Alabama School of Fine Arts 2019 Invitational Mathematics Tournament Algebra 1 Ciphering

Points and collecting papers Two minutes per question Correct in the 1st minute = five (5) points Correct in the 2nd minute = two (2) points Incorrect in either minute = zero (0) points A five-second warning will be given before the end of each interval. For your paper to be collected, it must be folded and held high above your head. Do not put your paper up until “Warning” is called. If your paper is not in the air before the call of “Interval,” your paper will not be collected. Runners will collect papers from behind you, not in front. Do not try to hand your paper to the runner in front of you.

Writing and formatting answers All answers must be written in the answer box on your answer sheet. Correct answers not in the box will not be counted. No units except for money (dollar and cent signs only). If an incorrect unit is included in the answer, it will be counted wrong. All fractions must be in lowest terms. Percent solutions must be written as a percent, not as the fraction or decimal equivalent. All denominators must be rationalized. No fractions under a radical All radicals must be simplified. All exponents must be positive.

Find the product of the solutions to the following equation: Practice Question Find the product of the solutions to the following equation: 𝑥 2 −5𝑥−6=0 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Practice Answer -6

Round 1

Question 1-1

Question 1-1 A standard deck of cards has four suits (♠♥♣♦). Each suit consists of 13 cards: number cards 2-10; three face cards J, Q, K; and an ace. In a standard deck of cards, what is the probability of drawing a King or a red card? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 1-1 7 13

Question 1-2

Question 1-2 How many ways can the letters in the word “GOOFIN” be arranged if the two O’s cannot be next to each other? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 1-2

Question 1-3

Question 1-3 If 𝑎➤𝑏=( 𝑎 2 − 𝑏 2 ), find 299➤298. 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 1-3 597

Question 1-4

Question 1-4 Solve for x: (243 ) 1/3 = 3 4𝑥+1 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 1-4 𝟏 𝟔

Question 1-5

Find the sum of the units digits of 1 9 20 and 1 8 19 . Question 1-5 Find the sum of the units digits of 1 9 20 and 1 8 19 . 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 1-5 3

Round 2

Question 2-1

Simplify the following expression without any negative exponents: Question 2-1 Simplify the following expression without any negative exponents: [( 𝑤 6 𝑥 −8 𝑦 2 𝑧 −5 𝑤 4 𝑥 −2 𝑦 5 𝑧 −6 )-1]2 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 2-1

Question 2-2

What is the sum of the odd positive integer factors 2022? Question 2-2 What is the sum of the odd positive integer factors 2022? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 2-2 1352

Question 2-3

Question 2-3 Points M and N cut the line segment AB with A(-5, 6) and B(19, -12) into three equal parts such that M is closer to A. If C is the midpoint of AB, what is the length of MC? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 2-3 5

Question 2-4

Question 2-4 The equation 𝑥 2 + 𝑦 2 =2𝑥𝑦𝑧 has two solutions: (𝑎, 𝑎, 𝑎), and (𝑏, 𝑏, 𝑏), where a is distinct from b. What is 𝑎+𝑏? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 2-4 1

Question 2-5

Question 2-5 When Anna took her new car to get gas, the odometer read 347 mi. The next time she got gas it read 564 mi. How many palindromes had the odometer shown between the two fill-ups? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 2-5

Round 3

Question 3-1

Question 3-1 Find the two solutions to the following system. Give your answer as two ordered pairs. 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 3-1 (5, 25), (-1, 1)

Question 3-2

Question 3-2 Find the mean of the following values: the mean, median, and mode of the set {1, 1, 2, 3, 5, 8, 1}. 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 3-2 2

Question 3-3

Question 3-3 Suppose a sphere with radius 𝑟 and a cube with a side length 𝑠 have the same volume. If 𝑟 𝑠 =𝑥, find 𝑥 3 . 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 3-3

Question 3-4

Find the distance between the vertices of the two parabolas: Question 3-4 Find the distance between the vertices of the two parabolas: 𝑦=−(𝑥−4 ) 2 −2 𝑦=2 𝑥 2 +12𝑥+21 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 3-4 𝟕𝟒

Question 3-5

Question 3-5 0:40 0:39 0:41 0:43 0:44 0:38 0:42 0:36 0:33 0:32 0:34 A square is drawn on a circle so that one vertex of the square is on the circle’s center, and the adjacent vertices are on the circle. If the circle’s radius is 3, what is the area of the shaded region in terms of 𝜋?   0:40 0:39 0:41 0:43 0:44 0:38 0:42 0:36 0:33 0:32 0:34 0:35 0:45 0:37 0:47 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:48 0:31 0:49 0:50 0:52 0:51 0:46 0:29 0:09 0:08 0:10 0:11 0:13 0:12 0:07 0:06 0:02 0:01 0:03 0:04 0:05 0:14 0:15 0:24 0:23 0:25 0:26 0:28 0:27 0:22 0:21 0:17 0:16 0:18 0:19 0:20 0:30 1:01 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:02 1:31 1:11 1:10 1:12 1:13 1:30 1:14 1:09 1:08 1:04 1:03 1:05 1:06 1:07 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:19 1:18 1:23 1:20 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 3-5 𝟗− 𝟗𝝅 𝟒

Round 4

Question 4-1

Question 4-1 The number 2019 can be written as in base 9 as 𝑎𝑏𝑐 𝑑 9 where a, b, c, and d represent the distinct digits of the number. What is 𝑏⋅𝑑+𝑎⋅𝑐 ? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 4-1

Question 4-2

Question 4-2 Two numbers have an arithmetic mean of 5 and a geometric mean of 3. What is the sum of the square roots of the two numbers? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 4-2

Question 4-3

Question 4-3 A triangle with vertices at (0, 8), (-3, 6), and (0, 0) has the same area as a square with side length x. Find 𝑥 4 . 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 4-3

Question 4-4

Question 4-4 Find the value of 1+2 1+2 1+2 1+... 0:41 0:42 0:40 0:44 1+2 1+2 1+2 1+... 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 4-4 𝟑+𝟐 𝟐

Question 4-5

Question 4-5 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 Riley the border collie is doing better than last year. The probability that Riley fetches the frisbee is now 9 10 , and the probability that she fetches the ball is 4 7 . If the frisbee and the ball are each thrown twice, what is the probability that Riley fetches the ball on the first throw but not the second throw, then fetches the frisbee on the second throw but not the first throw? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer 4-5 𝟐𝟕 𝟏𝟐𝟐𝟓

Extra Questions

Question E-1

Question E-1 Find the equation of a line perpendicular to the line 𝑦= 3𝑥−4 that passes through the point (-5, 13). Give your answer in slope-intercept form. 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer E-1 𝒚=− 𝟏 𝟑 𝒙+ 𝟑𝟒 𝟑

Question E-2

Question E-2 Two numbers have an arithmetic mean of 10 and a geometric mean of 8. What is the sum of the square roots of the two numbers? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer E-2 6

Question E-3

Question E-3 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 Amy lives five blocks south and four blocks east of the grocery store. She wants to walk there and back. If she can only travel north and west, how many paths could she take to get to the grocery store? 0:41 0:42 0:40 0:44 0:45 0:39 0:43 0:37 0:33 0:32 0:34 0:35 0:46 0:36 0:38 0:48 0:56 0:55 0:57 0:58 1:00 0:59 0:54 0:53 0:49 0:31 0:50 0:51 0:52 0:47 0:30 0:10 0:09 0:11 0:12 0:14 0:13 0:08 0:07 0:02 0:01 0:03 0:04 0:06 0:05 0:15 0:16 0:25 0:24 0:26 0:27 0:29 0:28 0:23 0:22 0:18 0:17 0:19 0:20 0:21 1:01 1:02 1:41 1:40 1:42 1:43 1:45 1:44 1:39 1:38 1:33 1:32 1:34 1:35 1:37 1:36 1:46 1:47 1:56 1:55 1:57 1:58 2:00 1:59 1:54 1:53 1:49 1:48 1:50 1:51 1:52 1:03 1:31 1:12 1:11 1:13 1:14 1:30 1:10 1:09 1:05 1:04 1:06 1:07 1:08 1:16 1:15 1:26 1:17 1:27 1:28 1:29 1:24 1:25 1:23 1:18 1:20 1:19 1:22 1:21 2nd Interval 1st Interval 5 Seconds 5 Seconds

Answer E-3 126