7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 2\",\"description\":\"Nonlinear equations and systems quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-nonlinear-equations-systems-of-equations-quiz-2\",\"educationalLevel\":\"Intermediate\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Math: Nonlinear Equations & Systems of Equations\"}}"}}],["$","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 2\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-nonlinear-equations-systems-of-equations-quiz-2\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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 2"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Nonlinear equations and systems 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":"Intermediate"}]]}]]}],["$","div",null,{"className":"flex items-center gap-3 p-4 bg-gray-50 rounded-xl border border-gray-200","children":[["$","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"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced Math: Nonlinear Equations & Systems of Equations"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2464,"prismaId":"cmpz9rk6n0e6ejgllvesz0zzg","slug":"psat-8-9-nonlinear-equations-systems-of-equations-quiz-2","title":{"rendered":"Quiz 2"},"content":{"rendered":"

Practice on nonlinear equations and systems of equations.

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

Nonlinear equations and systems quiz

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Intermediate","categorie":"Advanced Math: Nonlinear Equations & Systems of Equations","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8eyud0wz3jg8wwy6tzcye","texte_question":"

Given the system: $$y=50$$ $$y=x^2+14$$ The graphs intersect at $$(x,y)$$. What is a possible value of $$x$$?

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

Set the two expressions for $$y$$ equal to each other. $$50=x^2+14$$ Subtract $$14$$ from both sides. $$36=x^2$$ Take the square root of both sides. $$x=\\pm6$$ So the possible values of $$x$$ are $$-6$$ and $$6$$. Final answer: $$-6$$ or $$6$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$-6$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$6$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$8$$

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

$$10$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyug0wz9jg8wf5ce557d","texte_question":"

Given the system:

$$y=4x+3$$

$$y=4x^2+3$$

Which ordered pair $$(x,y)$$ is a solution to the system?

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

Set the two expressions for $$y$$ equal to each other. $$4x+3=4x^2+3$$ Subtract $$3$$ from both sides. $$4x=4x^2$$ Subtract $$4x$$ from both sides. $$0=4x^2-4x$$ Factor. $$0=4x(x-1)$$ So: $$x=0$$ or: $$x=1$$ If $$x=0$$: $$y=4(0)+3$$ $$y=3$$ So $$(0,3)$$ is a solution. If $$x=1$$: $$y=4(1)+3$$ $$y=7$$ So $$(1,7)$$ is also a solution. Final answer: $$(1,7)$$.

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

$$(1,3)$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$(1,7)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(2,11)$$

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

$$(3,15)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyui0wzfjg8wvkasgi9d","texte_question":"

Given the system: $$x=36$$ $$y=\\sqrt{x}+5$$ The graphs intersect at $$(x,y)$$. What is the value of $$y$$?

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

The system gives: $$x=36$$ Substitute $$x=36$$ into the second equation. $$y=\\sqrt{36}+5$$ Simplify. $$\\sqrt{36}=6$$ So: $$y=6+5$$ $$y=11$$ Final answer: $$11$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$6$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$11$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$41$$

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

$$129$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyul0wzljg8wg6cjjgri","texte_question":"

Given $$2x^2-8x+8=0$$, how many distinct real solutions are there?

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

Start with the equation. $$2x^2-8x+8=0$$ Factor out $$2$$. $$2(x^2-4x+4)=0$$ Factor the quadratic. $$2(x-2)^2=0$$ Divide by $$2$$. $$(x-2)^2=0$$ Take the square root. $$x-2=0$$ $$x=2$$ There is exactly one distinct real solution. Final answer: Exactly one.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\text{Zero}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\text{Exactly one}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\text{Exactly two}$$

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

$$\\text{Infinitely many}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyvc0wzrjg8w40rsvctv","texte_question":"

Given $$8r=4s+t$$, which equation correctly expresses $$s$$ in terms of $$r$$ and $$t$$?

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

Start with the equation. $$8r=4s+t$$ Subtract $$t$$ from both sides. $$8r-t=4s$$ Divide both sides by $$4$$. $$s=\\frac{8r-t}{4}$$ Final answer: $$s=\\frac{8r-t}{4}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$s=2r-t$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$s=\\frac{8r-t}{4}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$s=\\frac{4r}{t}-t$$

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

$$s=\\frac{4r-t}{8}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyvj0wzxjg8wslcmyn69","texte_question":"

Given the system: $$x+y=10$$ $$y=x^2$$ If $$(x,y)$$ is a solution, which of the following is a possible value of $$x$$?

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

Start with the system. $$x+y=10$$ $$y=x^2$$ Substitute $$x^2$$ for $$y$$ in the first equation. $$x+x^2=10$$ Rewrite. $$x^2+x-10=0$$ Use the quadratic formula. $$x=\\frac{-1\\pm\\sqrt{1^2-4(1)(-10)}}{2(1)}$$ Simplify. $$x=\\frac{-1\\pm\\sqrt{41}}{2}$$ A possible value of $$x$$ is: $$\\frac{-1+\\sqrt{41}}{2}$$ None of the listed integer choices satisfies the system. Final answer: $$\\frac{-1+\\sqrt{41}}{2}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$1$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$3$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4$$

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

$$\\frac{-1+\\sqrt{41}}{2}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyvo0x04jg8wwjt3pucq","texte_question":"

Given $$-2x^2-3x=-5$$, what is the positive solution to the equation?

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

Start with the equation. $$-2x^2-3x=-5$$ Move all terms to one side. $$-2x^2-3x+5=0$$ Multiply both sides by $$-1$$. $$2x^2+3x-5=0$$ Factor. $$(2x+5)(x-1)=0$$ Set each factor equal to $$0$$. $$2x+5=0$$ $$x=-\\frac{5}{2}$$ and: $$x-1=0$$ $$x=1$$ The positive solution is: $$1$$ Final answer: $$1$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{5}{2}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$1$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{5}{4}$$

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

$$2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyw00x0ajg8w83f01ge1","texte_question":"

Given $$3x^2-11x-4=0$$, what is the positive solution?

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

Start with the equation. $$3x^2-11x-4=0$$ Factor the quadratic. $$(3x+1)(x-4)=0$$ Set each factor equal to $$0$$. $$3x+1=0$$ $$x=-\\frac{1}{3}$$ and: $$x-4=0$$ $$x=4$$ The positive solution is: $$4$$ Final answer: $$4$$.

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

$$\\frac{1}{3}$$

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

$$4$$

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

$$\\frac{4}{3}$$

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

$$11$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eywb0x0gjg8w7fup1ri2","texte_question":"

Given $$(d-10)(d+10)-5=-5$$, what is the positive solution to the equation?

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

Start with the equation. $$(d-10)(d+10)-5=-5$$ Add $$5$$ to both sides. $$(d-10)(d+10)=0$$ Use the zero product property. $$d-10=0$$ $$d=10$$ or: $$d+10=0$$ $$d=-10$$ So a solution is $$10$$ or $$-10$$. Final answer: $$10$$

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

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyx80x0kjg8wxt6xz6kn","texte_question":"

Given $$\\frac{8}{n}-\\frac{1}{t}=-\\frac{1}{w}$$, which expression is equivalent to $$n$$?

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

Start with the equation. $$\\frac{8}{n}-\\frac{1}{t}=-\\frac{1}{w}$$ Add $$\\frac{1}{t}$$ to both sides. $$\\frac{8}{n}=\\frac{1}{t}-\\frac{1}{w}$$ Find a common denominator. $$\\frac{1}{t}-\\frac{1}{w}=\\frac{w-t}{tw}$$ So: $$\\frac{8}{n}=\\frac{w-t}{tw}$$ Cross multiply. $$8tw=n(w-t)$$ Divide by $$w-t$$. $$n=\\frac{8tw}{w-t}$$ Final answer: $$\\frac{8tw}{w-t}$$.

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

$$\\frac{t}{8w+t}$$

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

$$\\frac{w-t}{8w}$$

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

$$\\frac{8t}{w+t}$$

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

$$\\frac{8tw}{w-t}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["advanced-math-nonlinear-equations-and-systems-of-equations"],"date":"2026-06-04T09:04:47.088Z","modified":"2026-07-14T05:49:51.968Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"psat-8-9-nonlinear-equations-systems-of-equations-quiz-2"}]}]]}]}]]

Quiz 2

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