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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 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






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






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






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






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






6. Multiply the exponents






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. 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. Combine like terms






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






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






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






13. Factor out the perfect squares






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






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






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






17. 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






18. 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)






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






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






21. 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






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






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






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






25. 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






26. 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.






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






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






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






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






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






32. 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






33. 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






34. 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






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






36. pr^2






37. 2pr






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






39. 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






40. 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






41. To solve a proportion - cross multiply






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






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






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






45. 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






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






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






48. 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






49. 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






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