7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 5\",\"description\":\"Nonlinear functions quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-advanced-math-nonlinear-functions-quiz-05\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Math: Nonlinear functions\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Quiz 5\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-advanced-math-nonlinear-functions-quiz-05\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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":"Quiz 5"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Nonlinear functions quiz

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Practice on nonlinear functions.

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

Nonlinear functions quiz

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Advanced Math: Nonlinear functions","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8eyj50wrujg8w2ti0io9m","texte_question":"

For the function $$f(x)=x^3-4x^2+2x+1$$, what is the value of $$f(-2)$$?

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

Substitute $$x=-2$$ into the function. $$f(-2)=(-2)^3-4(-2)^2+2(-2)+1$$ Simplify the powers. $$(-2)^3=-8$$ $$(-2)^2=4$$ Substitute. $$f(-2)=-8-4(4)-4+1$$ Multiply. $$f(-2)=-8-16-4+1$$ Add. $$f(-2)=-27$$ Final answer: $$-27$$.

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

$$-19$$

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

$$-15$$

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

$$15$$

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

$$19$$

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

$$-27$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyj90ws1jg8w2sgtc4tg","texte_question":"

A company has $$1,500$$ users. Each month, the number of users increases by $$6\\%$$ from the previous month. Which equation represents the number of users $$U$$ after $$m$$ months?

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

The initial number of users is $$1,500$$. An increase of $$6\\%$$ means the growth factor is: $$1+0.06=1.06$$ For exponential growth, use: $$U=a(1+r)^m$$ Substitute the initial value and growth factor. $$U=1,500(1.06)^m$$ Final answer: $$U=1,500(1.06)^m$$.

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

$$U=1,500(0.06)^m$$

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

$$U=1,500(1.06)^m$$

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

$$U=1,500(6)^m$$

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

$$U=1,500(1.6)^m$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjc0ws7jg8wl7uy2kh1","texte_question":"

A ball is launched, and its height is modeled by $$y=-16(x-3)^2+256$$. Which of the following best describes the vertex?

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

The function is written in vertex form. $$y=a(x-h)^2+k$$ The vertex is: $$(h,k)$$ For the function: $$y=-16(x-3)^2+256$$ The vertex is: $$(3,256)$$ Since $$a=-16$$, the parabola opens downward. So the vertex represents a maximum value. This means the ball reaches a maximum height of $$256$$ feet after $$3$$ seconds. Final answer: The ball reaches a maximum height of $$256$$ feet after $$3$$ seconds.

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

$$\\text{The ball reaches a maximum height of }256\\text{ feet after }3\\text{ seconds}$$

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

$$\\text{The ball reaches a maximum height of }3\\text{ feet after }256\\text{ seconds}$$

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

$$\\text{The ball reaches a minimum height of }256\\text{ feet after }3\\text{ seconds}$$

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

$$\\text{The ball reaches a maximum height of }256\\text{ feet after }16\\text{ seconds}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjf0wsdjg8wg7703mg3","texte_question":"

The function $$f(t)=400(0.5)^{t/8}$$ models the intensity of a signal. What is the value of the signal at the surface $$(t=0)$$?

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

Substitute $$t=0$$ into the function. $$f(0)=400(0.5)^{0/8}$$ Simplify the exponent. $$0/8=0$$ So: $$f(0)=400(0.5)^0$$ Any nonzero number raised to the power $$0$$ equals $$1$$. $$(0.5)^0=1$$ Therefore: $$f(0)=400(1)$$ $$f(0)=400$$ Final answer: $$400$$.

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

$$400$$

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

$$0.5$$

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

$$8$$

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

$$50$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyji0wsjjg8whf93swl0","texte_question":"

The function $$g(x)=\\frac{x}{a}-6$$, where $$a<0$$. What is the product of $$g(2a)$$ and $$g(4a)$$?

","type_question":"TexteLibre","explication":"

Start with the function. $$g(x)=\\frac{x}{a}-6$$ Find $$g(2a)$$. $$g(2a)=\\frac{2a}{a}-6$$ Simplify. $$g(2a)=2-6$$ $$g(2a)=-4$$ Find $$g(4a)$$. $$g(4a)=\\frac{4a}{a}-6$$ Simplify. $$g(4a)=4-6$$ $$g(4a)=-2$$ Now multiply. $$g(2a)\\cdot g(4a)=(-4)(-2)$$ $$g(2a)\\cdot g(4a)=8$$ Final answer: $$8$$.

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjl0wsmjg8wbzwlfn2v","texte_question":"

The area of a rectangle is $$900$$ square inches. The length is $$10$$ inches more than the width. Which equation represents this situation?

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

Let the width be $$x$$. The length is $$10$$ inches more than the width. So the length is: $$x+10$$ The area of a rectangle is: $$A=lw$$ Substitute the area, length, and width. $$900=x(x+10)$$ Distribute. $$900=x^2+10x$$ Move all terms to one side. $$0=x^2+10x-900$$ Final answer: $$0=x^2+10x-900$$.

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

$$0=x^2-10x-900$$

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

$$0=x^2+10x-900$$

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

$$0=x^2-10x+900$$

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

$$0=x^2+10x+900$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjo0wssjg8wg4a5pofu","texte_question":"

A collectible increases in value according to $$V(x)=100(1.05)^x$$. Which statement best interprets $$V(6)\\approx134$$?

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

The function $$V(x)$$ gives the value of the collectible. The input $$x$$ represents the number of years. The output $$V(x)$$ represents the value in dollars. The statement $$V(6)\\approx134$$ means that when $$x=6$$, the value is about $$134$$ dollars. So after $$6$$ years, the value is about $$134$$ dollars. Final answer: After $$6$$ years, the value is about $$134$$.

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

$$\\text{After }6\\text{ years, the value is about }$134$$

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

$$\\text{The value increases by }$134\\text{ each year}$$

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

$$\\text{The original value was }$134$$

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

$$\\text{After }134\\text{ years, the value is }$6$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjr0wsyjg8wpn77qvkr","texte_question":"

The function $$f(x)=(1.21)^{x/2}$$ can be rewritten as $$f(x)=\\left(1+\\frac{p}{100}\\right)^x$$. What is the value of $$p$$?

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

Start with the function. $$f(x)=(1.21)^{x/2}$$ Rewrite the exponent. $$(1.21)^{x/2}=\\left((1.21)^{1/2}\\right)^x$$ Find the square root of $$1.21$$. $$(1.21)^{1/2}=1.1$$ So: $$f(x)=(1.1)^x$$ The function is also written as: $$f(x)=\\left(1+\\frac{p}{100}\\right)^x$$ Set the bases equal. $$1+\\frac{p}{100}=1.1$$ Subtract $$1$$. $$\\frac{p}{100}=0.1$$ Multiply by $$100$$. $$p=10$$ Final answer: $$10$$.

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

$$10$$

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

$$21$$

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

$$44$$

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

$$121$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyju0wt4jg8wdb31c6hq","texte_question":"

The function $$p(x)+16=x^2$$. What is the minimum value of $$p(x)$$?

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

Start with the equation. $$p(x)+16=x^2$$ Solve for $$p(x)$$. $$p(x)=x^2-16$$ The expression $$x^2$$ has a minimum value of $$0$$. So the minimum value of $$p(x)$$ occurs when $$x^2=0$$. Substitute. $$p(x)=0-16$$ $$p(x)=-16$$ Final answer: $$-16$$.

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

$$-16$$

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

$$0$$

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

$$16$$

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

$$-256$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyjx0wtajg8wogzzcy4k","texte_question":"

The function $$f(x)=(x-4)(x+6)$$. For what value of $$x$$ does $$f(x)$$ reach its minimum?

","type_question":"TexteLibre","explication":"

The zeros of the function are found from the factors. $$x-4=0$$ $$x=4$$ and: $$x+6=0$$ $$x=-6$$ For a quadratic function, the minimum occurs at the vertex. The $$x$$-coordinate of the vertex is halfway between the zeros. Find the average. $$x=\\frac{4+(-6)}{2}$$ Simplify. $$x=\\frac{-2}{2}$$ $$x=-1$$ Final answer: $$-1$$.

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

-1

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["advanced-math--non-linear-functions"],"date":"2026-06-04T09:04:46.754Z","modified":"2026-07-14T05:49:51.565Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"psat-8-9-advanced-math-nonlinear-functions-quiz-05"}]}]]}]}]]

Quiz 5

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