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






2. 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






3. 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






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






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






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






7. 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






8. 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






9. 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






10. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






11. 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






12. 2pr






13. 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






14. Part = Percent x Whole






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






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






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






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






20. 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






21. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






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






23. 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






24. 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






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






26. 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






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






28. Volume of a Cylinder = pr^2h






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






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






31. The whole # left over after division






32. Add the exponents and keep the same base






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






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






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






36. 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






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






38. 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.






39. pr^2






40. 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






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






42. 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






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






44. Subtract the smallest from the largest and add 1






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






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






47. 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






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






49. 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






50. Factor out the perfect squares