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Test your basic knowledge |
SAT Math: Concepts And Tricks
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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. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Interior Angles of a Polygon
Using an Equation to Find an Intercept
Multiplying/Dividing Signed Numbers
Multiplying and Dividing Roots
2. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Surface Area of a Rectangular Solid
Relative Primes
Setting up a Ratio
Prime Factorization
3. 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.
Multiples of 3 and 9
Dividing Fractions
Reciprocal
Number Categories
4. 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)
(Least) Common Multiple
Using Two Points to Find the Slope
Dividing Fractions
Length of an Arc
5. pr^2
Setting up a Ratio
Reducing Fractions
Counting Consecutive Integers
Area of a Circle
6. 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
Pythagorean Theorem
Similar Triangles
Characteristics of a Rectangle
Adding/Subtracting Signed Numbers
7. 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
Function - Notation - and Evaulation
Prime Factorization
Counting Consecutive Integers
Triangle Inequality Theorem
8. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Reducing Fractions
Multiplying and Dividing Powers
Solving a System of Equations
9. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Part-to-Part Ratios and Part-to-Whole Ratios
Average of Evenly Spaced Numbers
Using an Equation to Find an Intercept
Setting up a Ratio
10. 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
Even/Odd
Factor/Multiple
Isosceles and Equilateral triangles
Median and Mode
11. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Tangency
Intersecting Lines
Multiplying/Dividing Signed Numbers
Adding and Subtracting Roots
12. Sum=(Average) x (Number of Terms)
Area of a Sector
Using the Average to Find the Sum
Comparing Fractions
Volume of a Cylinder
13. 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
Average Formula -
Mixed Numbers and Improper Fractions
Adding and Subtraction Polynomials
Tangency
14. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Area of a Triangle
Factor/Multiple
Characteristics of a Rectangle
Rate
15. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Adding/Subtracting Signed Numbers
Comparing Fractions
Pythagorean Theorem
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)
Multiplying and Dividing Powers
Area of a Sector
Adding and Subtraction Polynomials
Greatest Common Factor
17. To solve a proportion - cross multiply
Solving an Inequality
Solving a Quadratic Equation
Isosceles and Equilateral triangles
Solving a Proportion
18. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Percent Formula
Union of Sets
Parallel Lines and Transversals
Finding the Original Whole
19. (average of the x coordinates - average of the y coordinates)
Area of a Sector
Adding and Subtracting monomials
Mixed Numbers and Improper Fractions
Finding the midpoint
20. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Relative Primes
Percent Formula
Triangle Inequality Theorem
21. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Isosceles and Equilateral triangles
Factor/Multiple
The 5-12-13 Triangle
22. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Negative Exponent and Rational Exponent
Union of Sets
Interior Angles of a Polygon
23. 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
Dividing Fractions
Raising Powers to Powers
Counting the Possibilities
Characteristics of a Parallelogram
24. Factor out the perfect squares
Direct and Inverse Variation
Characteristics of a Parallelogram
Simplifying Square Roots
Finding the Distance Between Two Points
25. The smallest multiple (other than zero) that two or more numbers have in common.
Interior Angles of a Polygon
(Least) Common Multiple
Circumference of a Circle
Union of Sets
26. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Intersecting Lines
Similar Triangles
Multiples of 2 and 4
Prime Factorization
27. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
The 5-12-13 Triangle
Parallel Lines and Transversals
Multiples of 3 and 9
Multiples of 2 and 4
28. 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
Finding the Distance Between Two Points
Finding the Original Whole
Characteristics of a Rectangle
PEMDAS
29. 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
Setting up a Ratio
Finding the Missing Number
Pythagorean Theorem
Using Two Points to Find the Slope
30. Combine like terms
Reciprocal
Adding and Subtraction Polynomials
Adding and Subtracting monomials
Using Two Points to Find the Slope
31. 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
Union of Sets
Similar Triangles
Determining Absolute Value
Multiplying/Dividing Signed Numbers
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
Interior and Exterior Angles of a Triangle
Adding and Subtracting Roots
Adding and Subtracting monomials
Prime Factorization
33. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 2 and 4
Factor/Multiple
Adding/Subtracting Fractions
Reciprocal
34. you can add/subtract when the part under the radical is the same
Triangle Inequality Theorem
Average of Evenly Spaced Numbers
Evaluating an Expression
Adding and Subtracting Roots
35. 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
Relative Primes
Characteristics of a Parallelogram
Using an Equation to Find an Intercept
Negative Exponent and Rational Exponent
36. The largest factor that two or more numbers have in common.
Area of a Circle
Greatest Common Factor
Adding and Subtracting Roots
Solving an Inequality
37. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Prime Factorization
Median and Mode
Solving a Proportion
Counting Consecutive Integers
38. 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
Finding the Distance Between Two Points
Solving an Inequality
Direct and Inverse Variation
Average Rate
39. Surface Area = 2lw + 2wh + 2lh
Triangle Inequality Theorem
Dividing Fractions
Surface Area of a Rectangular Solid
Adding and Subtraction Polynomials
40. Part = Percent x Whole
Multiplying Monomials
Multiples of 2 and 4
Percent Formula
Average Formula -
41. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Probability
Similar Triangles
Part-to-Part Ratios and Part-to-Whole Ratios
42. Add the exponents and keep the same base
Multiples of 2 and 4
Multiplying and Dividing Powers
Area of a Triangle
Simplifying Square Roots
43. 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
Union of Sets
Repeating Decimal
Finding the Missing Number
Setting up a Ratio
44. 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
(Least) Common Multiple
Using an Equation to Find an Intercept
Average of Evenly Spaced Numbers
PEMDAS
45. 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
Average Rate
Multiplying and Dividing Roots
Rate
Remainders
46. 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
Domain and Range of a Function
Comparing Fractions
Intersection of sets
Area of a Triangle
47. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Relative Primes
Interior and Exterior Angles of a Triangle
Intersection of sets
Adding/Subtracting Fractions
48. 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
Multiples of 2 and 4
Setting up a Ratio
Counting the Possibilities
Adding and Subtracting monomials
49. 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
Dividing Fractions
The 5-12-13 Triangle
Probability
Negative Exponent and Rational Exponent
50. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Parallel Lines and Transversals
Solving a Quadratic Equation
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent