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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 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






2. 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






3. Subtract the smallest from the largest and add 1






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






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






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






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






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






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






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






11. 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






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






13. 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






14. Add the exponents and keep the same base






15. Multiply the exponents






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






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






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






19. To solve a proportion - cross multiply






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






21. 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






22. pr^2






23. Part = Percent x Whole






24. 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






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






26. 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






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






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






29. 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






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






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






32. Factor out the perfect squares






33. 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)






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






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






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






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






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






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






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






41. 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






42. Volume of a Cylinder = pr^2h






43. 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






44. 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






45. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






48. 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






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






50. 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