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






3. Add the exponents and keep the same base






4. 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






5. 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






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






7. 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






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






9. 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






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






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






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






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






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






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






16. 2pr






17. Part = Percent x Whole






18. Subtract the smallest from the largest and add 1






19. Multiply the exponents






20. 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






21. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






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






24. pr^2






25. 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






26. 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






27. 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






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






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






30. 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






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






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






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






34. 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.






35. 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






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






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






38. 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)






39. 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






40. 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






41. 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






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






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






44. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






46. 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






47. Volume of a Cylinder = pr^2h






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






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






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