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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 solve a proportion - cross multiply






2. 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






3. 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






4. Part = Percent x Whole






5. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






6. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






7. 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






8. 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






9. 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






10. To multiply fractions - multiply the numerators and multiply the denominators






11. 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






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






13. 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






14. Volume of a Cylinder = pr^2h






15. 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






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






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






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






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






20. Probability= Favorable Outcomes/Total Possible Outcomes






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






22. 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






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






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






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






26. pr^2






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






28. 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






29. 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






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






31. The whole # left over after division






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






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






34. 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






35. 2pr






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






38. 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






39. 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






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






41. Combine like terms






42. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






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






44. 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






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






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






47. 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)






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






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






50. 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