $$f$$?

","type_question":"QCM","explication":"

The leading term is $$-3x^5$$

The degree is odd.

The leading coefficient is negative.

So, as $$x\\to\\infty$$,

$$f(x)\\to-\\infty$$

So, as $$x\\to-\\infty$$,

$$f(x)\\to\\infty$$

Final answer: $$\\lim_{x\\to-\\infty}f(x)=\\infty\\text{ and }\\lim_{x\\to\\infty}f(x)=-\\infty$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\lim_{x\\to-\\infty}f(x)=-\\infty\\text{ and }\\lim_{x\\to\\infty}f(x)=-\\infty$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\lim_{x\\to-\\infty}f(x)=-\\infty\\text{ and }\\lim_{x\\to\\infty}f(x)=\\infty$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\lim_{x\\to-\\infty}f(x)=\\infty\\text{ and }\\lim_{x\\to\\infty}f(x)=-\\infty$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\lim_{x\\to-\\infty}f(x)=-\\infty\\text{ and }\\lim_{x\\to\\infty}f(x)=\\infty$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc70160jg68mjahdskt","texte_question":"

Let $$a$$ and $$b$$ be positive constants. Which of the following is equivalent to $$3\\ln a-2\\ln b$$?

","type_question":"QCM","explication":"

Use the power rule.

$$3\\ln a=\\ln(a^3)$$

$$2\\ln b=\\ln(b^2)$$

Substitute.

$$3\\ln a-2\\ln b=\\ln(a^3)-\\ln(b^2)$$

Use the quotient rule.

$$\\ln(a^3)-\\ln(b^2)=\\ln\\left(\\frac{a^3}{b^2}\\right)$$

Final answer: $$\\ln\\left(\\frac{a^3}{b^2}\\right)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\ln\\left(\\frac{a^3}{b^2}\\right)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\ln(a^3b^2)$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\ln(3a-2b)$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\ln\\left(\\frac{3a}{2b}\\right)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc70165jg68k1vewes2","texte_question":"

The polynomial function $$p$$ is given by $$p(x)=(x-2)(x^2+4x+5)$$. Which of the following describes the zeros of $$p$$?

","type_question":"QCM","explication":"

One factor is $$(x-2)$$

So, one real zero is $$x=2$$

For the quadratic factor, $$x^2+4x+5$$ use the discriminant.

$$b^2-4ac=4^2-4(1)(5)$$

$$16-20=-4$$

Since the discriminant is negative, the quadratic has two non-real zeros. So the polynomial has exactly one real zero and two non-real zeros.

Final answer: $$\\text{A}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$p$$ has exactly one real zero and two non-real zeros.","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$p$$ has exactly two distinct real zeros.

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$p$$ has exactly three distinct real zeros.

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$p$$ has no real zeros.

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmo50vxc7016ajg68phqnne4l","texte_question":"

In the $$xy$$-plane, the graph of a rational function $$f$$ has a vertical asymptote at $$x=-5$$. Which of the following could be an expression for $$f(x)$$?

","type_question":"QCM","explication":"

A vertical asymptote occurs when a factor in the denominator is zero and does not cancel.

Check each option.

In option $$\\text{A}$$, the denominator is $$2(x-5)$$

So, the asymptote would be at $$x=5$$

In option $$\\text{B}$$, the denominator is $$(x-1)(x+5)$$ but the factor $$(x+5)$$ also appears in the numerator, so it cancels and gives a hole, not a vertical asymptote.

In option $$\\text{C}$$, the denominator is $$(x-5)(x+2)$$

So, the asymptotes would be at $$x=5$$ and $$x=-2$$

In option $$\\text{D}$$, the denominator is $$(x-3)(x+5)$$ and the factor $$(x+5)$$ does not cancel.

So, there is a vertical asymptote at $$x=-5$$

Final answer: $$\\text{D}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"

$$\\frac{(x-5)(x+5)}{2(x-5)}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{(x-4)(x+5)}{(x-1)(x+5)}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{(x+1)(x+5)}{(x-5)(x+2)}$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{(x-5)(x-3)}{(x-3)(x+5)}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["Timed-Mini-Exams"],"date":"2026-04-18T13:24:53.635Z","modified":"2026-04-19T00:23:26.598Z"}}]]}]}]]