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






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






3. 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)






4. 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






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






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






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






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






9. 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






10. 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






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






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






13. 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






14. 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






15. 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






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






17. 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






18. 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






19. 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






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






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






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






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






24. 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






25. To solve a proportion - cross multiply






26. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






28. 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






29. 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






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






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






32. Add the exponents and keep the same base






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






34. 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






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






36. 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)






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






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






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






40. 2pr






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






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






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






44. 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






45. 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






46. Combine like terms






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






48. Subtract the smallest from the largest and add 1






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






50. 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