Mathmatics : SAT and sequences

1. Mathmatics: SAT and sequences Term1, Math core project.

2. About the project In this project, we were asked to discuss more about what SAT’s are and how they are important to be tested on it. Furthermore, we had to prepare a SAT worksheet with specific instructions and also we had to answer loads of questions about sequences, their types and how to find certain elements. To be more specific, there are 3 main tasks that we will thoroughly discuss and answer throughout the presentation About the project

3. Rubric

4. What is the Sat exam • What is the target score for ATHS students ? • How the sat test is scored? • SAT stands for Scholastic Assessment Test. It is a worldwide standard college admission test that lets colleges show what you know and how well you can apply that understanding. • SAT scores are only one of many aspects that colleges and universities ponder when making admission decisions. • The target SAT scores for the Engineering science cluster is known to be 600. However, the target for the remaining three clusters (Health, ICT and Applied Engineering) is 500. • The SAT tests are scored in 3 main steps : • So adjacent side  • 1- Calculate the students’ raw scores: “Your raw scores are calculated for each section based on the number of questions you got correct or incorrect, or that you omitted”. • 2- Equate the scores: a statistical analysis is made to insure the test is an accurate representation of the students’ skill. The unscored section of the test also helps us ensure the test is fair. “Every SAT includes a 25-minute section, which doesn't count toward your final score. It may be a critical reading, mathematics, or multiple-choice writing section.” The reason for this is because it helps assess questions for next year's test, it also ensures that the SAT exam reflects your skills accurately. • 3- The final score: The raw score is by then converted to a score within the scare (200-800 scale) by a statistical process known as equating. “Equating ensures that the different forms of the test or the level of ability of the students with whom you are tested do not affect your score.” By equating, you can make it possible to compare between test takers who take different versions of the test scores. Task 1

5. Mention 10 tips to score more in SAT • “You are scored on a scale of 200 to 800 in each of the sections of SAT Reasoning Test and SAT Subject-based tests. Subject test sub scores also range between 20 and 80.” • For math 1 SAT subject you get 80 Multiple answer questions and by that you get a raw score and from there they convert it into a real scale score between 200 and 800 • So this means if we want above 500 we need to answer more than 50 questions CORRECTLY. Another way is to probably answer the whole answer sheet mostly right, if the it had error ¼ of the correct mark will be deducted. • An average SAT score is the middle value of scores. So, generally a score of about 500 in each section is considered an average SAT score. This will also give an average percentile to you. The percentile for the average score will be about 50. This will imply that you have scored more than about 50% of students who appeared in the test, while the rest 50% of students have done better than you. • What is the minimum number of correct answers you need in each section to reach the target? • 1- Use the process of Elimination: try to find out all the answers that you think are incorrect. • 2- Leave any question blank where you can't identify at least one wrong choice, except for the math grid-ins. This might come as a disappointed but somewhere along the test you will find a question that might seem impossible to solve. If you cannot find even one question you cannot cross out as wrong then it is best if you leave the question and keep going. • 3- Write in the test booklet. You can use the test booklet for your own advantage, write formulas, solve your math equations, and sketch things, cross off wrong answers. No one is going to read what you wrote. • 4- Don't second-guess yourself: Studies show that the first guess you choose is usually the right one, so it is best if you keep your answer. • 5- Know your special triangles. There will be frequent mathematical questions where the key realization has to do with special triangles. • 6- If you're stuck on a math problem, start writing. Start writing anything that comes to mind, try simplifying or factoring expressions, draw a picture or label the diagrams. Many times something will hit and you’ll remember or will be able to relate to a certain way that will give away the answer. • 7- Use official tests to practice with. Use unmarked official SAT exams to practice on constantly and time you self to notice any improvements. • 8- Don't Go In Order: there is no real obligation to the SAT test where you have to go in order. Answer as many easy questions as you can and skip the hard ones, you can go back to them if you have time left. • See adjacent for more  • 9- Don't Read The Directions: if you’ve solved similar SAT question sheets than you must be familiar with the directions, its better if you just start right away to save sometime. • 10- Weakness into Strength: try to find out the types of questions that are hard for you to solve and practice on them frequently. Task 1

6. SAT math worksheet • 1- If the median of a set of five consecutive integers is equal to 13, then what is the value of the largest of these five integers ?(statistic ) • 2- if ϰ+4ϰ-3ϰ+1=3 , then what is the value of ϰ? (Algebra ) • (A) 1 • (B) 2 • (c) 3 • (D) 4 • (E) 5 • (A) 11 • (B) 13 • (c) 15 • (D) 17 • (E) 19 • 3- If the probability of selecting a red marble is 13 and the probability of selecting a blue marble is 23 , what is the ratio of blue marbles to red marbles? (Arithmetic ) • (A) 1:2 • (B) 3:2 • (c) 2:1 • (D) 2:3 • (E) 3:1 • 4- if ϰ+4ϰ-3ϰ+1=3 , then what is the value of ϰ? (Algebra ) • (A) 6 • (B) 15 • (c) 21 • (D) 42 • (E) 81 Task 2: SAT math worksheet

7. 5- How many of the prime factors of 30 are greater than 2 ? (Arithmetic ) • 6- if xγz=z and the value of x is 0 , which of the following must be true?(Algebra ) • 7- In quadrilateral PQRS above , what is the value of a2+ b2? (geometry ) • One • Two • (c) Three • (D) Four • (E) Five • Y= 0 • Z= 0 • (c) Xy = 1 • (D) z= 1 • (E) y= 1 • 8 • 10 • (c) 11 • (D) 12 • (E) 13 Task 2

8. 9- In the figure below, if the area of triangle CAF is equal to the area of rectangle CDFE, what is the length of segment AD?(geometry) • 10- If the average (arithmetic mean) of r and s is 20, and the average of x, y, and z is 30, what is the average of r, s, x, y, and z? (Statistics) • 11- In the xy-coordinate plane above, line l pass through the points (0,0) and (1,2), imagine that a line called m contains the point (0,0) and perpendicular to l, what is the equation of m? • 12- What is the value of (-3)3+(-4)2? (Arithmetic) • 7/2 • 5 • (c) 7 • (D) 15/2 • (E) 15 • 23 • 24 • (c) 25 • (D) 26 • (E) 27 • -25 • -11 • (c) 0 • (D) 7 • (E) 11 Task 2

9. 13- A jar contains four blue marbles and two green marbles. Two marbles are removed randomly. What is the probability that two marbles with the same color will be selected?(probability) • 14-A bag contains only red , blue, and green tickets. The probability of picking a red ticket is 0.25 and the probability of picking a blue ticket is 0.40. What is the least number of tickets that could be in the bag?( probability) • 15- A= {-5,-3,-2,0,1} • B= {-1, 2,4,6} • If a is a number randomly selected from set A, and b is a number randomly selected from set B, what is the probability that ab<0?( probability) • 16- What is the median number of cups of lemonade sold per hour ?(statistics) • 5 • 10 • (c) 20 • (D) 30 • (E) 40 • 10 • 8 • (c) 12 • (D) 15 • (E) 20 Task 2

10. 17- The bar graph shows the number of employees at company X for each of the years from 1996 through 2000. Over which of the following periods was the average rate of increase in the number of employees at company X greatest?(Analysis) • 18- which of the following expressions describes the indicated values on the number line above ?(X doesn’t equal to 0)(Algebra) • 19- If X=4, then (x4-2)(4+x)= • 20- In the triangle below, if the measure of angle B is 52 degrees, then what is the value of y? • From 1996 to 1998 • From 1996 to 1999 • (c) From 1997 to 1999 • (D) From 1998to 1999 • (E) From 1998 to 2000 • 16 • 64 • 86 • (D) 98 • (E) 112 • 20 • 22 • 24 • (D) 28 • (E) 30 Task 2

11. Question 1 • Answer: C • These five numbers are:- • 11-12-13-14-15 • They are consecutive numbers with the median 13 and the largest is 15. • Question 2 • Answer: A • These five numbers are:- • 11-12-13-14-15 • They are consecutive numbers with the median 13 and the largest is 15. • Question 4 • Answer: B • Question 5 • Answer: C Question 8 Question 11 Task 2: Answer key Answer: E M=7+2=9 M<0 so m= -9 N=6+3=9 N<0 so n=-9 Mn= (-9)(-9)= 81 Answer: D Answer: A Question 9 Answer: C 0.5(b)(h)=LW 0.5(15)(h)=7x15 0.5(h)=7 h=7/0.5=14 AD=14-7=7 Question 3 Question 6 Question 10 Question 12 Answer: B Any number times 0 equals to 0, so if x =0 then:- (0)(y)(z)=z 0=z Answer: D Answer: B Put it as it is in the calculator Question 7 Answer: E Line QS is the hypotenuse of triangles QPS and QRS . If the hypotenuse of QRS is 32+22=13, then the hypotenuse of QPS is a2+b2=13.

12. Question 13 • Answer: D • Question 14 • Answer: C • if we add the probability of red and blue tickets then the answer will be the probability of red and blue tickets of the lest total number of tickets . • 1/4+2/5=13/20, the probability of red and blue tickets in the bag is13 of 20 , which mean that the total number of tickets could be 20. • Question 15 • Answer: A • if a negative number multiplied by a positive number the answer will be negative number. • We have 3 –ve numbers in set A if they multiplied with 3 +ve numbers of set B we will get 9 –ve numbers. • The 0 is a restriction . • The 1 in set A is positive kit will only be a –ve number if it multiplied by -1 from set B. • So we have 10 numbers less than 0 from 20 number. • 10/20=1/2 • Question 16 • Answer: E • Arrange the numbers of cups sold. • 10, 15,20,20,27 • 20 is the number in the middle. • Question 17 • Answer: D • You can notice that there was a wild increase from 1998 to 1999. • Question 18 • Answer: D • The number line shows positive and negative values. • The values of x must be greater than or equal to 1, or less than or equal to -1. • If you look at the choices, they show only expressions of 1. • Numbers those are greater than 1 are positive so we must take the absolute value of x. • Question 19 • Answer: D • Direct substitution. • Question 20 • Answer: A • 2x+2=52 • 2x=54 • X= 27 • Angle A= 4(27)= 108 • A0+B0+Y0= 180 • 180-(108+52) • 180-160=20 Task 2: Answer key

13. Given the sequence: 11, 7, 3, -1, …… • 1. Determine the type of sequence? • Arithmetic • 2. Find the next three terms of the sequence. • 11, 7, 3, -1, -5 , -9 , -13 • 3. Write a formula for the sequence. • An= a1+(n-1)d • An= 11+(n-1)-4 • An= 11-4n+4) • An= 15-4n • 4. In your own language write about this type of sequences. • This type of sequences is applied upon the operations addition and subtraction. • Given the sequence: 5, 25, 125, 625, …… • 1. Determine the type of sequence? • Geometric • 2. Find the next three terms of the sequence. • 5, 25, 125, 625, 3125, 15625, 78125 • 3. Write a formula for the sequence. • An= a1+(n-1)d • An= 5+(n-1)5 • An= 5+5n-5 • An= 5n • 4. In your own language write about this type of sequences. • This type of sequences is applied upon the operations division and multiplication. Task 3

14. Given the sequence: 0, 1, 1, 2, 3, …… • 1. Determine the type of sequence? • Fibonacci • 2. Find the next three terms of the sequence. • 0, 1, 1, 2, 3, 5, 8, 13, … • 3. Write a formula for the sequence. • The Rule is xn = xn-1 + xn-2 • where: • xn is term number "n" • xn-1 is the previous term (n-1) • xn-2 is the term before that (n-2) • 4. In your own language write about this type of sequences. • This type of sequence the numbers in which each number equals the sum of the two previous numbers Task 3

15. references for task 1 • Http://Andreasviklund.Com/, R. 2013. Ten Tips for Improving Your SAT Score. [online] Available at: http://www.sat-coach.com/tips.html [Accessed: 14 Oct 2013]. • Roell, K. 2013. Top Ten SAT Test Tips. [online] Available at: http://testprep.about.com/od/tipsfortesting/a/SAT_TestTips.htm [Accessed: 14 Oct 2013]. • Sat.collegeboard.org. 2013. About the Tests - What is the SAT. [online] Available at: http://sat.collegeboard.org/about-tests/sat [Accessed: 14 Oct 2013]. • Sat.collegeboard.org. 2013. How the SAT is Scored - Overview of SAT Scoring. [online] Available at: http://sat.collegeboard.org/scores/how-sat-is-scored [Accessed: 14 Oct 2013]. • Task s distributed as • Iman Alhosani Ppt& Task 1 • AsalaFadel Made the blog, helped AlAnood in task 2 • AlAnood Mohammed  Task 2 and the answer key • Noura Mohammed  task 3 and corrected by Asala References