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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. Multiply the exponents






2. 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






3. The whole # left over after division






4. 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






5. 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






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






7. 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






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






9. 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






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






11. Part = Percent x Whole






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






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






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






15. 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






16. 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






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






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






19. 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






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






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






22. To solve a proportion - cross multiply






23. 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






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






25. Factor out the perfect squares






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






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






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






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






30. 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






31. Probability= Favorable Outcomes/Total Possible Outcomes






32. 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






33. 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






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






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






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






37. 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)






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






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






40. 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






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






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






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






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






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






46. 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






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






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






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






50. Volume of a Cylinder = pr^2h






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