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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. Add the exponents and keep the same base






2. 2pr






3. 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






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






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






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






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






8. To solve a proportion - cross multiply






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






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






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






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. 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






15. 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






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






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






18. Multiply the exponents






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






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






21. 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






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






23. Volume of a Cylinder = pr^2h






24. 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






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






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






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






28. 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






29. 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






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






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






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






33. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






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






35. 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






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






37. 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






38. 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






39. 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)






40. 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






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






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






43. 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






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






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






46. 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






47. 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






48. 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






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






50. 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