## Test your basic knowledge |

# SAT Math: Concepts And Tricks

**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.**