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

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SAT Math Advanced Quizzes - Quiz 10.

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

SAT Math Advanced Quizzes Quiz 10

"},"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":"cmq0jythe01qwjgodrsbxetc1","texte_question":"$18","type_question":"QCM","explication":"

The area of the square is $$36$$. So, the side length is: $$s=6$$

The diagonal of the square is the diameter of the circle.

$$d=6\\sqrt{2}$$

So, the radius is:

$$r=3\\sqrt{2}$$

The shaded region is bounded by the top side of the square and the top arc of the circle.

The top arc is one-fourth of the circle.

Arc length:

$$\\frac{1}{4}(2\\pi r)$$ $$=\\frac{1}{4}(2\\pi(3\\sqrt{2}))$$

$$=\\frac{3\\sqrt{2}}{2}\\pi$$

Add the top side of the square.

$$6+\\frac{3\\sqrt{2}}{2}\\pi$$

Final answer: $$6+\\frac{3\\sqrt{2}}{2}\\pi$$

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

$$6+\\frac{3\\sqrt{2}}{2}\\pi$$

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

$$6+3\\pi$$

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

$$6+3\\sqrt{2}\\pi$$

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

$$36+6\\sqrt{2}\\pi$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jythn01r2jgody52zdka3","texte_question":"

What is the solution set for the equation $$\\sqrt{x+22}-2=x$$?

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

Start with the equation.

$$\\sqrt{x+22}-2=x$$

Add $$2$$ to both sides.

$$\\sqrt{x+22}=x+2$$

Square both sides.

$$x+22=(x+2)^2$$

Expand.

$$x+22=x^2+4x+4$$

Move all terms to one side.

$$0=x^2+3x-18$$

Factor.

$$(x+6)(x-3)=0$$

So:

$$x=-6$$ or $$x=3$$

Check in the original equation.

For $$x=-6$$, the right side is negative, but the left side is not equal to $$-6$$.

So, the only solution is: $$x=3$$

Final answer: $${3}$$

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

$$\\{-6,3\\}$$

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

$$\\{-6\\}$$

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

$$\\{3\\}$$

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

$$\\{-3,6\\}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jythr01r8jgodv478boo4","texte_question":"

A data set of $$27$$ different numbers has a mean of $$33$$ and a median of $$33$$. A new data set is created by adding $$7$$ to each number in the original data set that is greater than the median and subtracting $$7$$ from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

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

There are $$27$$ different numbers. The median is the middle value, so there are $$13$$ numbers below the median and $$13$$ numbers above the median. Each of the $$13$$ numbers above the median increases by $$7$$.

Total increase:

$$13(7)=91$$

Each of the $$13$$ numbers below the median decreases by $$7$$.

Total decrease:

$$13(7)=91$$

The total sum does not change, so the mean does not change. The median value stays $$33$$. However, the numbers move farther away from the mean, so the standard deviation changes.

Final answer: Standard deviation.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"Median","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"Mean","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"Sum of the numbers","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

Standard deviation

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jythw01rejgodd84zgewa","texte_question":"

The concentration of a chemical compound is equal to the amount of the substance, in moles, divided by the volume of the solution, in cubic centimeters. A chemist has two containers of different sizes in the shape of a cube. The edge length of the larger container is $$4$$ times the edge length of the smaller container. Each cube contains $$144$$ moles of a substance. The concentration of the compound in the larger container is $$3$$ moles per cubic centimeter. What is the positive difference between the larger container's volume and the smaller container's volume, in cubic centimeters?

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

Use the concentration formula.

$$\\text{concentration}=\\frac{\\text{moles}}{\\text{volume}}$$

For the larger container:

$$3=\\frac{144}{V}$$

Solve for $$V$$.

$$3V=144$$

$$V=48$$

The larger container volume is $$48$$ cubic centimeters.

If the larger edge length is $$4$$ times the smaller edge length, then the larger volume is: $$4^3=64$$ times the smaller volume.

So, the smaller volume is:

$$\\frac{48}{64}=\\frac{3}{4}$$

The positive difference is:

$$48-\\frac{3}{4}$$

$$=\\frac{192}{4}-\\frac{3}{4}$$

$$=\\frac{189}{4}$$

Final answer: $$\\frac{189}{4}$$

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

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

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

$$\\frac{189}{4}$$

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

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

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

$$\\frac{9}{4}$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jyti001rkjgodnn893tji","texte_question":"$19","type_question":"QCM","explication":"

The hypotenuse of the right triangle is the diameter of the circle.

Use the Pythagorean theorem.

$$6^2+8^2=10^2$$

So, the hypotenuse is: $$10$$

The radius of the circle is half the diameter. $$r=5$$

The area of the circle is:

$$\\pi r^2$$ $$=25\\pi$$

The area of the right triangle is:

$$\\frac{1}{2}(6)(8)=24$$

The shaded region is the circle minus the triangle.

$$25\\pi-24$$

Final answer: $$25\\pi-24$$

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

$$100\\pi$$

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

$$100\\pi-48$$

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

$$25\\pi-48$$

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

$$25\\pi-24$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jytif01rqjgodbg776gc2","texte_question":"

A researcher conducted a survey of $$1000$$ randomly selected residents to determine their favorite park. The survey showed that $$48\\%$$ of the residents preferred Park A, with a margin of error of $$3\\%$$. Which of the following is the best conclusion?

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

The survey estimate is: $$48\\%$$

The margin of error is: $$3\\%$$

So, the plausible interval is:

$$48\\%-3\\%$$ to $$48\\%+3\\%$$

$$45\\%$$ to $$51\\%$$

This applies to all residents in the city, not only the people surveyed.

Final answer: It is highly likely that between $$45\\%$$ and $$51\\%$$ of all residents in the city prefer Park A.

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

Exactly $$48\\%$$ of all residents in the city prefer Park A.

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

Between $$45\\%$$ and $$51\\%$$ of the people surveyed prefer Park A.

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

It is highly likely that between $$45\\%$$ and $$51\\%$$ of all residents in the city prefer Park A.

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

The survey is flawed because the margin of error is greater than $$0\\%$$.

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jytik01rwjgod0r65my52","texte_question":"

The function $$f$$ is defined by $$f(x)=5(0.92)^{3x}$$ The equation can be rewritten as $$f(x)=5\\left(1-\\frac{r}{100}\\right)^x$$, where $$r$$ is a constant. Which of the following is closest to the value of $$r$$?

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

Rewrite the expression.

$$5(0.92)^{3x}=5((0.92)^3)^x$$

So:

$$1-\\frac{r}{100}=(0.92)^3$$

Calculate.

$$(0.92)^3=0.778688$$

Thus:

$$1-\\frac{r}{100}=0.778688$$

Subtract from $$1$$.

$$\\frac{r}{100}=0.221312$$

Multiply by $$100$$.

$$r=22.1312$$

The closest choice is: $$22$$

Final answer: $$22$$

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"$$$8$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$12$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$22$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$24$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jytio01s2jgodh0rmgm3u","texte_question":"

A particular integer $$N$$ is divisible by two different prime numbers $$p$$ and $$q$$. Which of the following must be true?

I. $$N$$ is not a prime number.

II. $$N$$ is divisible by $$pq$$.

III. $$N$$ is an odd integer.

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

Since $$N$$ is divisible by two different prime numbers, $$N$$ must have at least two prime factors. Therefore, $$N$$ cannot be prime. Statement I is true.

Since $$p$$ and $$q$$ are different primes, they share no common factor other than $$1$$. If $$N$$ is divisible by both $$p$$ and $$q$$, then $$N$$ is divisible by their product: $$pq$$ Statement II is true.

Statement III is not always true because one of the primes could be $$2$$. For example, $$N=6$$ is divisible by $$2$$ and $$3$$, but $$6$$ is even.

Final answer: I and II only.

","points":1,"temps_limite":"$undefined","reponses":[{"texte":"I only","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"II only","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"I and II only","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"I and III only","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jytiu01s8jgodpkdb3254","texte_question":"

For an electric field passing through a flat surface perpendicular to it, the electric flux is the product of the electric field's strength and the area of the surface. A certain flat surface consists of two adjacent squares, where the side length of the larger square is $$3$$ times the side length of the smaller square. An electric field with strength $$29.00$$ volts per meter passes uniformly through this surface. If the total electric flux through this surface is $$4640$$ volt-meters, what is the electric flux, in volt-meters, of the electric field through the larger square?

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

Let the side length of the smaller square be $$s$$.

Then the side length of the larger square is: $$3s$$

The area of the smaller square is: $$s^2$$

The area of the larger square is:

$$(3s)^2=9s^2$$

The total area is:

$$s^2+9s^2=10s^2$$

The larger square accounts for:

$$\\frac{9s^2}{10s^2}=\\frac{9}{10}$$ of the total area.

Since the electric field is uniform, the larger square also accounts for $$\\frac{9}{10}$$ of the total flux.

$$\\frac{9}{10}(4640)=4176$$

Final answer: $$4176$$

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

4176

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmq0jytj001sbjgodfu1x4pcj","texte_question":"

Let $$p(x)=x^3-3x^2+kx-4$$, where $$k$$ is a constant. If the polynomial $$p(x)$$ is divisible by $$x-2$$, what is the value of $$k$$?

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

If $$p(x)$$ is divisible by $$x-2$$, then by the factor theorem: $$p(2)=0$$

Substitute $$x=2$$.

$$p(2)=2^3-3(2)^2+k(2)-4$$

$$p(2)=8-12+2k-4$$

$$p(2)=2k-8$$

Set equal to $$0$$.

$$2k-8=0$$

$$2k=8$$

$$k=4$$

Final answer: $$4$$

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

$$4$$

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

$$5$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]}]},"categories":["Advanced Quizzes"],"date":"2026-06-05T06:38:08.060Z","modified":"2026-06-05T06:38:08.060Z"}}],["$","div",null,{"className":"container mx-auto px-4 pb-12","children":["$","$L1a",null,{"targetType":"quiz","targetSlug":"sat-math-advanced-quizzes-quiz-10"}]}]]}]}]]

Quiz 10

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