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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. pr^2






3. 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






4. 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






5. 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






6. 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






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






8. 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






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






10. 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






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






12. 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






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






14. The smallest multiple (other than zero) that two or more numbers have in common.






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






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






17. 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






18. 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






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






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






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






22. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






23. Part = Percent x Whole






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






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






26. 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






27. 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






28. 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






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






30. 2pr






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






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






33. 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.






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






35. Domain: all possible values of x for a function range: all possible outputs of a function






36. 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






37. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






38. The whole # left over after division






39. 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






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. Change in y/ change in x rise/run






42. Factor out the perfect squares






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






44. 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






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






46. Probability= Favorable Outcomes/Total Possible Outcomes






47. Volume of a Cylinder = pr^2h






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






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






50. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact