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New SAT Writing and Language : New SAT

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Example Questions

Example Question #183 : Coordinate Geometry

The measure of the supplement of angle A is 40 degrees larger than twice the measure of the complement of angle A. What is the sum, in degrees, of the measures of the supplement and complement of angle A?

Possible Answers:

190

140

Correct answer:

190

Explanation:

Let A represent the measure, in degrees, of angle A. By definition, the sum of the measures of A and its complement is 90 degrees. We can write the following equation to determine an expression for the measure of the complement of angle A.

A + measure of complement of A = 90

Subtract A from both sides.

measure of complement of A = 90 – A

Similarly, because the sum of the measures of angle A and its supplement is 180 degrees, we can represent the measure of the supplement of A as 180 – A.

The problem states that the measure of the supplement of A is 40 degrees larger than twice the measure of the complement of A. We can write this as 2(90-A) + 40.

Next, we must set the two expressions 180 – A and 2(90 – A) + 40 equal to one another and solve for A:

180 – A = 2(90 – A) + 40

Distribute the 2:

180 - A = 180 – 2A + 40

Add 2A to both sides:

180 + A = 180 + 40

Subtract 180 from both sides:

A = 40

Therefore the measure of angle A is 40 degrees.

The question asks us to find the sum of the measures of the supplement and complement of A. The measure of the supplement of A is 180 – A = 180 – 40 = 140 degrees. Similarly, the measure of the complement of A is 90 – 40 = 50 degrees.

The sum of these two is 140 + 50 = 190 degrees.

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Example Question #242 : New Sat Math Calculator

$\dpi{100} \small \overline{AB}$ is a straight line. $\dpi{100} \small \overline{CD}$ intersects $\dpi{100} \small \overline{AB}$ at point $\dpi{100} \small E$ . If $\dpi{100} \small \angle AEC$ measures 120 degrees, what must be the measure of $\dpi{100} \small \angle BEC$ ?

Possible Answers:

$\dpi{100} \small 75$ degrees

None of the other answers

$\dpi{100} \small 70$ degrees

$\dpi{100} \small 60$ degrees

$\dpi{100} \small 65$ degrees

Correct answer:

$\dpi{100} \small 60$ degrees

Explanation:

$\dpi{100} \small \angle AEC$ & $\dpi{100} \small \angle BEC$ must add up to 180 degrees. So, if $\dpi{100} \small \angle AEC$ is 120, $\dpi{100} \small \angle BEC$ (the supplementary angle) must equal 60, for a total of 180.

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Example Question #11 : Plane Geometry

Two parallel lines are intersected by a transversal. If the minor angle of intersection between the first parallel line and the transversal is $36^{\circ}$ , what is the minor angle of intersection between the second parallel line and the transversal?

Possible Answers:

$18^{\circ}$

$66^{\circ}$

$54^{\circ}$

$144^{\circ}$

$36^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

When a line intersects two parallel lines as a transversal, it always passes through both at identical angles (regardless of distance or length of arc).

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Example Question #11 : Geometry

If $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ , $\overline{BE}\perp \overleftrightarrow{GC}$ , and $m\angle HGC=58^\circ$ , what is the measure, in degrees, of $\angle ABE$ ?

Alternate interior angles

Possible Answers:

122

148

Correct answer:

148

Explanation:

The question states that $\overleftrightarrow{FH} \parallel \overleftrightarrow{AD}$ . The alternate interior angle theorem states that if two parallel lines are cut by a transversal, then pairs of alternate interior angles are congruent; therefore, we know the following measure:

$m\angle GCA = 58^\circ$

The sum of angles of a triangle is equal to 180 degrees. The question states that $\overline{BE}\perp \overleftrightarrow{GC}$ ; therefore we know the following measure:

$m \angle BEC = 90^\circ$

Use this information to solve for the missing angle: $\angle EBC$

$180^\circ=m\angle EBC+58^\circ+90^\circ$

$m\angle EBC=32^\circ$

The degree measure of a straight line is 180 degrees; therefore, we can write the following equation:

$180^\circ=m\angle ABE+32^\circ$

$m\angle ABE=148^\circ$

The measure of $\angle ABE$ is 148 degrees.

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Example Question #2 : How To Find An Angle Of A Line

Lines A and B in the diagram below are parallel. The triangle at the bottom of the figure is an isosceles triangle.

Act2

What is the degree measure of angle ?

Possible Answers:

Correct answer:

Explanation:

Since A and B are parallel, and the triangle is isosceles, we can use the supplementary rule for the two angles, and 2x+30 which will sum up to 180 . Setting up an algebraic equation for this, we get 4x+2x+30=180 . Solving for , we get x=25 . With this, we can get either 2(25)+30=80 (for the smaller angle) or 4(25)=100 (for the larger angle - must then use supplementary rule again for inner smaller angle). Either way, we find that the inner angles at the top are 80 degrees each. Since the sum of the angles within a triangle must equal 180, we can set up the equation as 80+80+y=180

y=20 degrees.

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Example Question #1 : How To Simplify Square Roots

Which of the following is equal to $\sqrt{75}$ ?

Possible Answers:

$5\sqrt{3}$

$3\sqrt{5}$

$7.5\sqrt{10}$

Correct answer:

$5\sqrt{3}$

Explanation:

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

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Example Question #23 : Arithmetic

Simplify $\sqrt{a^{3}b^{4}c^{5}}$ .

Possible Answers:

$ab^{2}c^{2}\sqrt{ac}$

$a^{2}b^{2}c^{2}\sqrt{bc}$

$a^{2}bc^{2}\sqrt{ac}$

$a^{2}bc\sqrt{bc}$

$a^{2}b^{2}c\sqrt{ab}$

Correct answer:

$ab^{2}c^{2}\sqrt{ac}$

Explanation:

Rewrite what is under the radical in terms of perfect squares:

$x^{2}=x\cdot x$

$x^{4}=x^{2}\cdot x^{2}$

$x^{6}=x^{3}\cdot x^{3}$

Therefore, $\sqrt{a^{3}b^{4}c^{5}}= \sqrt{a^{2}a^{1}b^{4}c^{4}c^{1}}=ab^{2}c^{2}\sqrt{ac}$ .

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Example Question #2 : Simplifying Square Roots

What is $\sqrt{50}$ ?

Possible Answers:

$2\sqrt{5}$

$10\sqrt{2}$

$5\sqrt{2}$

Correct answer:

$5\sqrt{2}$

Explanation:

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves $\sqrt{2}$ which can not be simplified further.

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Example Question #25 : Arithmetic

Which of the following is equivalent to $\frac{x + \sqrt{3}}{3x + \sqrt{2}}$ ?

Possible Answers:

$\frac{3x^{2} + \sqrt{6}}{3x - 2}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

$\frac{3x^{2} - \sqrt{6}}{9x^{2} + 2}$

$\frac{3x^{2} + 3x\sqrt{2} + x\sqrt{3} +\sqrt{6}}{9x^{2} - 2}$

$\frac{4x + \sqrt{5}}{3x + 2}$

Correct answer:

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

Explanation:

Multiply by the conjugate and the use the formula for the difference of two squares:

$\frac{x + \sqrt{3}}{3x + \sqrt{2}}$

$\frac{x + \sqrt{3}}{3x + \sqrt{2}}\cdot \frac{3x - \sqrt{2}}{3x - \sqrt{2}}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{(3x)^{2} - (\sqrt{2})^{2}}$

$\frac{3x^{2} -x \sqrt{2} + 3x\sqrt{3} - \sqrt{6}}{9x^{2} - 2}$

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Example Question #3 : Simplifying Square Roots

Which of the following is the most simplified form of:

$\sqrt{468}$

Possible Answers:

$\sqrt{468}$

$17\sqrt{2}$

$2\sqrt{117}$

$6\sqrt{13}$

$4\sqrt{29}$

Correct answer:

$6\sqrt{13}$

Explanation:

First find all of the prime factors of 468

$468=6\ast78=6\ast6\ast13=2\ast3\ast2\ast3\ast13$

So $\sqrt{468}=\sqrt{2\ast2\ast3\ast3\ast13}=2\ast3\sqrt{13}=6\sqrt{13}$

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New SAT Writing and Language : New SAT

Study concepts, example questions & explanations for New SAT Writing and Language

All New SAT Writing and Language Resources

Example Questions

Example Question #183 : Coordinate Geometry

Example Question #242 : New Sat Math Calculator

Example Question #11 : Plane Geometry

Example Question #11 : Geometry

Example Question #2 : How To Find An Angle Of A Line

Example Question #1 : How To Simplify Square Roots

Example Question #23 : Arithmetic

Example Question #2 : Simplifying Square Roots

Example Question #25 : Arithmetic

Example Question #3 : Simplifying Square Roots

All New SAT Writing and Language Resources

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