...50 Keys To CAT Arithmetic, Algebra, Geometry and Modern Mathematics A collection of 50 very important formulae for Quantitative Ability Section of CAT from the pioneers of online CAT training ▪ EASY ▪ EFFECTIVE ▪ PERSONALISED 1. Averages 2. Mean For two numbers a and b, 3. Percentage Change For two successive changes of a% and b%, 4. Interest Amount = Principal + Interest © 2008 Enabilon Learning Pvt. Ltd. All rights reserved. 1 5. Population Formula [Here, P = Original population, P’ = population after n years, r% = rate of annual change] 6. Depreciation Formula [Here, P = original value, P’ = final value after n years, r% = rate of annual depreciation] 7. Growth Absolute Growth = Final Value – Initial Value [Here, S. A. G. R. = Simple Annual Growth Rate, A. A. G. R. = Average Annual Growth Rate and C. A. G. R. = Compound Annual Growth Rate] 8. Profit and Loss Profit = SP − CP Loss = CP − SP © 2008 Enabilon Learning Pvt. Ltd. All rights reserved. 2 9. False Weights If an item is claimed to be sold at cost price, using false weights, then the overall percentage profit is given by 10. Discount Discount = Marked Price − Selling Price Buy x and Get y Free If articles worth Rs. x are bought and articles worth Rs. y are obtained free along with x articles, then the discount is equal to y and discount percentage is given by Successive Discounts When a discount of a% is followed by another discount of b%,...
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...Simple Interest | Amount=Principal+Interest Where: | Amount | Final Amount | | Principal (P) | Amount invested | | Interest | Simple Interest (I) | Indices a6+a6=2a6 a6×a6=a12 a6÷a6=a0 a0=1 e.g.1 14h8÷2h3=14h82h3=7h8h3=7h5 e.g.2 x23=x6 e.g.3 2a53=2×2×2×a5×3=8a15 Pie Charts Constructing pie charts using protractor and calculate the angle: SectorTotal×360 Angles of Polygons Sum of Interior Angles S= n-2×180° Where S is the sum of the interior angles n is the number of sides of the polygon e.g. octagon 8 Pythagoras Theorem hyp2=opp2+adj2 Used when wanting to find a missing side in a right angled triangle Sequences Example: 1st term | 2 | 2nd term | 4 | 3rd term | 6 | 100th term | 100 x 2 = 200 | nth term | 2n | Circles Circumference C= 2πr Where: | C | Circumference | | π | π | | r | Radius | Area of a circle A= πr2 Where: | A | Area | | π | π | | r | Radius | Area of sector A= θ360×πr2 Where: | A | Area | | π | π | | r | Radius | | θ | Theta (angle of sector) | Length of arc Length of arc= θ360×2πr2 Where: | π | π | | r | Radius | | θ | Theta (angle of sector) | | | | Perimetre All the length of the shape Ratios Example: The ratio of biscuits is butter, sugar and flour 2:1:4. The total mass...
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...Running head: Pythagorean Quadratic Pythagorean Quadratic Sharlee M. Walker MAT 221 Instructor Xiaolong Yao December 2, 2013 Pythagorean Quadratic Ahmed’s half of the map doesn’t indicate which direction the 2x + 6 paces should go, we can assume that his and Vanessa’s paces should end up in the same place. I did this out on scratch piece of paper and I saw that it forms a right triangle with 2x + 6 being the length of the hypotenuse, and x and 2x + 4 being the legs of the triangle. Now I know how I can use the Pythagorean Theorem to solve for x. The Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, these lengths have the formula of a2 + b2 = c2. Let a = x, and b = 2x + 4, so that c = 2x + 6. Then, by putting these measurements into the Theorem equation we have x2 + (2x + 4)2 = (2x + 6)2. The binomials into the Pythagorean Thermo x2 + 4x2 + 16x + 16 = 4x2 + 24x + 36 are the binomials squared. Then 4x2 on both sides of the equation which can be (-4x2 -4x2) subtracted out first leaving the equation to be x2 + 16x + 16 = 24x + 36. Next we should subtract 16x from both sides of equation, which then leaves us with: x2 +16 = 8x + 36. The next step would then be to subtract 36 from both sides to get a result of. x2 -20= 8x. Finally we need to subtract 8x from both sides to get x2 – 8x...
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...Buried Treasure Allen Raikes MAT 221 DR. Steven Flanders Ahmed and Vanessa has a treasure that needs to be located. It’s up to me and to help find it, I will do that by using the Pythagorean quadratic. On page 371 we learned that the Ahmed has a half of the map and Vanessa has the other half. Ahmed half in say the treasure is buried in the desert 2x+6 paces from Castle Rock and Vanessa half says that when she gets to Castle Rock to walk x paces to the north, and then walk 2x+4 paces to the east. So with all the information I have I need to find x. the Pythagorean Theorem states that in every right triangle with legs of length a and b and hypotenuse c, which have of a relationship of a2+b2=c2. In this problem I will let a=x, and b= 2x+4, and c=2x+6. So know it time to put the measurements into the Theorem equation; 1) X2+ (2x+4)2=(2x+6)2 this is the Pythagorean Theorem 2) X2+4x2+16x+16 = 4x2+ 24x+36 are the binomials squared 3) 4x2 & 4x2 on both sides can be subtracted out. 4) X2+16x+16 = 24x +36 subtract 16x from both sides 5) X2+16 = 8x+36 now subtract 36 from both sides 6) X2-20 = 8x 7) X2-8x-20=0 this is the quadratic equation to solve by factoring using the zero factor. 8) (x-)(x+) Since the coefficient of x2 is 1 we have to start with pair of () is the 20 in negative there will be one + and one – in the binomials. 9) -2, 10: -10,2: -5,4; -4, -5 10) Looks I’m going to use -10 and 2 is...
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...1. N/a 2. using Law of Sines and Law of Cosines. You get two different triangles. The one combination you can't have is where A is opposite the b. Maybe your notation already specifies this, but I don't think so, otherwise there is no problem. If you try to construct a triangle with the 70 degree angle opposite the side of length 5, the Law of Sines would give sin x = (7/5)sin 70 = 1.316, which is impossible. With angle A = 70 opposite the side of length 7, the Law of Sines gives sin x = (5/7)sin 70, which is a lot more reasonable. using the inverse sine function to solve (on your graphing calculator) you get x = 42.16 degrees as the angle opposite side b = 5. The remaining angle is now 67.84 degrees since all three add up to 180 degrees. Now you have two sides and an included angle and you can use the Law of Cosines to solve for the third side. If 70 degrees were the included angle between sides of 7 and 5, this makes a triangle and we can solve for the third side with the Law of Cosines. If we call the third side c we have c² = 7² + 5² - 2(7)(5)cos 70°. Again, using your graphing calculator you get c = 7.075. Now you can get the remaining angles in this triangle, using the Law of Sines. 3. Let x be the base of the triangle between the perpendicular and AB; which projects 53 dgrees at B and 62 degrees at a point 300 yards from B on the opposite bank of A x*tan62=(x+300)*tan53 = the perpendicular x = 300*tan53/(tan62-tan53)=719.0295 yd AB=(x+300)/cos53=1019...
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...Score: ______ / ______ Name: ______________________________ Student Number: ______________________ | 1. Elsie is making a quilt using quilt blocks like the one in the diagram. a. How many lines of symmetry are there? Type your answer below. b. Does the quilt square have rotational symmetry? If so, what is the angle of rotation? Type your answers below. | | 2. Solve by simulating the problem. You have a 5-question multiple-choice test. Each question has four choices. You don’t know any of the answers. What is the experimental probability that you will guess exactly three out of five questions correctly? Type your answer below using complete sentences. | | 3. Use the diagram below to answer the following questions. Type your answers below each question. a. Name three points.b. Name four different segments.c. Write two other names for FG.d. Name three different rays. | | 4. Charlie is at a small airfield watching for the approach of a small plane with engine trouble. He sees the plane at an angle of elevation of 32. At the same time, the pilot radios Charlie and reports the plane’s altitude is 1,700 feet. Charlie’s eyes are 5.2 feet from the ground. Draw a sketch of this situation (you do not need to submit the sketch). Find the ground distance from Charlie to the plane. Type your answer below. Explain your work. | | _____ 5. Jason and Kyle both choose a number from 1 to 10 at random. What is the probability that both numbers are odd? Type...
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...RAFFLES GIRLS' PRIMARY SCHOOL SEMESTRAL ASSESSMENT 1 MATHEMATICS (PAPER 1) PRIMARY 5 Name: ( ) Form Class: P5 Banded Math Class: P5 Duration: 50 min Date: 10 May 2011 Your Score (Out of 100 marks) Your Score (Out of 40 marks) Parent's Signature INSTRUCTIONS TO HAMninATFS 1• Do not turn over this page until you are told to do 2. Follow all instructions carefully. so. 3. Answer ALL questions and show all working clearly. 4. NO calculator is allowed for this paper. Pagel of 12 SECTION A (20 marks) Questions 1 to 10 carry 1 mark each. Question 11 to 15 carry 2 marks each. For each question, four options are given. One of them is the correct answer. Make your choice (1, 2, 3 or 4). Shade your answer (1, 2, 3 or 4) on the OAS provided. All diagrams are not drawn to scale. 1. How many ten-dollar notes make up $201 010? (1) (2) (3) (4) 10 20 2 010 20101 2. What is the product of 83 * 700? (1) (2) 581 5 810 (3) 58100 (4) 581 000 Page 2 of 12 3. Find the volume of the cuboid shown below. 28 m (1) (2) 84 m3 140 m3 (3) (4) 168 m3 840 m3 What is the missing number in the box? • 9 d) 6 2 3 (2) (3) (4) 8 14 15 ->• k txpress — as a mixed number. c 38 (D (2) 3* 4 4 (3) (4) 94 9! 2 Page 3 of 12 6. Which of the following figures cannot be tessellated? (D (2) (3) (4) ( ) 7. In 43.21, which digit is...
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...particles, of mass 5.0 x 10-27 kg, moves along the positive y-axis with a speed of 6.0 x 106 m/s. Another particle of mass 8.4 x 10-27 kg, moves along the positive x-axis with a speed of 4.0 x 106 m/s. Determine the third particle’s speed and direction of motion. (Assume that mass is conserved) Write down what you know mnucl = 17 x 10-27 kg m1 = 5.0 x 10-27 kg m2 = 8.4 x 10-27 kg m3 = mnucl – (m1 + m2) = 17 x 10-27 kg – (5.0 x 10-27 kg + 8.4 x 10-27 kg) = 3.6 x 10-27 kg vnuci = 0 m/s v1 = 6.0 x 106 m/s @ y-axis v2 = 4.0 x 106 m/s @ x-axis v3 = ? Draw a vector diagram of the momentum Solve for the momentum of the third particle and then find its velocity Right angled triangle so use Pythagorean Theorem P12 + P22 = P32 therefore: ( (P12 + P22) = P3 ( ((m1v1)2 + (m2v2)2) = P3 ( ((5.0 x 10 –27 kg)(6.0x106m/s))2 + (8.4 x 10-27kg)(4.0 x 106 m/s))2 = P3 ((2.0 x 10-39 kg2m2/s2) = 4.50 x 10-20 kgm/s = P3 v3 = P3 / m3 = 4.50 x 10-20 kgm/s / 3.6 x 10-27 kg = 12.5 x 106 m/s Use...
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...Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Mathematics A Paper 2 (Calculator) Foundation Tier Friday 13 June 2014 – Morning Time: 1 hour 45 minutes Paper Reference 1MA0/2F You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Total Marks Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Answer the questions in the spaces provided – there may be more space than you need. Calculators may be used. If your calculator does not have a button, take the value of to be 3.142 unless the question instructs otherwise. Information The total mark for this paper is 100 The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over P43380A ©2014 Pearson Education Ltd. 5/5/6/c2/ *P43380A0132* GCSE Mathematics 1MA0 Formulae: Foundation Tier You must not write on this formulae page. Anything you write on this formulae...
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...w w ap eP m e tr .X w om .c s er UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS International General Certificate of Secondary Education 0580/04, 0581/04 MATHEMATICS May/June 2007 Paper 4 (Extended) 2 hours 30 minutes Additional Materials: *5128615949* Answer Booklet/Paper Electronic calculator Geometrical instruments Graph paper (2 sheets) Mathematical tables (optional) Tracing paper (optional) READ THESE INSTRUCTIONS FIRST If you have been given an Answer Booklet, follow the instructions on the front cover of the Booklet. Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. All working must be clearly shown. It should be done on the same sheet as the rest of the answer. Marks will be given for working which shows that you know how to solve the problem even if you get the answer wrong. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For π use either your calculator value or 3.142. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part...
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...Angelica Acevedo Week 1 - Information Systems Strategy Triangle Step 1: Create lists of case details that fit each side of the triangle. Step 2: Then look at each item and think about how that item affects the other sides of the triangle. Step 3: Take a look at the industry. Make a list of triangle attributes you find. Compare the industry items with the case company items. Step 1: Create lists of case details that fit each side of the triangle. Step 2: Then look at each item and think about how that item affects the other sides of the triangle. Step 3: Take a look at the industry. Make a list of triangle attributes you find. Compare the industry items with the case company items. Information Strategy Information Strategy Organizational Strategy Organizational Strategy Business Strategy Business Strategy Business Strategy Elements | Organizational Strategy Elements | Information Strategy Elements | New collection at start of each season | Changes color, cut, fabrics and other details throughout season | POS terminals not connected store to store or to headquarters | Less IT spending | Tries to understand, through its network of stores, not just what people are buying, but also, what they want to buy. | Use dial up modems to send daily sales and inventory orders | Introduce 11,000 new garments per year | Lead time from inception to delivery, of garment, can be as short as 3 weeks | IT staff of 50 – less than .5% of revenue | | No advertising – used...
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...In the AUL CSI teams case #46787-35 where Charles Drummer A.K.A snake a local gang ring leader’s body exactly 35.38 ft. from an open window on the 35th floor of a high rise building which we measured was 320 ft. from the ground. The only lead we had was a supposed witness phone call somewhere in the area about a person jumping from a building. We knew the location of the cell phone tower that received the call, the time of the call, that the distance between the cell phone tower to the satellite, which is directly above the cell phone tower and are at the same angle from one another, is 77,975 ft., and that the distance between the cell phone and the satellite was 78,000 ft.. With this information we needed to find out if this was a suicide or a homicide? The first thing we wanted to figure out was if he walked of the build by his own free will or did someone force him out of the window? To get this answer we would need to find out the distance that the victim feel, and we had already gotten this from the officers and the time it took him to reach the ground. To do this we put the information that we got from the police which was, that the victim was 35.38 feet from an open window on the 35th floor, on a 320 ft. high rise building into the falling time formula t=h16. So what we did next was insert the numbers in the proper place, so we replaced 320 with h because it is the height in this situation so we ended up with the equation t=32016 solved it and got t= 4.472. We used...
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...ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over P40619A ©2012 Pearson Education Ltd. *P40619A0120* 6/6/6/3 GCSE Mathematics 2MB01 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. 1 Area of trapezium = 2 (a + b)h a cross section Volume of prism = area of cross section × length h lengt h b Volume of sphere = 4 r3 3 Surface area of sphere = 4 r2 r Volume of cone = 1 r2h 3 Curved surface area of cone = rl l r h In any triangle ABC b A c C a B The Quadratic Equation The solutions of ax2 + bx + c = 0 where a ≠ 0, are given by...
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...The Fencing Problem - Math The task -------- A farmer has exactly 1000m of fencing; with it she wishes to fence off a level area of land. She is not concerned about the shape of the plot but it must have perimeter of 1000m. What she does wish to do is to fence off the plot of land which contains the maximun area. Investigate the shape/s of the plot of land that have the maximum area. Solution -------- Firstly I will look at 3 common shapes. These will be: ------------------------------------------------------ [IMAGE] A regular triangle for this task will have the following area: 1/2 b x h 1000m / 3 - 333.33 333.33 / 2 = 166.66 333.33² - 166.66² = 83331.11 Square root of 83331.11 = 288.67 288.67 x 166.66 = 48112.52² [IMAGE]A regular square for this task will have the following area: Each side = 250m 250m x 250m = 62500m² [IMAGE] A regular circle with a circumference of 1000m would give an area of: Pi x 2 x r = circumference Pi x 2 = circumference / r Circumference / (Pi x 2) = r Area = Pi x r² Area = Pi x (Circumference / (Pi x 2)) ² Pi x (1000m / (pi x 2)) ² = 79577.45m² I predict that for regular shapes the more sides the shape has the higher the area is. A circle has infinite sides in theory so I will expect this to be of the highest area. The above only tells us about regular shapes I still haven't worked out what the ideal shape is. Width...
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...| | |MIDTERM - 2nd SEMESTER [pic] | |Subject: |Mathematics for Business |Professor: |Ricardo Torres | |Timing: |2 hours |Student’s name: | | |Exam Date: | |Exam review date: | |Grade: | | This is a closed book examination. You may not use calculators. Clearly show all your calculations and intermediate steps. 1. Solve the following expressions and simplify the answers when possible. [1 pt] a. 32 + 5 [(8 – 23/2) + (15 - 3 + 42)/7] b. [pic] c. (x2)-4*x10*x½ d. [pic] 2. Sketch the following functions and show all relevant points. [1 pt] a. 4x2 - 12x + 5 b. −x2 + 8x - 12 3. A number is decreased by 40%. What percentage do we need to increase the result by so we obtain the original number again? [1 pt] 4. The population of a town went from 6250 in 2010 to 7500 in 2011. a) What was the percentage increase? b) If the population between 2009 and 2010...
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