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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 30 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. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






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






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






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






5. The whole # left over after division






6. Probability= Favorable Outcomes/Total Possible Outcomes






7. 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






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






9. 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






10. 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






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






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






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






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






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. 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)






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






18. 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






19. Combine like terms






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






21. 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






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






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






25. 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






26. 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






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






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






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






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






31. Add the exponents and keep the same base






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






33. Factor out the perfect squares






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






35. 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)






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






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






38. 2pr






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






40. 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






41. 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






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






43. 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






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






45. 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






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






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






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






49. 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






50. 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






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