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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 solve a proportion - cross multiply






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






3. 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






4. Subtract the smallest from the largest and add 1






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






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






7. 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






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






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






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






11. 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






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






13. 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)






14. 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.






15. 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






16. 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






17. 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






18. 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






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






20. 2pr






21. 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






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






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






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






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






26. The whole # left over after division






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






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






29. Part = Percent x Whole






30. 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






31. 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






32. 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






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






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






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






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






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






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






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






40. 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






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






42. Factor out the perfect squares






43. 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)






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






45. 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






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






47. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






48. 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






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. pr^2