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






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






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






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






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






7. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






8. 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






9. 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)






10. 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.






11. 2pr






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






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






14. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






15. pr^2






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






17. 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






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






19. 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






20. 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






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






22. 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






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






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






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. 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






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






28. 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






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






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






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






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






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






34. 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






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






36. 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






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






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






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






41. 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)






42. 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






43. Multiply the exponents






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






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






46. Part = Percent x Whole






47. 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






48. 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






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






50. 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