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






2. Subtract the smallest from the largest and add 1






3. Part = Percent x Whole






4. 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.






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






6. 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






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. 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






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






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






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






12. 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






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






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






15. 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






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






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






18. 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






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






20. The whole # left over after division






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






23. Volume of a Cylinder = pr^2h






24. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






28. 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)






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






30. 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






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






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






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






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






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






36. 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






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






38. 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






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






40. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






41. 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






42. 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






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






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






45. 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)






46. 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






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






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






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






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