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SAT II Math II : SAT Subject Test in Math II

Study concepts, example questions & explanations for SAT II Math II

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All SAT II Math II Resources

2 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Finding Angles

If two angles of a triangle are $\frac{2}{3}\pi, \frac{1}{4}\pi$ radians, what must be the other angle in degrees?

Possible Answers:

Correct answer:

Explanation:

Every pi radians equal 180 degrees.

We can choose to convert the radians to degrees first.

$\frac{2}{3}\pi = \frac{2}{3}(180) = 120$

$\frac{1}{4}\pi = \frac{1}{4}(180) = 45$

The sum of these two angles are:

120+45 = 165

Subtract this value from 180 to determine the third angle.

180-165 = 15

The answer is:

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Example Question #1 : Analyzing Figures

Thingy_5

Refer to the above diagram. Which of the following is not a valid name for $\angle DBF$ ?

Possible Answers:

$\angle B$

All of the other choices give valid names for the angle.

$\angle FBE$

$\angle FBD$

$\angle CBF$

Correct answer:

$\angle B$

Explanation:

$\angle B$ is the correct choice. A single letter - the vertex - can be used for an angle if and only if that angle is the only one with that vertex. This is not the case here. The three-letter names in the other choices all follow the convention of the middle letter being vertex and each of the other two letters being points on a different side of the angle.

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Example Question #371 : Sat Subject Test In Math Ii

Triangle

Use the rules of triangles to solve for x and y.

Possible Answers:

x=30, y=60

x=60, y=30

x=30, y=30

x=45, y=45

Correct answer:

x=60, y=30

Explanation:

Using the rules of triangles and lines we know that the degree of a straight line is 180. Knowing this we can find x by creating and solving the following equation:

x=180-120

x=60

Now using the fact that the interior angles of a triangle add to 180 we can create the following equation and solve for y:

y=180-(90+60)

y=180-150

y=30

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Example Question #372 : Sat Subject Test In Math Ii

Circle

Use the facts of circles to solve for x and y.

Possible Answers:

x=10, y=30

x=39.5, y=11

x=11, y= 39.5

x=13, y=10

Correct answer:

x=11, y= 39.5

Explanation:

In this question we use the rule that oppisite angles are congruent and a line is 180 degrees. Knowing these two facts we can first solve for x then solve for y.

2x=22

x=11

Then:

4y+2x=180

4y+2(11)=180

4y+22=180

4y=158

y=39.5

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Example Question #71 : Geometry

Rhombus

Solve for x and y using the rules of quadrilateral

Possible Answers:

x=2, y=4

x=6, y=10

x=6, y=9

x=9, y=6

Correct answer:

x=6, y=9

Explanation:

By using the rules of quadrilaterals we know that oppisite sides are congruent on a rhombus. Therefore, we set up an equation to solve for x. Then we will use that number and substitute it in for x and solve for y.

2x+4=16

2x=12

x=6

x+y=15

6+y=15

y=9

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Example Question #4 : Analyzing Figures

Chords $\overline{AB}$ and $\overline{CD}$ intersect at point . $\overline{BX}$ is twice as long as $\overline{AX}$ ; CX = 2 and DX = 9 .

Give the length of $\overline{AX}$ .

Possible Answers:

$5\frac{1}{2}$

$4\frac{1}{2}$

$3 \frac{2}{3}$

Correct answer:

Explanation:

If we let t = AX , then BX = 2t .

The figure referenced is below (not drawn to scale):

Chords

If two chords intersect inside the circle, then the cut each other so that for each chord, the product of the lengths of the two parts is the same; in other words,

$AX \cdot BX = CX \cdot DX$

Setting AX = t, BX = 2t, CX = 2, DX = 8 , and solving for :

$t \cdot 2t = 2 \cdot 9$

$2t^{2} =18$

$2t^{2} \div 2 =18 \div 2$

$t^{2} = 9$

Taking the positive square root of both sides:

$t = \sqrt{9} = 3$ ,

the correct length of $\overline{AX}$ .

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Example Question #72 : Geometry

Which of the following describes a triangle with sides of length 9 feet, 4 yards, and 180 inches?

Possible Answers:

The triangle is acute and scalene.

The triangle is right and scalene.

The triangle is right and isosceles, but not equilateral.

The triangle is acute and isosceles, but not equilateral.

The triangle is acute and equilateral.

Correct answer:

The triangle is right and scalene.

Explanation:

3 feet make a yard, so 9 feet is equal to 3 yards. 36 inches make a yard, so 180 inches is equal to $180 \div 36 = 5$ yards. That makes this a 3-4-5 triangle. 3-4-5 is a well-known Pythagorean triple; that is, they have the relationship

$3^{2}+ 4^{2}=5^{2}$

and any triangle with these three sidelengths is a right triangle. Also, since the three sides are of different lengths, the triangle is scalene.

The correct response is that the triangle is right and scalene.

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Example Question #73 : Geometry

Which of the following describes a triangle with sides of length two yards, eight feet, and ten feet?

Possible Answers:

The triangle is right and scalene.

The triangle cannot exist.

The triangle is acute and isosceles.

The triangle is acute and scalene.

The triangle is right and isosceles.

Correct answer:

The triangle is right and scalene.

Explanation:

Two yards is equal to six feet. The sidelengths are 6, 8, and 10, which form a well-known Pythagorean triple with the relationship

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

The triangle is therefore right. Since no two sides have the same length, it is also scalene.

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Example Question #72 : Geometry

Garden

The above figure shows a square garden (in green) surrounded by a dirt path feet wide throughout. Which of the following expressions gives the distance, in feet, from one corner of the garden to the opposite corner?

Possible Answers:

$\left (40 + x \right )\sqrt{2}$

$\left (40 - x \right )\sqrt{2}$

$\left (80 - x \right )\sqrt{2}$

$\left (160- 2x \right )\sqrt{2}$

$\left (80 - 2x \right )\sqrt{2}$

Correct answer:

$\left (80 - 2x \right )\sqrt{2}$

Explanation:

The sidelength of the garden is feet less than that of the entire lot - that is, 80 - 2x . Since the garden is square, the path from one corner to the other is a diagonal of a square, which has length $\sqrt{2}$ times the sidelength. This is

$d = \left (80 - 2x \right )\sqrt{2}$ feet.

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Example Question #4 : Other 2 Dimensional Geometry

Garden

The above figure shows a square garden (in green) surrounded by a dirt path six feet wide throughout. Which of the following expressions gives the distance, in feet, from one corner of the garden to the opposite corner?

Possible Answers:

$\left ( x - 6\right )\sqrt{2}$

$\left (2 x - 24\right )\sqrt{2}$

$12x\sqrt{2}$

$\left (2 x - 12\right )\sqrt{2}$

$\left ( x - 12\right )\sqrt{2}$

Correct answer:

$\left ( x - 12\right )\sqrt{2}$

Explanation:

The sidelength of the garden is $2 \times 6 = 12$ less than that of the entire lot - that is, x - 12 . Since the garden is square, the path from one corner to the other is a diagonal of a square, which has length $\sqrt{2}$ times the sidelength. This is

$d = (x - 12)\sqrt{2}$ feet.

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All SAT II Math II Resources

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SAT II Math II : SAT Subject Test in Math II

Study concepts, example questions & explanations for SAT II Math II

All SAT II Math II Resources

Example Questions

Example Question #13 : Finding Angles

Example Question #1 : Analyzing Figures

Example Question #371 : Sat Subject Test In Math Ii

Example Question #372 : Sat Subject Test In Math Ii

Example Question #71 : Geometry

Example Question #4 : Analyzing Figures

Example Question #72 : Geometry

Example Question #73 : Geometry

Example Question #72 : Geometry

Example Question #4 : Other 2 Dimensional Geometry

All SAT II Math II Resources

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