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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 whole # left over after division






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






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






4. Multiply the exponents






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






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






7. 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






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






9. 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






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






11. To solve a proportion - cross multiply






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






13. 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






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






15. 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






16. 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






17. 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






18. 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






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






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






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






23. pr^2






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






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






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






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






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






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






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






31. Probability= Favorable Outcomes/Total Possible Outcomes






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






33. 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






34. 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






35. Subtract the smallest from the largest and add 1






36. 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






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






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






39. 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






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






41. Factor out the perfect squares






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






43. 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






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






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






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






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






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