7:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Quiz 29\",\"description\":\"Advanced SAT Math Quiz 29\",\"url\":\"https://theschoolofmathematics.com/quiz/sat-math-advanced-quizzes-quiz-29\",\"educationalLevel\":\"Advanced\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Advanced Quizzes\"}}"}}],["$","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 29\",\"item\":\"https://theschoolofmathematics.com/quiz/sat-math-advanced-quizzes-quiz-29\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","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 29"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","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 29

"}}],["$","div",null,{"className":"grid grid-cols-2 md:grid-cols-3 gap-4","children":["$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":2304,"prismaId":"cmq0jyv2402lmjgodhzp1bp6f","slug":"sat-math-advanced-quizzes-quiz-29","title":{"rendered":"Quiz 29"},"content":{"rendered":"

Advanced SAT Math Quiz 29

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

Advanced SAT Math Quiz 29

"},"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":"cmq0jyv2902lojgodvpscik0a","texte_question":"

The function $$h$$ is defined by $$h(x)=-\\sqrt{x^2+bx+c}$$, where $$b$$ and $$c$$ are constants. In the $$xy$$-plane, the graph of $$y=h(x)$$ contains the points $$(2,0)$$ and $$(0,-\\sqrt{266})$$. If $$h(m)=0$$, what is the greatest possible value of $$m$$?

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

Since the graph contains $$(0,-\\sqrt{266})$$:

$$h(0)=-\\sqrt{c}=-\\sqrt{266}$$

So: $$c=266$$

Since the graph contains $$(2,0)$$:

$$h(2)=0$$

$$-\\sqrt{2^2+2b+266}=0$$

So, the expression inside the square root equals $$0$$.

$$4+2b+266=0$$

$$2b+270=0$$

$$b=-135$$

Now:

$$h(m)=0$$

So:

$$m^2-135m+266=0$$

Factor.

$$(m-2)(m-133)=0$$

The possible values of $$m$$ are $$2$$ and $$133$$.

Final answer: $$133$$

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

133

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2c02lrjgod255hk62u","texte_question":"

The function $$f$$ is defined by $$f(x)=\\frac{|x|}{a}-16$$, where $$a$$ < $$0$$. What is the product of $$f(17a)$$ and $$f(8a)$$?

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

Since $$a$$ < $$0$$, both $$17a$$ and $$8a$$ are negative.

So:

$$|17a|=-17a$$ and $$|8a|=-8a$$

Find $$f(17a)$$.

$$f(17a)=\\frac{|17a|}{a}-16$$

$$f(17a)=\\frac{-17a}{a}-16$$

$$f(17a)=-17-16$$

$$f(17a)=-33$$

Find $$f(8a)$$.

$$f(8a)=\\frac{|8a|}{a}-16$$

$$f(8a)=\\frac{-8a}{a}-16$$

$$f(8a)=-8-16$$

$$f(8a)=-24$$

Now multiply.

$$(-33)(-24)=792$$

Final answer: $$792$$

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

792

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2f02lujgod4bzb1qed","texte_question":"

Two spheres have radii in the ratio $$12:13$$. The difference in their surface areas is $$400\\pi$$ square inches. If the volume of the smaller sphere can be written as $$v\\pi$$, what is the value of $$v$$?

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

Let the radii be $$12x$$ and $$13x$$. The surface area of a sphere is: $$4\\pi r^2$$

The difference in surface areas is:

$$4\\pi(13x)^2-4\\pi(12x)^2=400\\pi$$

Factor.

$$4\\pi(169x^2-144x^2)=400\\pi$$

$$4\\pi(25x^2)=400\\pi$$

$$100\\pi x^2=400\\pi$$

Divide by $$100\\pi$$.

$$x^2=4$$

$$x=2$$

The smaller radius is: $$12(2)=24$$

The volume of the smaller sphere is:

$$V=\\frac{4}{3}\\pi r^3$$

$$V=\\frac{4}{3}\\pi(24)^3$$

$$V=18432\\pi$$

Final answer: $$18432$$

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

$$18432$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2i02lxjgod723mz58d","texte_question":"

The function $$q$$ is defined by $$q(x)=a|x-9|^2-53|x-9|+b$$ where $$a$$ and $$b$$ are constants, and $$a$$ > $$b$$ > $$53$$. If $$q(539)=h$$ and $$q(-521)=k$$, where $$h$$ and $$k$$ are constants, what is the value of $$32(-539)^{h-k}+347(9)^{k-h}$$?

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

Evaluate the absolute value expressions.

For $$x=539$$:

$$|539-9|=530$$

For $$x=-521$$:

$$|-521-9|=|-530|=530$$

So:

$$q(539)=q(-521)$$

Therefore: $$h=k$$

So:

$$h-k=0$$ and $$k-h=0$$

Substitute into the expression.

$$32(-539)^0+347(9)^0$$

Any nonzero number to the power $$0$$ equals $$1$$.

$$32(1)+347(1)=379$$

Final answer: $$379$$

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

379

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2m02m0jgodtwdx8dja","texte_question":"

A circle in the $$xy$$-plane has its center at $$(2,-3)$$ and has a radius of $$7$$. An equation of this circle is $$x^2+y^2+ax+by+c=0$$, where $$a$$, $$b$$, and $$c$$ are constants. What is the value of $$c$$?

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

Use the circle equation.

$$(x-2)^2+(y+3)^2=7^2$$

Expand.

$$x^2-4x+4+y^2+6y+9=49$$

Move all terms to one side.

$$x^2+y^2-4x+6y+13-49=0$$

$$x^2+y^2-4x+6y-36=0$$

So:

$$c=-36$$

Final answer: $$-36$$

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

$$-6$$

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

$$6$$

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

$$-36$$

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

$$-49$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2p02m6jgodubnkc48i","texte_question":"

A polynomial function $$P(x)$$ has roots at $$x=2$$, $$x=-3$$, and $$x=5$$. If the degree of $$P(x)$$ is $$3$$ and $$P(0)=90$$, what is the value of $$P(1)$$?

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

Since the roots are $$2$$, $$-3$$, and $$5$$, write:

$$P(x)=a(x-2)(x+3)(x-5)$$

Use $$P(0)=90$$.

$$90=a(0-2)(0+3)(0-5)$$

$$90=a(-2)(3)(-5)$$

$$90=30a$$

$$a=3$$

Now find $$P(1)$$.

$$P(1)=3(1-2)(1+3)(1-5)$$

$$P(1)=3(-1)(4)(-4)$$

$$P(1)=48$$

Final answer: $$48$$

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

$$8$$

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

$$25$$

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

$$37$$

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

$$48$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2u02mcjgod6tqcvk7x","texte_question":"

In right triangle $$\\triangle ABC$$, angle $$C$$ is the right angle. An altitude $$CD$$ is drawn from vertex $$C$$ to the hypotenuse $$AB$$, with point $$D$$ on $$AB$$. If the length of $$CD$$ is $$12$$ units and $$\\sin(\\angle A)=\\frac{3}{5}$$, what is the perimeter, in units, of $$\\triangle ABC$$?

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

Since $$\\sin(\\angle A)=\\frac{3}{5}$$, the triangle has side ratio: $$3:4:5$$

Let the legs be $$3s$$ and $$4s$$, and the hypotenuse be $$5s$$.

The altitude from the right angle to the hypotenuse is: $$\\frac{(3s)(4s)}{5s}$$

Simplify.

$$\\frac{12s^2}{5s}=\\frac{12s}{5}$$

Given the altitude is $$12$$:

$$\\frac{12s}{5}=12$$ $$s=5$$

The perimeter is:

$$3s+4s+5s=12s$$

$$12(5)=60$$

Final answer: $$60$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$48$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$60$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$72$$

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

$$84$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv2y02mijgod5qqrng6y","texte_question":"

A circle in the $$xy$$-plane has the equation $$(x-3)^2+(y+2)^2=25$$. Point $$P$$ has coordinates $$(10,8)$$. A line segment is drawn from point $$P$$ tangent to the circle at point $$T$$. What is the length of segment $$PT$$?

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

The center of the circle is: $$(3,-2)$$

The radius is: $$5$$

Find the distance from $$P(10,8)$$ to the center.

$$PC=\\sqrt{(10-3)^2+(8-(-2))^2}$$

$$PC=\\sqrt{7^2+10^2}$$

$$PC=\\sqrt{149}$$

The radius to the tangent point is perpendicular to the tangent segment.

So:

$$PT^2=PC^2-r^2$$

$$PT^2=149-25$$

$$PT^2=124$$

$$PT=2\\sqrt{31}$$

Final answer: $$2\\sqrt{31}$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$5$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$\\sqrt{149}$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2\\sqrt{31}$$

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

$$\\sqrt{174}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv3202mojgod3eks3aq8","texte_question":"

In a right triangle, one of the acute angles, $$\\theta$$, has a sine of $$\\frac{5}{13}$$. If the perimeter of this triangle is $$120$$, what is the length of the shortest side?

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

Since: $$\\sin\\theta=\\frac{5}{13}$$

The right triangle has side ratio: $$5:12:13$$

The perimeter of this basic triangle is:

$$5+12+13=30$$

The actual perimeter is $$120$$.

So, the scale factor is:

$$\\frac{120}{30}=4$$

The shortest side is:

$$5(4)=20$$

Final answer: $$20$$

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

$$20$$

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

$$24$$

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

$$48$$

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

$$52$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyv3602mujgodug7gs68q","texte_question":"

A small factory produces two types of custom-made furniture: chairs and tables. Each chair requires $$2$$ hours for assembly and $$1$$ hour for finishing. Each table requires $$3$$ hours for assembly and $$2$$ hours for finishing. The factory has a maximum of $$180$$ assembly hours available per week and a maximum of $$100$$ finishing hours available per week. Due to customer demand, the factory must produce at least $$20$$ chairs per week and at least $$10$$ tables per week. Let $$x$$ represent the number of chairs and $$y$$ represent the number of tables produced per week. Which of the following systems of inequalities describes the possible number of chairs and tables that the factory can produce per week?

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

Each chair requires $$2$$ assembly hours, and each table requires $$3$$ assembly hours.

The assembly constraint is: $$2x+3y\\le180$$

Each chair requires $$1$$ finishing hour, and each table requires $$2$$ finishing hours.

The finishing constraint is: $$x+2y\\le100$$

The factory must produce at least $$20$$ chairs.

$$x\\ge20$$

The factory must produce at least $$10$$ tables.

$$y\\ge10$$

Final answer: $$2x+3y\\le180,\\ x+2y\\le100,\\ x\\ge20,\\ y\\ge10$$

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

$$2x+3y\\ge180$$

$$x+2y\\ge100$$

$$x\\le20$$

$$y\\le10$$

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

$$2x+3y\\le180$$

$$x+2y\\ge100$$

$$x\\ge20$$

$$y\\le10$$

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

$$2x+3y\\le180$$

$$x+2y\\le100$$

$$x\\ge20$$

$$y\\ge10$$

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

$$2x+3y\\le180$$

$$x+2y\\ge100$$

$$x\\le20$$

$$y\\ge10$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["Advanced Quizzes"],"date":"2026-06-05T06:38:10.108Z","modified":"2026-06-05T06:38:10.108Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L18",null,{"targetType":"quiz","targetSlug":"sat-math-advanced-quizzes-quiz-29"}]}]]}]}]]

Quiz 29

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