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






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






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






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






5. 2pr






6. 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






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






8. 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






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






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






11. Factor out the perfect squares






12. 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






13. The smallest multiple (other than zero) that two or more numbers have in common.






14. The whole # left over after division






15. 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






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






17. 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






18. Multiply the exponents






19. To solve a proportion - cross multiply






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






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






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






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






24. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






25. 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






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






27. 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






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






29. 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)






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






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






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






33. 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






34. 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






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






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






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






38. 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






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






40. 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






41. 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






42. 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






43. 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






44. pr^2






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






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






47. 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






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






49. 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






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