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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. 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






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






3. 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






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. 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. 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






8. pr^2






9. 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






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






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






12. 2pr






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






14. Part = Percent x Whole






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






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






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






18. 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






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






20. 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






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






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






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






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






25. 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






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






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






28. 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






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






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






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






32. 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






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






34. Subtract the smallest from the largest and add 1






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






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






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






38. 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)






39. 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






40. 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






41. Combine equations in such a way that one of the variables cancel out






42. A square is a rectangle with four equal sides; Area of Square = side*side






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






44. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






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






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






48. 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






49. 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






50. 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