You may use a calculator for these practice questions. You may

Transcription

1 660 Math Smart Practice Questions You may use a calculator for these practice questions. You may not know all the math to complete these practice questions yet, but try to think them through! 1. Eric lives 15 miles directly north of the center of town, and Casey lives 20 miles directly east of the center of town. How far do Eric and Casey live from each other? Enter your answer on the answer grid:

2 Math Smart A circle with its center at Point A that passes through Point B will also pass through which other point? 1) (0, 2) 2) (0, 3) 3) (2, 2) 4) (4, 1) 5) (2, 4)

3 662 Math Smart 3. Patricia s firm builds custom walls out of cubes that measure ½ foot on each side. She is using a spreadsheet to calculate the number of cubes that are needed to build a wall. The spreadsheet includes: B1 B2 B3 Length of Wall in Feet Width of Wall in Feet Height of Wall in Feet Which of the following formulas can Patricia enter to find the quantity of cubes needed to build a wall? 1) B1 + B2 + B3 2) B1 B2 B3 3) (B1 2) (B2 2) (B3 2) 4) (B1 2) (B2 2) (B3 2) 5) (B1 B2) B3 4. Margareta, Jason, and Melinda all play a collectable card game. Margareta has 120 cards in her collection, and Jason has 250 cards. Melinda has 130 cards. They want to play with their friends Ashley and Enrique, so they want to give Ashley and Enrique enough cards so that all five friends have an equal number of cards. If each current player divides his or her extra cards evenly between the new players, how many cards will Margareta give Ashley? 1) 5 2) 10 3) 15 4) 30 5) 35

4 Math Smart In the following diagram, lines AD and BE are parallel. This diagram shows the layout of Jordan s backyard. The corners of the yard are at points A, B, E, and D. Jordan is trying to buy sod for the yard. In square feet, how much sod does Jordan need? 1) 6,408 square feet 2) 7,129 square feet 3) 7,860 square feet 4) 8,522 square feet 5) 9,390 square feet

5 664 Math Smart 6. Joyce s restaurant has a completely circular dining room, 20 feet in diameter. There are two concrete pillars, 4 feet in diameter, that break up the floor. According to the following diagram, approximately how many square feet of carpet will Joyce need to cover the floor, without the pillars? Use 3.14 to approximate pi. 1) square feet 2) square feet 3) square feet 4) square feet 5) square feet

6 Math Smart In the following equation, what are the possible values for x? 1) 3, 4 2) 3, 4 3) 3, 4 4) 3, 4 5) 7, 3 x 2 7x 3 = John s used car lot has 7 cars on special. The sale prices of the cars are $4,509; $9,842; $3,506; $12,534; $11,039; $2,683; and $5,899. What is the median price of the cars? 1) $4,509 2) $4,933 3) $5,899 4) $7,145 5) $9,212

7 666 Math Smart 9. Jonathan owns a gift shop. The following chart represents Jonathan s sales from last year. If Jonathan s total sales were $680,000 for the year, how much were total candle sales? 1) $69,548 2) $75,030 3) $81,600 4) $89,960 5) $92,300

8 Math Smart At what point does the graph of 3x + 1y = 6 cross the y-axis? Give your answer on the coordinate plane grid.

9 668 Math Smart Practice Question Answers Practice Question 1 This is a question where it s important to look for right triangles hidden in the question. It will help you to sketch out what the question is saying, so you can see it. Here s a sketch of the question: The center of town, Eric s house, and Casey s house form a right triangle. Remember, you can use the Pythagorean relationship to find the missing side of a right triangle.

10 Math Smart 669 The math looks like this: a 2 + b 2 = c = c = c = c = c c = 25 Eric and Casey live 25 miles from each other. You would enter your answer like this:

11 670 Math Smart Practice Question 2 To complete this question, you need to know something about circles, and also how to graph points on a coordinate grid. It might help to sketch the circle that the question is talking about on your scratch paper. The center of the circle is at point A, and the circle runs through point B: Now that you have a picture of the circle, you should be able to figure out which point it goes through, if you know how to find the points on the graph. Find the first number in the set of points on the x-axis (labeled x), and from there, go up or down until you re directly across from the second number in the set of points on the y-axis (labeled y). The only point in the answers that falls on the circle is (0, 3).

12 Math Smart 671 The answer is answer 2, (0,3). Practice Question 3 This question asks you to figure out which formula will find the right answer. So, you re looking for the formula that will show how many ½-foot by ½-foot by ½-foot cubes will be needed to build a wall. This question has to do with volume of a rectangle (the wall): length width height. You might think that the answer was B1 B2 B3, which is length by width by height of the wall. But that will give you the answer in cubic feet, and the cubes are smaller than that. To get the correct answer, you ll need to multiply each dimension of the wall by 2, to put the sizes in halffeet (one foot = 2 half-feet). The correct choice is answer 3, (B1 2) (B2 2) (B3 2).

13 672 Math Smart Practice Question 4 This is a multi-step word problem. It's a difficult one because there s a lot of information to sort out, and you need to go through a few steps to get the right answer. Let s break it down. Margareta has 120 cards. Jason has 250 cards. Melinda has 130 cards. Ashley has 0 cards. Enrique has 0 cards. The goal is for each person to have an equal number of cards. To figure it out, start out by finding out how many cards, total, all the people have together = 500 Now, how many players are there? Five. For each person to have an equal number of cards, how many cards will each have? = 100 cards

14 Math Smart 673 That s one part of the solution. Now you know how many cards each player should have. But the final question you need to answer is: If each current player gives an equal number of his or her extra cards to each new player, how many cards will Margareta give Ashley? Margareta has 120 cards. She should have 100 cards. First, find out how many cards Margareta will give away: = 20 Margareta will give away 20 cards. If she s giving an equal number of her extra cards to each of the new players, find the amount she ll give Ashley by dividing by = 10 The correct answer is answer 2, 10.

15 674 Math Smart Practice Question 5 This problem presents you with a confusing diagram. There s more information than you need, and with all the lines on the diagram, you might not be able to focus on what the question is asking. So, try to pin it down. Jordan s backyard is between points A, B, E, and D. Try sketching the diagram on scratch paper and marking the portion that you re concerned with: So, what is this question asking? If Jordan wants enough sod to cover the yard, it s a question about area. One of the things that might help you is knowing that, no matter what geometry concept it s asking about, the formula will be one of the ones in the test booklet. If you figure out that this is a question about area, then you have to figure out what the shape of the yard is. The formulas you have are for a square, a rectangle, a parallelogram, a triangle, a trapezoid, and a circle. You can probably rule out a square, a rectangle, a triangle, and a circle right away. That leaves a trapezoid and a parallelogram. On a parallelogram, both sets of opposite

16 Math Smart 675 sides are parallel, and line AB is not parallel to line DE. Only lines AD and BE are parallel. That leaves a trapezoid. Now, don t let the words base and height fool you. This trapezoid is on its side. The height is the distance between the parallel lines, 120 feet. The bases are 112 feet and 44.5 feet. So, those are the numbers you need to put into the formula: Area = ½ ( ) 120 Using your calculator, you can figure out that the area is 9,390 square feet. You can also do some rounding: is 150, and half of that is 75. You can break 120 up into 100 and is 7,500, and is 1,500. That s approximately 9,000 square feet. The closest answer is answer 5, 9,390.

17 676 Math Smart Practice Question 6 One important piece of information to know is that you can add or subtract areas or volumes from each other. No matter how odd the shape you see on the test is, the formulas in the front of the test booklet give you all the information you need. This question is about area, and the shapes are obviously circles! The formula for area of a circle is pi times radius squared. Since pi is approximately 3.14, the formula is: Area = 3.14 radius 2 The first step in solving this problem is to find the area of the whole floor. Remember, the radius is ½ of the diameter, or halfway across the circle: Area = = = 314 The next step is to find the area of the two pillars: Area of one pillar = = = Area of both pillars = = Then, find the area of the floor without the pillars.

18 Math Smart = The correct answer is answer 4, Practice Question 7 Here is the dreaded quadratic equation! How can you solve it? Don t tear your hair out. The multiple choice answers can really work in your favor. Try plugging the answers into the equation for x to see which ones work. Start with 3: 3 2 7(3) 3 = = = = 15 Three works! So, you can cross off any answer that doesn t include three, and that narrows it down to answer 1 and answer 3. (Remember, a 3 is definitely not the same as 3!) So, try 4 to see if it works also.

19 678 Math Smart 4 2 7(4) 3 = = = = 15 Four works, too! That means the correct answer is answer 1; the possible values are 3 and 4. And you don t need to solve a quadratic equation to find it. Practice Question 8 This question asks for the median. The median is the middle value of a group of numbers put in order from lowest to highest. Start by putting the numbers in order: $2,683 $3,506 $4,509 $5,899 $9,842 $12,534 $11,039 Since there are an odd number of numbers in the group, the median is simply the number in the middle. $2,683 $3,506 $4,509 $5,899 $9,842 $12,534 $11,039 The right choice is answer 3, $5,899. Median is in the middle.

20 Math Smart 679 Practice Question 9 This question asks you to be able to read and understand a chart, and to make a calculation based on the information in the chart. To answer this question, first locate on the chart the percentage of sales that is candle sales, 12%. To find out the dollar amount of candle sales, multiply the percentage times the total sales for the year: $680,000 12% = 680, = 81,60 The correct answer is answer 3, $81,600. Practice Question 10 This question asks about graphing a line. That might be something you don t know yet, but the important thing to realize is that if you put a value for x or y into the equation, you can find the value for y or x that will be a point on the line. Since you re looking for the location where the line crosses the y axis, the value for x will be 0. Every place where the value for x = 0, the point will fall on the y-axis line. So, solve the equation if x = 0: 3(0) + 1y = y = 6 y = 6

21 680 Math Smart The correct answer is the point at (0, 6). You should mark your answer in the coordinate plane grid like this: