7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 26\",\"description\":\"Advanced SAT Math Quiz 26\",\"url\":\"https://theschoolofmathematics.com/quiz/sat-math-advanced-quizzes-quiz-26\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":13,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Quizzes\"}}"}}],["$","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 26\",\"item\":\"https://theschoolofmathematics.com/quiz/sat-math-advanced-quizzes-quiz-26\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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 26"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-8 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Advanced SAT Math Quiz 26

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$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":2442,"prismaId":"cmq0jyusx02gpjgodmhlt7u6b","slug":"sat-math-advanced-quizzes-quiz-26","title":{"rendered":"Quiz 26"},"content":{"rendered":"

Advanced SAT Math Quiz 26

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

Advanced SAT Math Quiz 26

"},"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":"cmq0jyut202grjgod8ae07zdz","texte_question":"

A function is defined by $$f(x)=2x^2-5x+1$$. If $$f(a)=f(4)$$, where $$a\\ne4$$, what is the value of $$a$$?

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

First find $$f(4)$$.

$$f(4)=2(4)^2-5(4)+1$$

$$f(4)=32-20+1$$

$$f(4)=13$$

Since $$f(a)=f(4)$$:

$$2a^2-5a+1=13$$

Subtract $$13$$ from both sides.

$$2a^2-5a-12=0$$

Factor.

$$(2a+3)(a-4)=0$$

So:

$$a=-\\frac{3}{2}$$ or $$a=4$$

Since $$a\\ne4$$

Final answer: $$-\\frac{3}{2}$$

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

$$\\frac{1}{2}$$

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

$$\\frac{3}{2}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyut502gxjgodzuy5cfnq","texte_question":"

In the coordinate plane, the graph of $$y=ax^2+bx+c$$ has $$x$$-intercepts at $$-\\frac{2}{3}$$ and $$5$$. The graph passes through the point $$(0,-20)$$. What is the value of $$a$$?

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

Since the $$x$$-intercepts are $$-\\frac{2}{3}$$ and $$5$$, write the function as:

$$y=a\\left(x+\\frac{2}{3}\\right)(x-5)$$

The graph passes through $$(0,-20)$$.

Substitute $$x=0$$ and $$y=-20$$.

$$-20=a\\left(0+\\frac{2}{3}\\right)(0-5)$$

$$-20=a\\left(\\frac{2}{3}\\right)(-5)$$

$$-20=-\\frac{10a}{3}$$

Multiply by $$3$$.

$$-60=-10a$$

$$a=6$$

Final answer: $$6$$

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

$$4$$

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

$$6$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyut902h3jgoddb6ejyur","texte_question":"

A company's profit $$P$$, in thousands of dollars, is modeled by $$P(t)=200(1.08)^t-150$$, where $$t$$ is the number of years after the company was founded. According to the model, after approximately how many years will the company's profit first exceed $$300$$ thousand dollars?

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

The profit must first exceed $$300$$.

$$200(1.08)^t-150$$ > $$300$$

Add $$150$$.

$$200(1.08)^t$$ > $$450$$

Divide by $$200$$.

$$(1.08)^t$$ > $$2.25$$

Solve using logarithms.

$$t$$ > $$\\frac{\\ln(2.25)}{\\ln(1.08)}$$

$$t\\approx10.54$$

The first whole number of years after this is: $$11$$

Final answer: $$11$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$11$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$13$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$15$$

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

$$17$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyutd02h9jgodmyjhq4vm","texte_question":"

The expression $$\\frac{x^3+8}{x+2}+\\frac{x^2-4}{x-2}$$ is equivalent to which of the following for all appropriate values of $$x$$?

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

Factor each numerator.

$$x^3+8=(x+2)(x^2-2x+4)$$

So:

$$\\frac{x^3+8}{x+2}=x^2-2x+4$$

Also:

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

So:

$$\\frac{x^2-4}{x-2}=x+2$$

Add the expressions.

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

Final answer: $$x^2-x+6$$

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

$$x^2+2x$$

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

$$2x^2+2x+4$$

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

$$x^2-x+6$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyuth02hfjgodv7h9ck9h","texte_question":"

In the coordinate plane, the circle $$(x-2)^2+(y+1)^2=r^2$$ passes through the point $$(8,7)$$. What is the area of the circle?

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

The center of the circle is: $$(2,-1)$$

The circle passes through: $$(8,7)$$

Find $$r^2$$ using the distance formula.

$$r^2=(8-2)^2+(7-(-1))^2$$

$$r^2=6^2+8^2$$

$$r^2=36+64$$

$$r^2=100$$

The area of the circle is:

$$A=\\pi r^2$$

$$A=100\\pi$$

Final answer: $$100\\pi$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$50\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$72\\pi$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$100\\pi$$

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

$$136\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyutl02hljgod18c2q287","texte_question":"

A data set consists of $$13$$ distinct integers arranged in increasing order. The median is $$18$$ and the mean is $$22$$. Each of the $$6$$ integers greater than the median is increased by $$4$$, and each of the $$6$$ integers less than the median is decreased by $$4$$. Which of the following must be true?

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

There are $$13$$ integers, so the median is the $$7$$th value.

The $$6$$ values greater than the median are each increased by $$4$$.

The total increase is:

$$6(4)=24$$

The $$6$$ values less than the median are each decreased by $$4$$.

The total decrease is:

$$6(4)=24$$

So, the total sum does not change.

Since the number of values is still $$13$$, the mean remains unchanged.

The median value itself is not changed.

Final answer: The mean remains unchanged and the median remains unchanged.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"The mean increases and the median increases.","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"The mean remains unchanged and the median remains unchanged.","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

The mean remains unchanged and the median increases.

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

The mean decreases and the median remains unchanged.

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyutp02hrjgodx8ns6c9t","texte_question":"

If $$\\frac{a}{b}+\\frac{b}{a}=14$$, what is the value of $$\\frac{a^2}{b^2}+\\frac{b^2}{a^2}$$?

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

Square both sides of the given equation.

$$\\left(\\frac{a}{b}+\\frac{b}{a}\\right)^2=14^2$$

Expand.

$$\\frac{a^2}{b^2}+2+\\frac{b^2}{a^2}=196$$

Subtract $$2$$.

$$\\frac{a^2}{b^2}+\\frac{b^2}{a^2}=194$$

Final answer: $$194$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$192$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$194$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$196$$

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

$$198$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyutt02hxjgodbx3td8ws","texte_question":"

A regular decagon is inscribed in a circle of radius $$12$$. What is the perimeter of the decagon?

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

A regular decagon has $$10$$ equal sides. Each side is a chord of the circle. The central angle for each side is:

$$\\frac{360^\\circ}{10}=36^\\circ$$

The chord length is:

$$2R\\sin\\left(\\frac{36^\\circ}{2}\\right)$$

$$=2(12)\\sin(18^\\circ)$$

$$=24\\sin(18^\\circ)$$

The perimeter is:

$$10\\cdot24\\sin(18^\\circ)=240\\sin(18^\\circ)$$

Final answer: $$240\\sin(18^\\circ)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$120\\sin(18^\\circ)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$240\\sin(18^\\circ)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$120\\sin(36^\\circ)$$

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

$$240\\sin(36^\\circ)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyutw02i3jgodjolstm8a","texte_question":"

In triangle $$ABC$$, point $$D$$ lies on side $$BC$$ such that $$\\frac{BD}{DC}=3:2$$. If the area of triangle $$ABC$$ is $$50$$, what is the area of triangle $$ABD$$?

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

Triangles $$ABD$$ and $$ADC$$ share the same altitude from $$A$$ to line $$BC$$. Therefore, their areas are proportional to their bases.

Given:

$$BD:DC=3:2$$

The total ratio is:

$$3+2=5$$

Triangle $$ABD$$ has $$\\frac{3}{5}$$ of the total area.

$$[ABD]=\\frac{3}{5}(50)$$

$$[ABD]=30$$

Final answer: $$30$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$20$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$25$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$30$$

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

$$35$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyuu002i9jgods75j4ryb","texte_question":"

The polynomial $$P(x)=64x^3-nk^3$$ has a factor of $$4x-3k$$, where $$k$$ > $$0$$. What is the value of $$n$$?

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

Since $$4x-3k$$ is a factor, the polynomial equals $$0$$ when:

$$4x-3k=0$$

Solve for $$x$$.

$$x=\\frac{3k}{4}$$

Substitute into the polynomial.

$$64\\left(\\frac{3k}{4}\\right)^3-nk^3=0$$

Simplify.

$$64\\cdot\\frac{27k^3}{64}-nk^3=0$$

$$27k^3-nk^3=0$$

Factor.

$$k^3(27-n)=0$$

Since $$k$$ > $$0$$,

$$k^3\\ne0$$.

So:

$$27-n=0$$

$$n=27$$

Final answer: $$27$$

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

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyuu302icjgodst3115d2","texte_question":"

A manufacturer produces two products, $$A$$ and $$B$$. Product $$A$$ generates a profit of $$p$$ dollars per unit and Product $$B$$ generates a profit of $$q$$ dollars per unit. Last month, the company sold $$30\\%$$ more units of Product $$A$$ than Product $$B$$. If the company sold a total of $$N$$ units and generated a total profit of $$T$$ dollars, which of the following expressions represents $$T$$?

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

Let the number of units of Product $$B$$ be $$x$$.

Then the number of units of Product $$A$$ is: $$1.3x$$

The total number of units is:

$$x+1.3x=2.3x$$

So:

$$2.3x=N$$

$$x=\\frac{N}{2.3}$$

The total profit is:

$$T=p(1.3x)+q(x)$$

Factor out $$x$$.

$$T=x(1.3p+q)$$

Substitute $$x=\\frac{N}{2.3}$$.

$$T=\\frac{N}{2.3}(1.3p+q)$$

Final answer: $$\\frac{N}{2.3}(1.3p+q)$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$\\frac{N}{2}(1.3p+q)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\frac{N}{2.3}(1.3p+q)$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$\\frac{N}{2.3}(p+1.3q)$$

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

$$\\frac{N}{1.3}(p+q)$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyuu802iijgodkyhuuytu","texte_question":"

In the coordinate plane, points $$A(0,0)$$, $$B(10,0)$$, and $$C(16,8)$$ are vertices of a triangle. A line through $$A$$ is parallel to $$BC$$, and a line through $$B$$ is parallel to $$AC$$. The two lines intersect at point $$D$$. What is the $$x$$-coordinate of $$D$$?

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

Find the slope of $$BC$$.

$$m_{BC}=\\frac{8-0}{16-10}$$

$$m_{BC}=\\frac{8}{6}$$

$$m_{BC}=\\frac{4}{3}$$

The line through $$A(0,0)$$ parallel to $$BC$$ is:

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

Find the slope of $$AC$$.

$$m_{AC}=\\frac{8-0}{16-0}$$

$$m_{AC}=\\frac{1}{2}$$

The line through $$B(10,0)$$ parallel to $$AC$$ is:

$$y=\\frac{1}{2}(x-10)$$

Set the equations equal.

$$\\frac{4}{3}x=\\frac{1}{2}(x-10)$$

Multiply by $$6$$.

$$8x=3x-30$$

$$5x=-30$$

$$x=-6$$

Final answer: $$-6$$

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

-6

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyuuc02iljgodwxngsx34","texte_question":"

If $$x+\\frac{1}{x}=5$$, what is the value of $$x^3+\\frac{1}{x^3}$$?

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

Use the identity:

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

Given:

$$x+\\frac{1}{x}=5$$

Substitute.

$$x^3+\\frac{1}{x^3}=5^3-3(5)$$

$$=125-15$$

$$=110$$

Final answer: $$110$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$110$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$115$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$120$$

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

$$125$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["Advanced Quizzes"],"date":"2026-06-05T06:38:09.777Z","modified":"2026-06-05T06:38:09.777Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"sat-math-advanced-quizzes-quiz-26"}]}]]}]}]]

Quiz 26

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