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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. The largest factor that two or more numbers have in common.






2. Factor out the perfect squares






3. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






4. Multiply the exponents






5. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






6. To find the reciprocal of a fraction switch the numerator and the denominator






7. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






8. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






9. Add the exponents and keep the same base






10. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex






11. Subtract the smallest from the largest and add 1






12. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






13. Probability= Favorable Outcomes/Total Possible Outcomes






14. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






15. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






16. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






17. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






18. To divide fractions - invert the second one and multiply






19. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






20. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






21. A square is a rectangle with four equal sides; Area of Square = side*side






22. Combine equations in such a way that one of the variables cancel out






23. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






24. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






25. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






26. 1. Re-express them with common denominators 2. Convert them to decimals






27. To solve a proportion - cross multiply






28. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






29. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






30. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






31. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






32. (average of the x coordinates - average of the y coordinates)






33. pr^2






34. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






35. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






36. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






37. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






38. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






39. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






40. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






41. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






42. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






43. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






44. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






45. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






46. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






47. For all right triangles: a^2+b^2=c^2






48. The median is the value that falls in the middle of the set - the mode is the value that appears most often






49. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






50. Volume of a Cylinder = pr^2h