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Q1<img src="asset:assets/questions/360f142c864c3e8b.gif"> <br/><br/>In the circle above, O is the center and points <em>P</em>, <em>Q</em>, <em>R</em>, <em>S</em>, <em>T</em>, <em>U</em>, <em>V, W, X </em>and <em>Y </em>are spaced equally on the circle. <br/><br/>What is the value of <em>d?</em>
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✓ 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°.
Q2<img src="asset:assets/questions/02a4075892b2a35e.jpg"><br/><br/>On a certain circular dartboard, the diameter of the circular bullseye is 4 inches and the diameter of the entire board is 20 inches. If a dart hits the board in a random location, what is the probability that it hits the bullseye target?
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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>.
Q3Choose the answer that best simplifies the following expression:<br/><br/><tex>\displaystyle (5r^2 +3r - 5) - (4r^2+5r - 8)</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>
Q4If <tex>\displaystyle f(x)=\sqrt{x^2-2x+1}</tex>, what is <tex>\displaystyle f(9)</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.
Q5<img src="asset:assets/questions/0e9d1690abcd6d06.gif"><br/><br/>A polynomial function <em>p</em>(<em>x</em>) is graphed on this <em>xy</em>-plane. <br/><br/>Which binomial is a factor of <em>p</em>(<em>x</em>)?
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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).
Q6Eddie is 7 years older than Brian. If Brian is x years old, then how old was Eddie 11 years ago?
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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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