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SAT II Math I : SAT Subject Test in Math I

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

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : 2 Dimensional Geometry

Thingy

Note: figure NOT drawn to scale.

Refer to the above figure. Quadrilateral BCDE is a square. What is the area of Polygon ABCDE ?

Possible Answers:

Insufficient information is given to calculate the area.

109

189

139

149

Correct answer:

109

Explanation:

Polygon ABCDE is a composite of $\Delta ABE$ and Square BCDE ; its area is the sum of the areas of the two figures.

$\Delta ABE$ is a right triangle; its area is half the product of its legs, which is

$A = \frac{1}{2} \cdot 5 \cdot 8 = 20$

$\overline{BE }$ is both one side of Square BCDE and the hypotenuse of $\Delta ABE$ ; its hypotenuse can be calculated from the lengths of the legs using the Pythagorean Theorem:

$BE = \sqrt{5^{2}+8^{2}} = \sqrt{25 + 64 } = \sqrt{89}$ .

Square BCDE has area the square of this, which is 89.

Polygon ABCDE has as its area the sum of these two areas:

20 + 89 = 109 .

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Example Question #441 : Sat Subject Test In Math I

Find the area of a circle with a diameter of .

Possible Answers:

$32\pi$

$64\pi$

$256\pi$

$81\pi$

$16\pi$

Correct answer:

$64\pi$

Explanation:

Write the formula for the area of a circle.

$A_{circle}= \pi r^2 = \frac{\pi d^2}{4}$

Substitute the diameter and solve.

$\frac{\pi (16)^2}{4} = \frac{\pi (16)(16)}{4}=\pi (16)(4)= 64\pi$

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Example Question #2 : Geometry

Rectangle example

Figure not drawn to scale.

Find the area of the rectangle above when the perimeter is 36 in.

Possible Answers:

72 in²

36 in²

144 in²

70 in²

84 in²

Correct answer:

72 in²

Explanation:

Rectangle example

Because we know the perimeter is 36 inches, we can determine the length of side w based on the equation of the perimeter of a rectangle:

$\small Perimeter= 2(length)+2(width)$

$\small 36=2(12)+2w$

$\small 36=24+2w$

$\small 12=2w$

$\small w=6$

Side w is 6 in long.

Now that we know that side w is 6 inches long, we have everythinng we need to calculate the area of the rectangle.

$\small Area=(length)(width)$

$\small (12)(6)=72$

The area of the rectangle is 72 in²

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Example Question #1 : Geometry

Which of the following shapes is a kite?

Shapes

Possible Answers:

A, B

Correct answer:

A, B

Explanation:

A kite is a four-sided shape with straight sides that has two pairs of sides. Each pair of adjacent sides are equal in length. A square is also considered a kite.

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Example Question #1 : How To Find The Area Of A Kite

What is the area of the following kite?

Kites

Possible Answers:

15m^2

10m^2

30m^2

8m^2

20m^2

Correct answer:

10m^2

Explanation:

The formula for the area of a kite:

$A = \frac{1}{2} (a)(b)$ ,

where represents the length of one diagonal and represents the length of the other diagonal.

Plugging in our values, we get:

$A = \frac{1}{2} (4\: m)(5\: m)$

$A = \frac{1}{2} (20\: m^2) = 10\: m^2$

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Example Question #2 : How To Find The Area Of A Kite

Find the area of a kite if the diagonal dimensions are x+3 and x-6 .

Possible Answers:

$(x^2-3x-18)\sqrt2$

$\frac{x^2-3x+18}{2}$

x^2+3x-18

$\frac{x^2-3x-18}{2}$

$\frac{x^2+3x-18}{2}$

Correct answer:

$\frac{x^2-3x-18}{2}$

Explanation:

The area of the kite is given below. The FOIL method will need to be used to simplify the binomial.

$A=\frac{d1\cdot d2}{2}=\frac{(x+3)(x-6)}{2}= \frac{x^2-6x+3x-18}{2}$

$A= \frac{x^2-3x-18}{2}$

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Example Question #3 : How To Find The Area Of A Kite

The diagonals of a kite are $\sqrt10\:cm$ and $\sqrt5\:cm$ . Find the area.

Possible Answers:

$5\:cm^2$

$\frac{5\sqrt2}{2}\:cm^2$

$5\sqrt2\:cm^2$

$\sqrt5\:cm^2$

$\frac{2\sqrt5}{2}\:cm^2$

Correct answer:

$\frac{5\sqrt2}{2}\:cm^2$

Explanation:

The formula for the area for a kite is

$A=\frac{d_1\cdot d_2}{2}$ , where d_1 and d_2 are the lengths of the kite's two diagonals. We are given the length of these diagonals in the problem, so we can substitute them into the formula and solve for the area:

$A = \frac{d1\cdot d2}{2} = \frac{\sqrt10 \cdot \sqrt5}{2} = \frac{\sqrt50}{2} = \frac{5\sqrt2}{2}\:cm^2$

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Example Question #1 : How To Find The Area Of A Kite

Find the area of a kite with diagonal lengths of a+b and 2a-2b .

Possible Answers:

2a^2-2b^2

a^2-ab-b^2

2a^2+2b^2

a^2+b^2

a^2-b^2

Correct answer:

a^2-b^2

Explanation:

Write the formula for the area of a kite.

$A= \frac{d1\cdot d2}{2}$

Plug in the given diagonals.

$A= \frac{(a+b)\cdot (2a-2b)}{2}$

Pull out a common factor of two in 2a-2b and simplify.

$A= \frac{(a+b)\cdot2(a-b)}{2}$

A=(a+b)(a-b)

Use the FOIL method to simplify.

A=(a+b)(a-b)= (a)(a)+(a)(-b)+(b)(a)+(b)(-b)

A= a^2-b^2

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Example Question #11 : How To Find The Area Of A Rhombus

Find the area of a rhombus if the diagonals lengths are $20\:cm$ and $40\:cm$ .

Possible Answers:

$600\:cm^2$

$200\:cm^2$

$400\:cm^2$

$800\:cm^2$

$900\:cm^2$

Correct answer:

$400\:cm^2$

Explanation:

Write the formula for the area of a rhombus:

$A=\frac{d_1 \cdot d_2}{2}$

Substitute the given lengths of the diagonals and solve:

$A=\frac{d1 \cdot d2}{2} = \frac{20\:cm \cdot 40\:cm}{2} =\frac{800\:cm^2}{2} = 400\:cm^2$

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Example Question #11 : How To Find The Area Of A Rhombus

Find the area of a rhombus if the diagonals lengths are and 5a^2 .

Possible Answers:

10a^3

5a^3

5a^2

2a+5a^2

7a^3

Correct answer:

5a^3

Explanation:

Write the formula for finding the area of a rhombus. Substitute the diagonals and evaluate.

$A=\frac{d1\cdot d2}{2}= \frac{2a \cdot 5a^2}{2}= 5a^3$

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All SAT II Math I Resources

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SAT II Math I : SAT Subject Test in Math I

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

All SAT II Math I Resources

Example Questions

Example Question #5 : 2 Dimensional Geometry

Example Question #441 : Sat Subject Test In Math I

Example Question #2 : Geometry

Find the area of the rectangle above when the perimeter is 36 in.

Side w is 6 in long.

The area of the rectangle is 72 in²

Example Question #1 : Geometry

Example Question #1 : How To Find The Area Of A Kite

Example Question #2 : How To Find The Area Of A Kite

Example Question #3 : How To Find The Area Of A Kite

Example Question #1 : How To Find The Area Of A Kite

Example Question #11 : How To Find The Area Of A Rhombus

Example Question #11 : How To Find The Area Of A Rhombus

All SAT II Math I Resources

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SAT II Math I : SAT Subject Test in Math I

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

All SAT II Math I Resources

Example Questions

Example Question #5 : 2 Dimensional Geometry

Example Question #441 : Sat Subject Test In Math I

Example Question #2 : Geometry

Find the area of the rectangle above when the perimeter is 36 in.

Side w is 6 in long.

The area of the rectangle is 72 in2

Example Question #1 : Geometry

Example Question #1 : How To Find The Area Of A Kite

Example Question #2 : How To Find The Area Of A Kite

Example Question #3 : How To Find The Area Of A Kite

Example Question #1 : How To Find The Area Of A Kite

Example Question #11 : How To Find The Area Of A Rhombus

Example Question #11 : How To Find The Area Of A Rhombus

All SAT II Math I Resources

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DMCA Complaint

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The area of the rectangle is 72 in²