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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. 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






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






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






4. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






5. 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






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






7. 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






8. 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






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






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






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






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






13. 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






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






15. 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






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






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






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






19. Multiply the exponents






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






21. The whole # left over after division






22. 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






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






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






25. 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






26. 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)






27. 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)






28. 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.






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






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






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






32. 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






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






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






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






36. To solve a proportion - cross multiply






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






38. Add the exponents and keep the same base






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






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






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






42. 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






43. 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






44. Sum=(Average) x (Number of Terms)






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






46. Part = Percent x Whole






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






48. 2pr






49. 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






50. 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