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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Study First
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. Combine like terms
PEMDAS
Adding and Subtraction Polynomials
Interior and Exterior Angles of a Triangle
Adding and Subtracting Roots
2. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Adding and Subtracting monomials
Adding and Subtracting Roots
Characteristics of a Rectangle
Combined Percent Increase and Decrease
3. Add the exponents and keep the same base
Multiplying and Dividing Powers
Volume of a Cylinder
Characteristics of a Parallelogram
Characteristics of a Square
4. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Average Rate
Using an Equation to Find the Slope
Median and Mode
Intersecting Lines
5. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Solving an Inequality
Remainders
Counting Consecutive Integers
Median and Mode
6. To solve a proportion - cross multiply
Solving a Proportion
Remainders
Surface Area of a Rectangular Solid
Finding the Distance Between Two Points
7. 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
Multiplying Fractions
Finding the Missing Number
Adding and Subtracting Roots
Characteristics of a Rectangle
8. 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
Reciprocal
Using the Average to Find the Sum
Function - Notation - and Evaulation
Factor/Multiple
9. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Probability
Multiples of 3 and 9
(Least) Common Multiple
10. 2pr
Circumference of a Circle
Multiples of 2 and 4
Probability
Percent Increase and Decrease
11. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Parallel Lines and Transversals
Surface Area of a Rectangular Solid
Function - Notation - and Evaulation
Determining Absolute Value
12. Factor out the perfect squares
Using an Equation to Find the Slope
Simplifying Square Roots
Finding the midpoint
Combined Percent Increase and Decrease
13. 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)
Comparing Fractions
Prime Factorization
Length of an Arc
Area of a Triangle
14. 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.
Area of a Circle
PEMDAS
Number Categories
Finding the Original Whole
15. To divide fractions - invert the second one and multiply
Surface Area of a Rectangular Solid
Finding the midpoint
The 3-4-5 Triangle
Dividing Fractions
16. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Raising Powers to Powers
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Quadratic Equation
17. 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
Surface Area of a Rectangular Solid
(Least) Common Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Triangle
18. Part = Percent x Whole
Average Rate
Finding the Original Whole
Percent Formula
Length of an Arc
19. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Domain and Range of a Function
Prime Factorization
Average Rate
Characteristics of a Square
20. 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
Average of Evenly Spaced Numbers
Probability
Simplifying Square Roots
Multiplying/Dividing Signed Numbers
21. For all right triangles: a^2+b^2=c^2
Solving a Quadratic Equation
Rate
Pythagorean Theorem
Using Two Points to Find the Slope
22. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Characteristics of a Rectangle
Adding/Subtracting Fractions
Domain and Range of a Function
Number Categories
23. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Multiples of 3 and 9
PEMDAS
Function - Notation - and Evaulation
Counting Consecutive Integers
24. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Volume of a Rectangular Solid
Multiplying/Dividing Signed Numbers
Multiples of 2 and 4
Using an Equation to Find an Intercept
25. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Multiplying and Dividing Roots
Similar Triangles
Isosceles and Equilateral triangles
26. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
(Least) Common Multiple
Prime Factorization
Intersection of sets
The 5-12-13 Triangle
27. Multiply the exponents
Probability
Area of a Sector
Raising Powers to Powers
Multiples of 3 and 9
28. pr^2
Using the Average to Find the Sum
Intersection of sets
Area of a Circle
Interior Angles of a Polygon
29. 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
The 5-12-13 Triangle
Similar Triangles
Relative Primes
Multiplying/Dividing Signed Numbers
30. Surface Area = 2lw + 2wh + 2lh
Intersecting Lines
Negative Exponent and Rational Exponent
Surface Area of a Rectangular Solid
Direct and Inverse Variation
31. 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
Area of a Sector
Raising Powers to Powers
Using an Equation to Find the Slope
Part-to-Part Ratios and Part-to-Whole Ratios
32. 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
Finding the Missing Number
Negative Exponent and Rational Exponent
Repeating Decimal
Dividing Fractions
33. 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
Triangle Inequality Theorem
Direct and Inverse Variation
Rate
Function - Notation - and Evaulation
34. 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
Simplifying Square Roots
The 5-12-13 Triangle
Counting the Possibilities
(Least) Common Multiple
35. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Multiplying Monomials
Function - Notation - and Evaulation
Pythagorean Theorem
36. 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
Simplifying Square Roots
Characteristics of a Parallelogram
Repeating Decimal
Adding and Subtraction Polynomials
37. 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
Direct and Inverse Variation
Area of a Sector
Multiplying Monomials
Relative Primes
38. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Characteristics of a Parallelogram
Multiplying Monomials
Adding and Subtraction Polynomials
Multiples of 3 and 9
39. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Exponential Growth
Multiplying Fractions
Interior and Exterior Angles of a Triangle
Parallel Lines and Transversals
40. 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
Reciprocal
The 3-4-5 Triangle
Triangle Inequality Theorem
Identifying the Parts and the Whole
41. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Tangency
Reciprocal
Simplifying Square Roots
Intersecting Lines
42. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Volume of a Cylinder
Domain and Range of a Function
Intersection of sets
Multiplying and Dividing Roots
43. 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
Counting the Possibilities
Even/Odd
Mixed Numbers and Improper Fractions
Setting up a Ratio
44. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Area of a Sector
Interior Angles of a Polygon
Reducing Fractions
Solving a Proportion
45. 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
PEMDAS
Percent Increase and Decrease
Circumference of a Circle
Median and Mode
46. 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
Factor/Multiple
Average Rate
Intersecting Lines
Rate
47. The whole # left over after division
Remainders
Probability
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
48. Subtract the smallest from the largest and add 1
Determining Absolute Value
The 5-12-13 Triangle
Counting Consecutive Integers
Solving a Proportion
49. 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
Evaluating an Expression
Adding/Subtracting Signed Numbers
Prime Factorization
Parallel Lines and Transversals
50. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Determining Absolute Value
Characteristics of a Square
Reducing Fractions
Dividing Fractions