7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 4\",\"description\":\"Nonlinear functions quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-advanced-math-nonlinear-functions-quiz-04\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Math: Nonlinear functions\"}}"}}],["$","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 4\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-advanced-math-nonlinear-functions-quiz-04\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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 4"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","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

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$undefined",["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M8.228 9c.549-1.165 2.03-2 3.772-2 2.21 0 4 1.343 4 3 0 1.4-1.278 2.575-3.006 2.907-.542.104-.994.54-.994 1.093m0 3h.01M21 12a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Questions"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":10}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Level"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced"}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","div",null,{"className":"w-10 h-10 bg-gray-900 rounded-lg flex items-center justify-center flex-shrink-0","children":["$","svg",null,{"className":"w-5 h-5 text-white","fill":"none","stroke":"currentColor","viewBox":"0 0 24 24","children":["$","path",null,{"strokeLinecap":"round","strokeLinejoin":"round","strokeWidth":2,"d":"M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z"}]}]}],["$","div",null,{"children":[["$","div",null,{"className":"text-xs text-gray-500 font-medium","children":"Category"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced Math: Nonlinear functions"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2422,"prismaId":"cmpz9rjvy0dx7jgllfsp5mz43","slug":"psat-8-9-advanced-math-nonlinear-functions-quiz-04","title":{"rendered":"Quiz 4"},"content":{"rendered":"

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":"cmrk8eyhb0wq8jg8wi68krnzq","texte_question":"$18","type_question":"QCM","explication":"

The equation $$f(x)=0$$ asks where the graph crosses the $$x$$-axis. The $$x$$-axis is the horizontal line $$y=0$$. From the graph, the curve stays below the $$x$$-axis for all shown values of $$x$$. The curve approaches a horizontal value below $$0$$ on the left and decreases further on the right. Since the graph never touches or crosses the $$x$$-axis, there are no values of $$x$$ for which $$f(x)=0$$. Final answer: $$0$$.

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

$$\\text{Three}$$

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

$$\\text{Two}$$

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

$$\\text{One}$$

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

$$\\text{Zero}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhf0wqejg8weloejbk2","texte_question":"

For the function $$f(x)=2x^3-5x^2+4x-3$$, what is the value of $$f(-1)$$?

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

Substitute $$x=-1$$ into the function. $$f(-1)=2(-1)^3-5(-1)^2+4(-1)-3$$ Simplify each power. $$(-1)^3=-1$$ $$(-1)^2=1$$ Now substitute. $$f(-1)=2(-1)-5(1)+4(-1)-3$$ Multiply. $$f(-1)=-2-5-4-3$$ Add. $$f(-1)=-14$$ Final answer: $$-14$$.

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

$$-14$$

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

$$-10$$

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

$$10$$

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

$$14$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhi0wqkjg8ww5woooef","texte_question":"

A social media account has $$2,000$$ followers in January. Each month, the number of followers increases by $$5\\%$$ from the previous month. Which equation represents the number of followers $$F$$ after $$m$$ months?

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

The account starts with $$2,000$$ followers. An increase of $$5\\%$$ means the growth factor is: $$1+0.05=1.05$$ For exponential growth, use: $$F=a(1+r)^m$$ Here, the initial value is $$2,000$$ and the growth factor is $$1.05$$. So the equation is: $$F=2,000(1.05)^m$$ Final answer: $$F=2,000(1.05)^m$$.

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

$$F=2,000(0.05)^m$$

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

$$F=2,000(1.05)^m$$

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

$$F=2,000(5)^m$$

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

$$F=2,000(1.5)^m$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhl0wqqjg8wo8uk23rc","texte_question":"

A ball is thrown upward, and its height is modeled by $$y=-16(x-4)^2+300$$. Which of the following is the best interpretation of 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: $$y=-16(x-4)^2+300$$ The vertex is: $$(4,300)$$ Since the coefficient $$-16$$ is negative, the parabola opens downward. That means the vertex represents a maximum value. So the ball reaches a maximum height of $$300$$ feet after $$4$$ seconds. Final answer: The ball reaches a maximum height of $$300$$ feet after $$4$$ seconds.

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

$$\\text{The ball reaches a maximum height of }300\\text{ feet after }4\\text{ seconds}$$

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

$$\\text{The ball reaches a maximum height of }4\\text{ feet after }300\\text{ seconds}$$

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

$$\\text{The ball reaches a minimum height of }300\\text{ feet after }4\\text{ seconds}$$

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

$$\\text{The ball reaches a maximum height of }300\\text{ feet after }16\\text{ seconds}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyho0wqwjg8wfulq9wxa","texte_question":"

The function $$f(t)=600(0.4)^{t/10}$$ models the intensity of a signal. What is the value of the signal at $$t=0$$?

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

Substitute $$t=0$$ into the function. $$f(0)=600(0.4)^{0/10}$$ Simplify the exponent. $$0/10=0$$ So: $$f(0)=600(0.4)^0$$ Any nonzero number raised to the power $$0$$ equals $$1$$. $$(0.4)^0=1$$ Therefore: $$f(0)=600(1)$$ $$f(0)=600$$ Final answer: $$600$$.

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

$$600$$

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

$$0.4$$

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

$$10$$

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

$$24$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhr0wr2jg8wfwu1kman","texte_question":"

The function $$g(x)=\\frac{x}{a}+8$$, where $$a<0$$. What is the product of $$g(3a)$$ and $$g(5a)$$?

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

Start with the function. $$g(x)=\\frac{x}{a}+8$$ Find $$g(3a)$$. $$g(3a)=\\frac{3a}{a}+8$$ Simplify. $$g(3a)=3+8$$ $$g(3a)=11$$ Find $$g(5a)$$. $$g(5a)=\\frac{5a}{a}+8$$ Simplify. $$g(5a)=5+8$$ $$g(5a)=13$$ Now find the product. $$g(3a)\\cdot g(5a)=11\\cdot13$$ $$11\\cdot13=143$$ Final answer: $$143$$.

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

143

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyht0wr5jg8we2z8e5ix","texte_question":"

The area of a rectangle is $$1,200$$ square inches. The length is $$15$$ inches more than the width. Which equation represents this situation?

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

Let the width be $$x$$. The length is $$15$$ inches more than the width. So the length is: $$x+15$$ The area of a rectangle is: $$A=lw$$ Substitute the width, length, and area. $$1,200=x(x+15)$$ Distribute. $$1,200=x^2+15x$$ Move all terms to one side. $$0=x^2+15x-1,200$$ Final answer: $$0=x^2+15x-1,200$$.

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

$$0=x^2-15x-1,200$$

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

$$0=x^2+15x-1,200$$

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

$$0=x^2-15x+1,200$$

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

$$0=x^2+15x+1,200$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhw0wrbjg8wc7t8uze8","texte_question":"

A collectible card increases in value according to $$V(x)=80(1.04)^x$$, where $$x$$ is the number of years. Which statement best interprets $$V(5)\\approx97$$?

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

The function $$V(x)$$ gives the value of the collectible card. The input $$x$$ represents the number of years. The output $$V(x)$$ represents the value of the card in dollars. The statement $$V(5)\\approx97$$ means that when $$x=5$$, the card value is about $$97$$ dollars. So after $$5$$ years, the card is worth about $$97$$ dollars. Final answer: After $$5$$ years, the card is worth about $$97$$ dollars.

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

$$\\text{After }5\\text{ years, the card is worth about }$97$$

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

$$\\text{The card increases by }$97\\text{ each year}$$

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

$$\\text{The card was originally worth }$97$$

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

$$\\text{After }97\\text{ years, the card is worth }$5$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyhz0wrhjg8wb0s6xxtb","texte_question":"

The function $$f(x)=(1.44)^{x/2}$$ 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. $$f(x)=(1.44)^{x/2}$$ Rewrite the exponent. $$(1.44)^{x/2}=\\left((1.44)^{1/2}\\right)^x$$ Find the square root of $$1.44$$. $$(1.44)^{1/2}=1.2$$ So: $$f(x)=(1.2)^x$$ The function is also written as: $$f(x)=\\left(1+\\frac{p}{100}\\right)^x$$ Set the bases equal. $$1+\\frac{p}{100}=1.2$$ Subtract $$1$$. $$\\frac{p}{100}=0.2$$ Multiply by $$100$$. $$p=20$$ Final answer: $$20$$.

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

$$20$$

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

$$40$$

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

$$44$$

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

$$144$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyi10wrnjg8w6fu42xeu","texte_question":"

The function $$p(x)+25=x^2$$. What is the minimum value of $$p(x)$$?

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

Start with the equation. $$p(x)+25=x^2$$ Solve for $$p(x)$$. $$p(x)=x^2-25$$ The expression $$x^2$$ has a minimum value of $$0$$. So the minimum value of $$p(x)$$ occurs when $$x^2=0$$. Substitute. $$p(x)=0-25$$ $$p(x)=-25$$ Final answer: $$-25$$.

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

$$-25$$

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

$$0$$

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

$$25$$

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

$$-625$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["advanced-math--non-linear-functions"],"date":"2026-06-04T09:04:46.703Z","modified":"2026-07-14T05:49:51.498Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L19",null,{"targetType":"quiz","targetSlug":"psat-8-9-advanced-math-nonlinear-functions-quiz-04"}]}]]}]}]]

Quiz 4

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