## 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. 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**

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

**3. 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**

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

**5. 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**

**6. To divide fractions - invert the second one and multiply**

**7. 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**

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

**9. Part = Percent x Whole**

**10. To multiply fractions - multiply the numerators and multiply the denominators**

**11. Volume of a Cylinder = pr^2h**

**12. 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.**

**13. 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)**

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

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

**16. 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)**

**17. 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**

**18. 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**

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

**20. 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**

**21. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520**

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

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

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

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

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

**28. To solve a proportion - cross multiply**

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

**30. 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**

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

**32. 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**

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

**34. Combine like terms**

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

**36. 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**

**37. 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**

**38. Probability= Favorable Outcomes/Total Possible Outcomes**

**39. 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**

**40. 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**

**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. The whole # left over after division**

**43. 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**

**44. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is**

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

**46. The sum of the measures of the interior angles of a polygon = (n - 2) 180 - where n is the number of sides**

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

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

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