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






2. 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.






3. Volume of a Cylinder = pr^2h






4. The whole # left over after division






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






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






7. 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






8. Probability= Favorable Outcomes/Total Possible Outcomes






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






10. Subtract the smallest from the largest and add 1






11. 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






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






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






14. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






15. 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






16. Factor out the perfect squares






17. 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






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






20. 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






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






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






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






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






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






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






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






28. 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






29. 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






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






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






32. Part = Percent x Whole






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






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






35. 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






36. 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






37. 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






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






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






40. 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






41. 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)






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






43. 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






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






45. 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






46. 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






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






48. 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






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






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