MAC CASA Study Guide Part What is the equation of the line that passes through (2, 5) with intercept y=7?

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1 Slope and Distance to Midpoint MAC CASA Study Guide Part 2 1. What is the equation of the line that passes through (2, 5) with intercept y=7? a) y = x + 7 b) y = x 7 c) y = -x 7 d) y = -x + 7 e) y = -x 2. A line with a slope of 3 passes through the point (3,5). What is the set of coordinates where that line passes through the y intercept? a) (0, -4) b) (0, 0) c) (0, 4) d) (-4, 0) e) (4, 0) 3. 6x + 8y = 14 16x 12y = 18 Are the above lines parallel or perpendicular? a) Parallel b) Perpendicular c) Neither d) Cannot be determined 4. Which line is parallel to? a) b) c) d) MAC CASA Study Guide Part 2 - Page 1 of 12

2 5. What is the equation of the line passing through (2,4) and (5,10)? a) y = x b) y = 2x c) y = 2x + 2 d) y = x 2 Geometry A B C CD = 8cm FD= 12cm BC =6cm F E D 1. In this figure, BE bisects FD. BAF, BEF, BED, and BCD are all right angles. What is the length of BF? a) 2cm b) 4cm c) 6cm d) 8cm e) 10cm MAC CASA Study Guide Part 2 - Page 2 of 12

3 2. In the figure, there are four circles within a square. The length of one side of the square is 12 cm. Approximately what is the area of the region if we were to cut the circles out? a) b) c) d) 3. The original diameter of a circle is 4cm, and its area is If we double the diameter, what factor will the area increase by? a) 2 b) 4 c) 6 d) 8 MAC CASA Study Guide Part 2 - Page 3 of 12

4 4. In the following triangle ABC, what is the measure of angle D? A 36 D B C a) 54 b) 306 c) 144 d) The length of a rectangle is 5 times its width. If the width of the rectangle is 4 x inches, and the perimeter of the rectangle is 24 inches, what is x? a) 2 b) 0 c) -2 d) cannot be determined Fundamental Counting Principle 1. The wardrobe of a studio contains 3 hats, 4 suits, 2 shirts, 5 pants, and 3 pairs of shoes. How many different ways can these items be put together? a) 60 b) 360 c) 420 d) At a buffet, there are 4 choices for an appetizer, 5 choices for a beverage, and 4 choices for an entrée. How many different ways can I select food from all the food choices? a) 13 b) 24 c) 20 MAC CASA Study Guide Part 2 - Page 4 of 12

5 d) Lacey lost all of her clothes in a fire. So she went to the store and bought 2 scarves, 3 pairs of pants, 4 shirts, and 2 pairs of shoes. How many different outfits can she put together? a) 48 b) 11 c) 19 d) 52 Ratios, Proportions, Rate of Change 1. A store has 50% more fruits than vegetables. What is the ratio of fruits to vegetables? a) 7:5 b) 10:7 c) 3:2 d) 4:3 2. A bag holds 350 marbles. Of those marbles, 20% are red, 30% blue, 40% green, and 10% are yellow. How many marbles of each color are present in the bag? a) Red= 70 Blue= 140 Green= 105 Yellow= 35 b) Red= 60 Blue= 100 Green= 120 Yellow= 35 c) Red= 70 Blue= 105 Green= 140 Yellow= 35 d) Red= 60 Blue=105 Green= 110 yellow= Two students from a student body of 40 boys and 60 girls will be selected to serve as hall monitors. What is the probability that first a boy will be chosen, and then a girl? a) b) c) d) MAC CASA Study Guide Part 2 - Page 5 of 12

6 4. If number n, divided by m, gives a result of.25, what is the relationship between n and m? a) n is four times as big as m b) m is two times as big as n c) m is a negative number d) n is ¼ of m 5. In a fruit basket, there are 15 apples, 10 oranges, 5 pears, and 3 figs. If I select two fruits, what is the probability that I will first pick an orange then a fig? a).031 b).028 c).027 d).288 Answer Key Slope and Distance to Midpoint 1. Answer: D Explanation: The equation of a line is y = mx + b. m = slope b = y-intercept So, we need to find the slope. The equation to do this is Now, plug back into the original equation: y= -x Answer: A Explanation: We know the slope along with a few points that we can plug into the slope equation. We have the given coordinates (3,5) and we know the y- intercept is where the line crosses the y axis, so x = 0 here. Now we can plug our values into the slope equation and solve for the missing y value. MAC CASA Study Guide Part 2 - Page 6 of 12

7 So the y-intercept is the point (0, -4) 3. Answer: B Explanation: We need to be able to determine what the slope of each line is because that is how you can tell if lines are parallel, perpendicular, or neither, so plug each into y = mx + b form. The slopes are: Since slope one is the negative inverse of slope two, the lines are perpendicular to each other. 4. Answer: A Explanation: In order for a line to be parallel to another they have to have identical slopes, and a different y-intercept. 5. Answer: B Explanation: First we should find the slope of the coordinates given. MAC CASA Study Guide Part 2 - Page 7 of 12

8 Then, we can plug one of our points into the slope equation to solve for the y- intercept knowing x = 0 here in order to find the equation of the line. Which gives us the y-intercept of 0. Now plug the slope and y-intercept in, which give the equation of the line: y=2x. Geometry 1. Answer: E Explanation: Since we know CD is 8 and BC is 6, along with the fact that BCD is a right angle we should be able to recognize the 3, 4, 5 Pythagorean triple. Here, we can see the lengths we were given are divided by 2 in order to see the Pythagorean triple, so in order to find the missing length we multiply the 5 by 2, giving us 10. Then with the rest of the given information we can follow this pattern around to find the length of BF which is 10. MAC CASA Study Guide Part 2 - Page 8 of 12

9 A 6 B 6 3 C F 6 E 6 D 2. Answer: C Explanation: First you must realize that if 12cm is the length of one side of the square the area is (A=lw. A= 12cm x 12cm. A= 144 ). The diameter of each circle will be 6cm since there are two circles that go from edge to edge on the square. The equation to find the area of a circle is, so, A= 3.14 x 3 2 cm => A= 3.14 x 9cm 2 => A= Now it is important to realize there are four circles so take the area of the one circle (which is ) and multiply it by 4, giving us Then you subtract the area of the four circles from the area of the square. ( = ). 3. Answer: B Explanation: The radius is half of the diameter. So the radius is 4/2 or 2. To find the area of a circle, you square the radius, so you go from 2 = 4 to 4 = 16. Going from 4 to 16 is increasing by a factor of 4 and that will Affect the entire solution. MAC CASA Study Guide Part 2 - Page 9 of 12

10 Original Area: Increased Area: Checked Work(Original area x4): 4. Answer: D Explanation: = 126. The total sum of a triangle is 180. So, to find angle C: = 54. In order to find angle D, you must know it and angle C are supplementary (Their sum is 180 ). So, = Answer: A Explanation: Length = 5(4-x) 20-5x Width= 4-x Perimeter= 2L+2W 24 =2(20-5x)+2(4-x) 40-10x+8-2x 24=48-12x =-12x =x Fundamental Counting Principle 1. Answer: B Explanation: 3 x 4 x 2 x 5 x 3 = Answer: D Explanation: 4 x 5 x 4 = 80 MAC CASA Study Guide Part 2 - Page 10 of 12

11 3. Answer: A Explanation: 2 x 3 x 4 x 2 = 48 Ratios, Proportions, and Rate of Change 1. Answer: C Explanation: 3:2. 50% of 2 is 1, and if there are 50% more fruits than vegetables there is fruits. 2. Answer: C Explanation: 350 x.20 = 70 Red 350 x.30 = 105 Blue 350 x.40 = 140 Green 350 x.10 = 35 Yellow To check your work it is best to add up the results and make sure the sum is 350, this can also help you to eliminate choices in the beginning. 3. Answer: B Explanation: The probability of selecting a boy first is. Once someone has been chosen there are now 99 students left making the probability for 60 selecting a girl next is. Since this is a chain of events, to find the 99 overall probability you multiply the two together: x =. 4. Answer: D Explanation: So.25m=n or ¼ of m = n 5. Answer: B Explanation: There are 33 pieces of fruit total. If we pick an orange first that probability would be. Now there are only 32 pieces left. If the next pick happened to be a fig, that probability would be. To find the combined probability you must multiply the two: x = or.028. MAC CASA Study Guide Part 2 - Page 11 of 12

12 MAC CASA Study Guide Part 2 - Page 12 of 12