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






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






3. 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






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






5. 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






6. 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






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






8. 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






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






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






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






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






14. Change in y/ change in x rise/run






15. 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)






16. 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)






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






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






19. 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






20. 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






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






22. 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






23. Factor out the perfect squares






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






25. 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






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






27. To solve a proportion - cross multiply






28. Multiply the exponents






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






30. 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






31. you can add/subtract when the part under the radical is the same






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






33. 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






34. 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






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






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






37. 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






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






39. Add the exponents and keep the same base






40. 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






41. Subtract the smallest from the largest and add 1






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






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






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






45. pr^2






46. 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






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






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






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






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