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# Math project core the MSW ( 1 )

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### Math project core the MSW ( 1 )

1. 1. Done By: Grade: 12.01 ESE Teacher: HadiNasserdine Math Project – Term 1
2. 2. Task1:  What is the SAT exam? SAT is an exam that is used to know the level of college students and open up branches of opportunities for their proficiency.      What is the target score for ATHS students? The Target score for ATHS students is 500 out of 800. But scores may defer in college depending on apprentice's proficiency.      How the SAT test is scored? The candidate gets 1 point for each correct question he gets and subtracts ¼ for every wrong answer.  
3. 3.     Mention 10 tips to score more in SAT. -Review well before embarking. -Don’t take chances. -Don’t answer randomly. -Solve what you know first. -Do the easy ones first. -Don’t get swayed. -Use all your time. -Re-apply formulas and strategies. -Know all the formulas. -do lots of trainings. -Start early. -write on the questions booklets if you need to. -convert words to math givens. -read carefully. -don’t use many time on a problem.
4. 4.  What is the minimum number of correct answers you need in each section to reach the target? 10 Questions correct in each section with ignoring incorrect answers probability.
5. 5. Task 2: SAT Worksheet Name: Class: ID: 1) Which of the following describes ?(Algebra1) a. Irrational number √ b. Integer c. Real number √ d. Natural number Answer and Explanation : Natural numbers are counting numbers. So, is not a natural number. Integers are natural numbers including 0 . So its also not an integer. √7 = 2.64575 so its irrational number and also Real number because real number is include all types of numbers. 2) Which of the following is an integer ?(Algebra1) e. f. 3 4 g. 8 5 h. -9 √ Answer and Explanation : Because the integers is positive or negative numbers but without decimals and -9 is the only answer apply that.
6. 6. 3) Solve for q : (Geometry –> Solve linear equations) i. 2√ j. 4 k. 8 l. 16 Answer and Explanation : -> -> -> 4) 0 = s -10 -3 ?(Geometry –> Solve linear equations) m. 1 n. 10 √ o. 50 p. 100 Answer and Explanation : 0 = s -10 -3 ->0x-3 = s -10 -3 x-3-> -> 5) If an object travels at five feet per second, how many feet does it travel in one hour?(Ratios) q. 30 r. 300 s. 7200 t. 18000 √ Answer and Explanation : There is 60 seconds In a minute and 60 minutes in one hour. So you should multiply 1 second by 60 and 60. 1x60x60= 3600. And the object travels 5 feet per 1 second so : = -> -> feets
7. 7. 6) Of the following, which is greater than 1 2 ?(Ratio) u. 2 5 v. 3 6 w. 4 7 √ x. 9 19 Answer and Explanation : Because = 0.50 , and = 0.57 So is greater and it’s the only one more than 0.5 7) (Algebra1) y. z. aa. bb. √ Answer and Explanation : Try all values by the calculator and is the only value will match that question. 8) If and what is the value of the ?(Algebra1) cc. 6√ dd. 9 ee. 15 ff. 20 Answer and Explanation : -> -> – -> ->
8. 8. 9) Which of the following could be a value of x, in the diagram above?(Algebra1) gg. 10 hh. 20 √ ii. 40 jj. Any of above Answer and Explanation : The marked angle, ABC must be more than 90 degrees because it is the external angle of triangle BDC, and must be equal to the sum of angles BDC (90) and DCB.   Also ABC is not a straight line and must be less than 180.  Therefore 90 < 5x < 180  The only value of x which satisfies this relation is 20. 10)Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?(Algebra1) kk. 10√ ll. 15 mm. 20 nn. 25 Answer and Explanation : 20 large cakes will require the equivalent of 10 helpers working for one hour. 700 small cakes will require the equivalent of 20 helpers working for one hour. This means if only one hour were available we would need 30 helpers. But since three hours are available we can use 10 helpers.
9. 9. 11)n and p are integers greater than 1.  5n is the square of a number.  75np is the cube of a number. The smallest value for n + p is ? (Algebra1) oo. 14√ pp. 18 qq. 20 rr. 30 Answer and Explanation : The smallest value for n such that 5n is a square is 5.  75np can now be written as 75 x 5 x p.  This gives prime factors.... 3 x 5 x 5 x 5 x p  To make the expression a perfect cube, p will have to have factors 3 x 3 , and hence p =9  n + p = 5 + 9 = 14. 12)After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce? (Geometric) ss. 20 tt. 15 uu. 8√ vv. 5 Answer and Explanation : If after each bounce it reaches 2/5 of the previous height, then after the second bounce it will reach 2/5 x 125. After the third it will reach 2/5 x 2/5 x 125. After the fourth it will reach 2/5 x 2/5 x 2/5 x 125. This cancels down to 2 x 2 x 2 = 8. 13)If n ≠ 0, which of the following must be greater than n? I 2n II n² III 2 - n (Algebra1) ww. I only xx. II only yy. I and II only zz. II and III only aaa. None √
10. 10. Answer and Explanation : Remember that n could be positive negative or a fraction. Try out a few cases:  In case I, if n is -1, then 2n is less than n.  In case II, if n is a fraction such as ½ then n2 will be less than n.  In case III, if n is 2, then 2-n = 0, which is less than n.  Therefore, none of the choices must be greater than n. 14)ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?(Algebra1) bbb. 2.25 ccc. 2.5 ddd. 4.5√ eee. 5 Answer and Explanation : (Total area of square - sum of the areas of triangles ADE and DCF) will give the area of the quadrilateral  9 - (2 x ½ x 3 x 1.5) = 4.5 15)If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?(Algebra1) fff. F(1)√ ggg. F(2) hhh. F(3) √ iii. F(4) Answer and Explanation : You can solve this by back solving – substitute the answer choices in the expression and see which gives the greatest value.  A (-1 + 2) / (-1-2) = -2 / 2 = -1;  B (0 + 2) / (0-2) = 2/ -2 = -1;  C (1 + 2) / (1-2) = 3/-1 = -3;  D (3 + 2) / (3-2) = 5/1 = 5;  E (4+ 2) / (4-2) = 6/2 = 3  If you had just chosen the largest value for x you would have been wrong. So although it looks a long method, it is actually quick and accurate since the numbers are really simple and you can do the math in your head.
11. 11. 16)Which of the following describes ?(Algebra1) jjj. Irrational number √ kkk. Integer lll. Real number √ mmm. Natural number Answer and Explanation : Natural numbers are counting numbers. So, is not a natural number. Integers are natural numbers including 0 . So its also not an integer. √7 = 2.64575 so its irrational number and also Real number because real number is include all types of numbers. 17)Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?(Algebra1) nnn. 4 ooo. 8 ppp. 12√ qqq. it cannot be determined from the information given. Answer and Explanation : If two sets of four consecutive integers have one integer in common, the total in the combined set is 7., and we can write the sets as  n + (n + 1) + (n + 2) + (n + 3 ) and  (n + 3) + (n + 4) + (n + 5) + (n + 6)  Note that each term in the second set is 3 more than the equivalent term in the first set. Since there are four terms the total of the differences will be 4 x 3 = 12. 18)A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle? (Algebra1) rrr.2.5π sss.5π√ ttt. 7.5 π uuu. 10 π Answer and Explanation : Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle, and is therefore, 5.  Circumference = π.diameter = 5π.
12. 12. 19)Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?(Algebra1) vvv. 5 : 1 www. 10 : 5 xxx. 20 : 2 yyy. 25 : 2√ Answer and Explanation : Indian stamps are common to both ratios. Multiply both ratios by factors such that the Indian stamps are represented by the same number.  US : Indian = 5 : 2, and Indian : British = 5 : 1. Multiply the first by 5, and the second by 2.   Now US : Indian = 25 : 10, and Indian : British = 10 : 2  Hence the two ratios can be combined and US : British = 25 : 2 20)What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?(Arithmetic) zzz. 90 aaaa. 95 bbbb. 100√ cccc. 110 Answer and Explanation : You could add up all the multiples of 10 (10 + 20 + 30 ....+190), and divide by the number of terms (19). Or you could realize that the average of an evenly spaced series of numbers is equal to the value of the middle term (or the average of the two middle terms if there are an even number of terms). The middle term out of 19 is the tenth term in the series = 100.
13. 13. Task 3:  Given the sequence: 11, 7, 3, -1, … It is an arithmetic sequence that deducts 4 each time, the next 3 terms are: -5, -9 and -13. The sequence formula is: F(n): n-4 Given the sequence: 5, 25, 125, 625, … It is aGeometric sequence that times by5 each time, the next 3 terms are: 3,125, 16,625 and 78,125. The sequence formula is: F(n): 5n Given the sequence: 0, 1, 2, 3, … It is a arithmetic sequence that adds 1 each time, the next 3 terms are: 4, 5 and 6. The sequence formula is: F(n): n+1