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






2. 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






3. 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






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






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






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






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






8. 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






9. 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






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






11. 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






12. 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






13. 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






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






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






16. 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






17. 2pr






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. 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






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






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






22. Part = Percent x Whole






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






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






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






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






27. 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






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






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






30. 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






31. 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






32. 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






33. 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






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






35. 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






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. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






41. pr^2






42. Combine like terms






43. The whole # left over after division






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






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






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






47. Volume of a Cylinder = pr^2h






48. 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






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