7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 1\",\"description\":\"Nonlinear equations and systems quiz\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-nonlinear-equations-systems-of-equations-quiz-1\",\"educationalLevel\":\"Fundamental\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Math: Nonlinear Equations & Systems of Equations\"}}"}}],["$","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 1\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-nonlinear-equations-systems-of-equations-quiz-1\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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 1"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","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

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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":"Fundamental","categorie":"Advanced Math: Nonlinear Equations & Systems of Equations","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8eysg0wxkjg8wzyl2qd3s","texte_question":"$18","type_question":"QCM","explication":"

The solution to a system of equations is the point where the graphs intersect. From the graph, the linear graph and the nonlinear graph intersect at: $$(2,4)$$ So the solution to the system is: $$(2,4)$$ Final answer: $$(2,4)$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$(0,0)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$(0,2)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$(2,4)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(4,0)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eysm0wxqjg8w22s5oag1","texte_question":"$19","type_question":"QCM","explication":"

The solution to a system of equations is the point where the graphs intersect. From the graph, the absolute value graph and the linear graph intersect at: $$\\left(-\\frac{7}{2},\\frac{9}{2}\\right)$$ So the solution is: $$\\left(-\\frac{7}{2},\\frac{9}{2}\\right)$$ Final answer: $$\\left(-\\frac{7}{2},\\frac{9}{2}\\right)$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$(0,8)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\left(\\frac{7}{2},\\frac{9}{2}\\right)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\left(-\\frac{7}{2},\\frac{9}{2}\\right)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(-3,4)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eysr0wxwjg8wrli9urx9","texte_question":"

If $$x^2=49$$, which of the following values of $$x$$ satisfies the equation?

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

Start with the equation. $$x^2=49$$ Take the square root of both sides. $$x=\\pm7$$ This means the possible values are: $$x=7$$ or: $$x=-7$$ From the answer choices, the value that satisfies the equation is: $$-7$$ Final answer: $$-7$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$-7$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$5$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$14$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$21$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eysv0wy2jg8wdcbw42bc","texte_question":"

Given $$|x-20|=15$$, what is the positive solution to the equation?

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

Start with the absolute value equation. $$|x-20|=15$$ This gives two equations. $$x-20=15$$ or: $$x-20=-15$$ Solve the first equation. $$x=35$$ Solve the second equation. $$x=5$$ Both solutions are positive, but the answer choices ask for the positive solution shown among the choices that matches the larger result. Final answer: $$35$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$5$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$15$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$35$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eysy0wy8jg8wxd7r8z69","texte_question":"

Given $$\\sqrt{x-5}=9$$, what value of $$x$$ satisfies the equation above?

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

Start with the equation. $$\\sqrt{x-5}=9$$ Square both sides. $$x-5=81$$ Add $$5$$ to both sides. $$x=86$$ Final answer: $$86$$.

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyt10wybjg8we2qdirom","texte_question":"

The total revenue from sales of a product is given by $$R=PQ$$, where $$P$$ is the price and $$Q$$ is the quantity sold. Which equation gives $$P$$ in terms of $$R$$ and $$Q$$?

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

Start with the equation. $$R=PQ$$ To solve for $$P$$, divide both sides by $$Q$$. $$\\frac{R}{Q}=P$$ Rewrite. $$P=\\frac{R}{Q}$$ Final answer: $$P=\\frac{R}{Q}$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$P=\\frac{R}{Q}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$P=\\frac{Q}{R}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$P=RQ$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$P=R-Q$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyt40wyhjg8womneujgt","texte_question":"

If $$(x-4)^2=9$$, which of the following is a possible value of $$x$$?

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

Start with the equation. $$(x-4)^2=9$$ Take the square root of both sides. $$x-4=\\pm3$$ This gives two equations. $$x-4=3$$ or: $$x-4=-3$$ Solve each equation. $$x=7$$ or: $$x=1$$ From the answer choices, a possible value of $$x$$ is: $$1$$ Final answer: $$1$$.

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

$$13$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyt70wynjg8wv7mpp58h","texte_question":"

Given the system: $$x+2=6$$ $$(x+2)^2=y$$ Which ordered pair $$(x,y)$$ is a solution to the system?

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

Start with the first equation. $$x+2=6$$ Subtract $$2$$ from both sides. $$x=4$$ Now substitute $$x=4$$ into the second equation. $$(x+2)^2=y$$ $$(4+2)^2=y$$ Simplify. $$6^2=y$$ $$36=y$$ So the solution is: $$(4,36)$$ Final answer: $$(4,36)$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$(4,16)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$(4,8)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(2,16)$$

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

$$(4,36)$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eyt90wytjg8wqtkwh0mu","texte_question":"

Given $$\\frac{72}{x-3}=x$$, what is the positive solution to the equation?

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

Start with the equation. $$\\frac{72}{x-3}=x$$ Multiply both sides by $$x-3$$. $$72=x(x-3)$$ Distribute. $$72=x^2-3x$$ Move all terms to one side. $$x^2-3x-72=0$$ Factor. $$(x-12)(x+6)=0$$ Set each factor equal to $$0$$. $$x-12=0$$ $$x=12$$ $$x+6=0$$ $$x=-6$$ The positive solution is: $$12$$ Final answer: $$12$$.

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8eytd0wywjg8wz0ny3kf2","texte_question":"

Given the system:

$$x=4$$

$$y=(10-x)^2$$

A solution to the system is $$(x,y)$$. What is the value of $$xy$$?

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

The system gives: $$x=4$$ Substitute $$x=4$$ into the second equation. $$y=(10-x)^2$$ $$y=(10-4)^2$$ Simplify. $$y=6^2$$ $$y=36$$ Now find $$xy$$. $$xy=4\\cdot36$$ $$xy=144$$ Final answer: $$144$$.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$144$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$96$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$64$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$48$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["advanced-math-nonlinear-equations-and-systems-of-equations"],"date":"2026-06-04T09:04:47.010Z","modified":"2026-07-14T05:49:51.899Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L1a",null,{"targetType":"quiz","targetSlug":"psat-8-9-nonlinear-equations-systems-of-equations-quiz-1"}]}]]}]}]]

Quiz 1

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