Test your basic knowledge |

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. Add the exponents and keep the same base






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






4. To solve a proportion - cross multiply






5. 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






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






7. The whole # left over after division






8. 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






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






10. 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)






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






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






13. Part = Percent x Whole






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






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






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






17. 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






18. 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






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






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






21. Combine like terms






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






23. 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






24. 2pr






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






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






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






28. 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






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






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






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






32. 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






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






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






35. 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






36. 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






37. Probability= Favorable Outcomes/Total Possible Outcomes






38. 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






39. 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






40. 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






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






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






43. Subtract the smallest from the largest and add 1






44. 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






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






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






47. Multiply the exponents






48. pr^2






49. 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






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