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






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






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






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






5. Part = Percent x Whole






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. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






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






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






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






11. 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.






12. Add the exponents and keep the same base






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






14. To solve a proportion - cross multiply






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






16. 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






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






18. 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






19. 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)






20. Volume of a Cylinder = pr^2h






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






22. 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






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






24. 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






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






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






27. The whole # left over after division






28. Multiply the exponents






29. Factor out the perfect squares






30. 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






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






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






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






34. 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






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






36. 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






37. Probability= Favorable Outcomes/Total Possible Outcomes






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






39. 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






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






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






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






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






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






46. 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






47. 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






48. 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






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






50. 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