7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 5\",\"description\":\"SAT Math Advanced Quizzes Quiz 5\",\"url\":\"https://theschoolofmathematics.com/quiz/sat-math-advanced-quizzes-quiz-5\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Quizzes\"}}"}}],["$","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/sat-math-advanced-quizzes-quiz-5\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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":"

SAT Math Advanced Quizzes Quiz 5

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$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"}],["$","div",null,{"className":"text-sm font-bold text-gray-900","children":"Advanced Quizzes"}]]}]]}]]}]]}]]}],["$","$L17",null,{"quiz":{"id":2315,"prismaId":"cmq0jysxr01j0jgodw8dcgr84","slug":"sat-math-advanced-quizzes-quiz-5","title":{"rendered":"Quiz 5"},"content":{"rendered":"

SAT Math Advanced Quizzes - Quiz 5.

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

SAT Math Advanced Quizzes Quiz 5

"},"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Advanced","categorie":"Advanced Quizzes","nombre_questions":10,"score_minimum":70,"ordre_questions":"Fixe","questions":[{"id":"cmq0jysxx01j2jgodzymyy5a0","texte_question":"

If $$\\frac{4x}{x-2}-\\frac{3}{ax+1}=\\frac{8x^2-5x-10}{(x-2)(ax+1)}$$ and $$x\\ne-\\frac{1}{a}$$, where $$a$$ is a constant, what is the value of $$a$$?

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

Use a common denominator on the left side.

The common denominator is: $$(x-2)(ax+1)$$

Rewrite the left side.

$$\\frac{4x}{x-2}-\\frac{3}{ax+1}=\\frac{4x(ax+1)-3(x-2)}{(x-2)(ax+1)}$$

Expand the numerator.

$$4x(ax+1)-3(x-2)=4ax^2+4x-3x+6$$

$$=4ax^2+x+6$$

Since the denominator already matches, compare the leading coefficient with the right side.

$$4a=8$$

$$a=2$$

Final answer: $$2$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$-4$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$-2$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

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

$$4$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysy201j8jgod21j4na89","texte_question":"

Consider the system of equations:

$$y-2x=0$$

$$x^2+y^2=80$$

If $$(x,y)$$ is a solution to the system and $$y$$ > $$0$$, what is the value of $$y$$?

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

From the first equation:

$$y-2x=0$$

Solve for $$y$$.

$$y=2x$$

Substitute $$y=2x$$ into the second equation.

$$x^2+y^2=80$$

$$x^2+(2x)^2=80$$

$$x^2+4x^2=80$$

$$5x^2=80$$

Divide by $$5$$.

$$x^2=16$$

So:

$$x=4$$ or $$x=-4$$

Since $$y=2x$$ and $$y$$ > $$0$$, use $$x=4$$.

$$y=2(4)$$

$$y=8$$

Final answer: $$8$$

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

$$4\\sqrt{5}$$

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

$$8\\sqrt{5}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysy701jejgodr9xyx8aq","texte_question":"

Consider the system:

$$xy+3y=6$$

$$\\left(\\frac{1}{x+3}\\right)^2+\\left(\\frac{1}{x+3}\\right)-2=0$$

If $$(x,y)$$ is a solution to the system above, what is a possible value of $$|y|$$?

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

Factor the first equation.

$$xy+3y=6$$

$$y(x+3)=6$$

So:

$$y=\\frac{6}{x+3}$$

Let: $$u=\\frac{1}{x+3}$$

Then: $$y=6u$$

The second equation becomes:

$$u^2+u-2=0$$

Factor.

$$(u+2)(u-1)=0$$

So:

$$u=-2$$ or $$u=1$$

Then:

$$y=6(-2)=-12$$ or $$y=6(1)=6$$

Thus, possible values of $$|y|$$ are: $$12$$ and $$6$$

From the given choices, the possible value is $$6$$.

Final answer: $$6$$

","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":"

$$6$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyb01jkjgod4fke979t","texte_question":"

Consider the system of equations:

$$y=\\sqrt{x+5}$$

$$\\sqrt{9x}-y=1$$

If $$(x,y)$$ is the solution to the system, what is the value of $$y$$?

","type_question":"QCM","explication":"$18","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$7$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$8$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$9$$

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

$$\\frac{1+3\\sqrt{41}}{8}$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyf01jqjgod3sc9zm8c","texte_question":"

A factory contracts work to two machines. Machine A can produce $$90$$ parts per hour, and Machine B can produce $$150$$ parts per hour. The factory must produce more than $$1,350$$ parts in $$10$$ hours total. If Machine A operates for $$x$$ hours and Machine B operates for the remaining hours, which inequality represents all possible values of $$x$$?

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

Machine A operates for $$x$$ hours.

Machine A produces $$90$$ parts per hour, so it produces: $$90x$$ parts.

The total time is $$10$$ hours, so Machine B operates for: $$10-x$$ hours.

Machine B produces $$150$$ parts per hour, so it produces: $$150(10-x)$$ parts.

The total number of parts must be more than $$1350$$.

So, the inequality is:

$$90x+150(10-x)$$ > $$1350$$

Final answer: $$90x+150(10-x)$$ > $$1350$$

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

$$90x+150(10-x)$$ > $$1350$$

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

$$150x+90(10-x)$$ > $$1350$$

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

$$\\frac{90}{x}+\\frac{150}{10-x}$$ > $$1350$$

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

$$90x+150(x-10)$$ > $$1350$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyj01jwjgod8uke69no","texte_question":"

If $$-\\frac{17}{4}$$ < $$3x-5$$ < $$\\frac{7}{4}$$ what is one possible value of $$x+1$$?

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

Start with the compound inequality.

$$-\\frac{17}{4}$$ < $$3x-5$$ < $$\\frac{7}{4}$$

Add $$5$$ to all three parts.

$$-\\frac{17}{4}+5$$ < $$3x$$ < $$\\frac{7}{4}+5$$

Rewrite $$5$$ as $$\\frac{20}{4}$$.

$$\\frac{3}{4}$$ < $$3x$$ < $$\\frac{27}{4}$$

Divide all three parts by $$3$$.

$$\\frac{1}{4}$$ < $$x$$ < $$\\frac{9}{4}$$

Add $$1$$ to all parts:

$$\\frac{5}{4}$$ < $$x+1$$ < $$\\frac{13}{4}$$

Final answer: $$2$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$0$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$1$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

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

$$5$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyn01k2jgodjvynafv1","texte_question":"

If the line $$ax+4y=20$$ where $$a$$ is a constant, has an $$x$$-intercept that is three times the value of the $$y$$-intercept, what is the value of $$a$$?

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

Find the $$x$$-intercept by setting $$y=0$$.

$$ax+4(0)=20$$

$$ax=20$$

$$x=\\frac{20}{a}$$

Find the $$y$$-intercept by setting $$x=0$$.

$$a(0)+4y=20$$

$$4y=20$$

$$y=5$$

The $$x$$-intercept is three times the $$y$$-intercept.

$$\\frac{20}{a}=3(5)$$

$$\\frac{20}{a}=15$$

Multiply by $$a$$.

$$20=15a$$

$$a=\\frac{4}{3}$$

Final answer: $$\\frac{4}{3}$$

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

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

$$6$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyr01k8jgodm2nrlqw2","texte_question":"

Line $$m$$ has slope $$\\frac{3}{4}$$ and passes through the point $$(8,2)$$. If line $$n$$ is perpendicular to line $$m$$ and passes through the same point, which of the following could be the equation of line $$n$$?

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

Line $$m$$ has slope: $$\\frac{3}{4}$$

A line perpendicular to it has slope equal to the negative reciprocal.

So, the slope of line $$n$$ is: $$-\\frac{4}{3}$$

Line $$n$$ passes through $$(8,2)$$.

Use point-slope form.

$$y-2=-\\frac{4}{3}(x-8)$$

Distribute.

$$y-2=-\\frac{4}{3}x+\\frac{32}{3}$$

Add $$2$$.

$$y=-\\frac{4}{3}x+\\frac{32}{3}+2$$

$$y=-\\frac{4}{3}x+\\frac{32}{3}+\\frac{6}{3}$$

$$y=-\\frac{4}{3}x+\\frac{38}{3}$$

Final answer: $$y=-\\frac{4}{3}x+\\frac{38}{3}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$y=-\\frac{4}{3}x+\\frac{38}{3}$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$y=\\frac{4}{3}x-\\frac{26}{3}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$y=\\frac{3}{4}x-4$$

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

$$y=-\\frac{4}{3}x+8$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyv01kejgodrnu568vr","texte_question":"

Functions $$f$$ and $$g$$ are defined by $$f(x)=2x-1$$ and $$g(x)=\\frac{x}{3}$$ If $$f(g(f(k)))=9$$, what is the value of $$k$$?

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

Start from the inside.

$$f(k)=2k-1$$

Now apply $$g$$.

$$g(f(k))=\\frac{2k-1}{3}$$

Now apply $$f$$ again.

$$f(g(f(k)))=2\\left(\\frac{2k-1}{3}\\right)-1$$

Set this equal to $$9$$.

$$2\\left(\\frac{2k-1}{3}\\right)-1=9$$

Add $$1$$ to both sides.

$$2\\left(\\frac{2k-1}{3}\\right)=10$$

Divide by $$2$$.

$$\\frac{2k-1}{3}=5$$

Multiply by $$3$$.

$$2k-1=15$$

Add $$1$$.

$$2k=16$$

Divide by $$2$$.

$$k=8$$

Final answer: $$8$$

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

$$8$$

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

$$10$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jysyz01kkjgodjxqqn7bp","texte_question":"

If the graph of the function $$f$$ has $$x$$-intercepts at $$-4$$ and $$1$$, and a $$y$$-intercept at $$-16$$, which of the following could define $$f$$?

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

The $$x$$-intercepts are $$-4$$ and $$1$$.

So, the function must have factors:

$$(x+4)(x-1)$$

Write the function as:

$$f(x)=a(x+4)(x-1)$$

Use the y-intercept $$-16$$.

Since the y-intercept occurs when $$x=0$$:

$$f(0)=-16$$

Substitute:

$$a(0+4)(0-1)=-16$$

$$a(4)(-1)=-16$$

$$-4a=-16$$

$$a=4$$

Therefore:

Final answer:

$$f(x)=4(x+4)(x-1)$$

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

$$f(x)=(x+4)^2(x-1)$$

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

$$f(x)=(x+4)(x-1)^2$$

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

$$f(x)=(x-4)^2(x+1)$$

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

$$f(x)=4(x+4)(x-1)$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["Advanced Quizzes"],"date":"2026-06-05T06:38:07.359Z","modified":"2026-06-05T06:38:07.359Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L19",null,{"targetType":"quiz","targetSlug":"sat-math-advanced-quizzes-quiz-5"}]}]]}]}]]

Quiz 5

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