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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. The largest factor that two or more numbers have in common.
Adding and Subtraction Polynomials
Domain and Range of a Function
Simplifying Square Roots
Greatest Common Factor
2. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Triangle Inequality Theorem
Setting up a Ratio
(Least) Common Multiple
Similar Triangles
3. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Missing Number
Pythagorean Theorem
Simplifying Square Roots
Finding the Distance Between Two Points
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
Function - Notation - and Evaulation
The 5-12-13 Triangle
The 3-4-5 Triangle
Using an Equation to Find the Slope
5. Combine equations in such a way that one of the variables cancel out
Even/Odd
Greatest Common Factor
Solving a System of Equations
Parallel Lines and Transversals
6. 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
Union of Sets
Comparing Fractions
Finding the Missing Number
Part-to-Part Ratios and Part-to-Whole Ratios
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
Identifying the Parts and the Whole
Adding and Subtracting Roots
Adding and Subtraction Polynomials
Solving a System of Equations
8. 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
Combined Percent Increase and Decrease
Reciprocal
Prime Factorization
The 5-12-13 Triangle
9. 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
Pythagorean Theorem
Repeating Decimal
Similar Triangles
Area of a Triangle
10. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Repeating Decimal
Median and Mode
Solving a Proportion
11. 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
Interior Angles of a Polygon
Remainders
Finding the midpoint
Area of a Triangle
12. Part = Percent x Whole
Reciprocal
Percent Formula
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
13. 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
Factor/Multiple
Length of an Arc
Direct and Inverse Variation
Median and Mode
14. 1. Re-express them with common denominators 2. Convert them to decimals
Using Two Points to Find the Slope
Isosceles and Equilateral triangles
Comparing Fractions
PEMDAS
15. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiplying Monomials
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
Direct and Inverse Variation
16. 2pr
Solving a System of Equations
Adding and Subtracting Roots
Circumference of a Circle
Average Formula -
17. Combine like terms
Prime Factorization
Multiplying and Dividing Powers
Area of a Sector
Adding and Subtraction Polynomials
18. 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
Percent Formula
Multiplying Monomials
Adding/Subtracting Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
19. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Using the Average to Find the Sum
Solving a Quadratic Equation
Rate
Counting the Possibilities
20. 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
Characteristics of a Parallelogram
Counting the Possibilities
The 5-12-13 Triangle
Reciprocal
21. For all right triangles: a^2+b^2=c^2
Factor/Multiple
Pythagorean Theorem
Using an Equation to Find the Slope
Adding and Subtraction Polynomials
22. Subtract the smallest from the largest and add 1
Surface Area of a Rectangular Solid
Solving a Proportion
Counting Consecutive Integers
PEMDAS
23. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Finding the Original Whole
Median and Mode
Triangle Inequality Theorem
Negative Exponent and Rational Exponent
24. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Using Two Points to Find the Slope
Parallel Lines and Transversals
Function - Notation - and Evaulation
Median and Mode
25. 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
Even/Odd
Probability
Exponential Growth
Intersecting Lines
26. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Multiplying Fractions
Parallel Lines and Transversals
Intersection of sets
Circumference of a Circle
27. 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
Characteristics of a Rectangle
The 3-4-5 Triangle
Percent Formula
Raising Powers to Powers
28. 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)
Prime Factorization
Function - Notation - and Evaulation
Union of Sets
Length of an Arc
29. 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
Adding/Subtracting Signed Numbers
Surface Area of a Rectangular Solid
Using an Equation to Find an Intercept
Direct and Inverse Variation
30. pr^2
Area of a Circle
Simplifying Square Roots
Volume of a Rectangular Solid
Comparing Fractions
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
Average Formula -
Median and Mode
Interior and Exterior Angles of a Triangle
Multiplying/Dividing Signed Numbers
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
Even/Odd
Volume of a Rectangular Solid
Reducing Fractions
Percent Increase and Decrease
33. Factor out the perfect squares
(Least) Common Multiple
Simplifying Square Roots
Using an Equation to Find an Intercept
Area of a Sector
34. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Characteristics of a Parallelogram
Length of an Arc
Part-to-Part Ratios and Part-to-Whole Ratios
Characteristics of a Rectangle
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
PEMDAS
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
36. 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.
Pythagorean Theorem
Evaluating an Expression
Number Categories
Adding and Subtracting monomials
37. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Similar Triangles
The 5-12-13 Triangle
Multiples of 2 and 4
38. 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
Factor/Multiple
The 5-12-13 Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Triangle Inequality Theorem
39. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Percent Increase and Decrease
Average of Evenly Spaced Numbers
Pythagorean Theorem
Greatest Common Factor
40. Add the exponents and keep the same base
Identifying the Parts and the Whole
Multiplying and Dividing Powers
Average Formula -
Percent Increase and Decrease
41. 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
Finding the Distance Between Two Points
Multiplying/Dividing Signed Numbers
Reducing Fractions
Interior Angles of a Polygon
42. To find the reciprocal of a fraction switch the numerator and the denominator
Probability
Area of a Sector
Interior and Exterior Angles of a Triangle
Reciprocal
43. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Adding/Subtracting Fractions
Dividing Fractions
Setting up a Ratio
Mixed Numbers and Improper Fractions
44. To divide fractions - invert the second one and multiply
Percent Formula
Parallel Lines and Transversals
Dividing Fractions
Counting Consecutive Integers
45. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
The 3-4-5 Triangle
Prime Factorization
Even/Odd
Union of Sets
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
Relative Primes
Multiplying/Dividing Signed Numbers
Evaluating an Expression
Adding/Subtracting Signed Numbers
47. (average of the x coordinates - average of the y coordinates)
Percent Increase and Decrease
Finding the midpoint
Median and Mode
Interior and Exterior Angles of a Triangle
48. 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
Adding and Subtracting monomials
Triangle Inequality Theorem
Finding the Missing Number
Finding the Original Whole
49. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Adding and Subtraction Polynomials
Percent Increase and Decrease
Multiples of 2 and 4
Simplifying Square Roots
50. Volume of a Cylinder = pr^2h
Intersection of sets
Volume of a Cylinder
Percent Increase and Decrease
Characteristics of a Parallelogram