SAT Practice Questions

✓ Correct answer: 144

You can eliminate choice A as a Clunker right away. 90 degrees would represent a perfect quarter of the circle. The angle labeled d° is between 90 and 180 degrees. (Remember, on geometry diagrams where you are not specifically told that the figure is not drawn to scale, you can assume that it is. When a figure is drawn to scale, you can make judgments about its measurements based upon the way things look.) Since a circle contains 360 degrees, the regions between each of the ten equally spaced points each contain 36°: 360° ÷ 10 = 36°. Since the angle labeled d° is composed of four of these regions, it measures 144°: 36° × 4 = 144°.

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✓ Correct answer: <tex>\displaystyle \frac{1}{25}</tex>

While this problem asks about probability, it's essentially an area of a circle problem. The probability of hitting the bullseye is just the area of the bullseye divided by the area of the dartboard in total.<br/><br/>Since <tex>\displaystyle Area=\pi r^2</tex> your job becomes to find the radius of each circle. You're quoted the diameters, so to find the radius just divide the diameter by 2.<br/><br/>Bullseye: Diameter = 4 so Radius = 2. Area = <tex>\displaystyle \pi (2^2)=4\pi</tex><br/><br/>Dartboard: Diameter = 20 so Radius = 10. Area = <tex>\displaystyle \pi (10^2)=100\pi</tex><br/><br/>So the probability of hitting the bullseye is <tex>\displaystyle \frac{4\pi }{100\pi }</tex> which reduces to <tex>\displaystyle \frac{1}{25}</tex>.

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✓ Correct answer: <tex>\displaystyle r^2 -2r +3</tex>

To simplify, remove parentheses and combine like terms, remembering the ever-important step of applying the negative sign to each term within the second set of parentheses:<br/><br/><tex>\displaystyle 5r^2 +3r - 5 -4r^2 -5r +8</tex><br/><br/><tex>\displaystyle 5r^2 -4r^2 +3r-5r-5+8</tex><br/><br/><tex>\displaystyle r^2 -2r +3</tex>

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✓ Correct answer: 8

Function questions tend to derive most of their difficulty from the abstract function notation itself. So being comfortable with approaching function notation is most of the battle. When you see function notation such as <tex>\displaystyle f(x)</tex>, keep in mind that <tex>\displaystyle x</tex> is the "input" (whatever they tell you <tex>\displaystyle x</tex> is, put that into the equation), and that <tex>\displaystyle f(x)</tex> is the "output" (once you've put your input through the equation, the result is the value of <tex>\displaystyle f(x)</tex>).<br/><br/>So when you're given <tex>\displaystyle f(x)=\sqrt{x^2-2x+1}</tex>, what the problem is really saying is that "whatever we put in the parentheses of <tex>\displaystyle f()</tex>, plug that value in wherever you see an <tex>\displaystyle x</tex> in <tex>\displaystyle f(x)=\sqrt{x^2-2x+1}</tex>. <br/><br/>Which means you'll take the input value, square it, subtract the product of the input value and two, add one to that, and then take the square root of the whole thing. With 9, that looks like:<br/><br/><tex>\displaystyle f(9)=\sqrt{9^2-2(9)+1}</tex><br/><br/>You can then simplify the math underneath the radical to get:<br/><br/><tex>\displaystyle \sqrt{81-18+1}=\sqrt{64}</tex><br/><br/>And since you know that <tex>\displaystyle \sqrt{64}=8</tex> you have your answer.

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✓ Correct answer: <i>x </i>+ 2

The curve representing p(x) crosses the x-axis at x = -2, so x - (-2) = x + 2 must be a factor of p(x).

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✓ Correct answer: X - 4

We can model this by getting Eddie’s age now and then figuring out how old he was 11 years ago. Right now, he is x+7 . Eleven years ago, Eddie was x + 7 -11 = x - 4 years old. This is answer B.<br/><br/>a. The correct calculation should be x+ 7 (to get Eddie’s age now) - 11 , which is x - 4 .<br/><br/>b. Correct<br/><br/>c. This is an incorrect calculation of Eddie’s present age.<br/><br/>d. This response does not relate their ages properly.<br/><br/>e. This also does not express their age relationship properly.

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✓ Correct answer: <tex>\displaystyle x \lt \frac{5}{3}</tex>

Whenever you're dealing with absolute values and inequalities, you need to consider two possibilities. In case one, the expression within the absolute value directly satisfies the inequality. In case two, the expression within the absolute value will satisfy the opposite, taken by flipping the inequality sign and negating the entire other side of the inequality (think "a is greater than 1 or less than negative-one" --> case two is that "less than negative..." case). Let's examine both here.<br/><br/>Case 1<br/><br/><tex>\displaystyle 2x+1 \gt 5x-4</tex><br/><br/>Here you can subtract <tex>\displaystyle 2x</tex> from both sides and add <tex>\displaystyle 4</tex> to both sides to isolate the variable:<br/><br/><tex>\displaystyle 5 \gt 3x</tex><br/><br/>Then divide both sides by <tex>\displaystyle 3</tex> and you have:<br/><br/><tex>\displaystyle x \lt \frac{5}{3}</tex><br/><br/>It's a good idea to try a number that just barely satisfies your new inequality to ensure that it fits with the given inequality. If you try <tex>\displaystyle x=1</tex> here, you'll see that you have a fit: <tex>\displaystyle \left | 2(1)+1 \right | \gt 5(1)-4</tex> simplifies to <tex>\displaystyle 3 \gt 1</tex>, proving that you have a fit.<br/><br/>Case 2<br/><br/><tex>\displaystyle 2x+1 \lt -5x+4</tex> (notice that the sign is flipped, and all terms on the right are negated)<br/><br/>Here you can add <tex>\displaystyle 5x</tex> to both sides and subtract <tex>\displaystyle 1</tex> from both sides to get:<br/><br/><tex>\displaystyle 7x \lt 3</tex><br/><br/>So <tex>\displaystyle x \lt \frac{3}{7}</tex><br/><br/>Notice here that this does not add new information. Any number less than <tex>\displaystyle \frac{3}{7}</tex> is already less than <tex>\displaystyle \frac{5}{3}</tex> and you've already tried a number between them (1) to ensure that it works. So the full solution set here is just any number less than <tex>\displaystyle \frac{5}{3}</tex>, making the correct answer <tex>\displaystyle x \lt \frac{5}{3}</tex>.

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✓ Correct answer: 16π

The area of a circle is A = πr². <br/><br/>Since the diameter is 4 inches, then the radius is 2 inches, and the area of the can's base is A = π(2)² = 4<span style="font-family: Times New Roman;">π</span>. <br/><br/>The volume of the can is V = h × A. Since the can is only <img src="asset:assets/questions/4fafeb79c1b2ac88.gif">full, the volume of the juice is<br/><br/><img src="asset:assets/questions/9653c87c6710bba2.gif">

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✓ Correct answer: 6<em>x</em>² - 5<em>x</em> - 6

Use FOIL to multiply:<br/><br/><img src="asset:assets/questions/b9c087c622ad46fb.gif">

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✓ Correct answer: 85

The average marks for all four subjects is 75 and so total marks are 4 x 75 = 300<br/><br/>The marks for three subjects are given and their total is 100 +60 + 55 = 215. Hence the marks for the fourth subject = 300- 215 = 85<br/><br/><b>Key takeaway: </b>GMAT always refers to an average as average (arithmetic mean) The average ( arithmetic mean ) of a set of numbers is their sum divded by the number of numbers in the set. For average problems, think Total divided by number of items.

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