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. Factor out the perfect squares






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






3. 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






4. Probability= Favorable Outcomes/Total Possible Outcomes






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






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. Multiply the exponents






8. 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






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






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






11. 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






12. 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






13. 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






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






15. pr^2






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






17. Combine like terms






18. 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






19. 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






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






21. 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






22. 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






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






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






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






26. Volume of a Cylinder = pr^2h






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






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






29. Part = Percent x Whole






30. To solve a proportion - cross multiply






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






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






33. 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






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






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






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






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






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






39. 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






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






41. 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






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






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






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






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






46. 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






47. 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






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






49. 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






50. 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