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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. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






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






3. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






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






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






8. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






9. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






10. The whole # left over after division






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






12. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






13. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






14. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






15. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






16. 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






17. 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






18. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






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. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






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






22. 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






23. 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






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






25. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






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






27. 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






28. 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






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






30. 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






31. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






32. Surface Area = 2lw + 2wh + 2lh






33. 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






34. 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)






35. Part = Percent x Whole






36. Add the exponents and keep the same base






37. Volume of a Cylinder = pr^2h






38. Probability= Favorable Outcomes/Total Possible Outcomes






39. pr^2






40. 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






41. 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






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. 2pr






44. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






45. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






46. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






47. 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






48. The largest factor that two or more numbers have in common.






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






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