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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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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. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Parallel Lines and Transversals
Adding and Subtracting monomials
(Least) Common Multiple
2. 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
Intersecting Lines
Area of a Circle
Multiplying/Dividing Signed Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
3. The whole # left over after division
Simplifying Square Roots
Percent Increase and Decrease
Remainders
Solving an Inequality
4. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Interior and Exterior Angles of a Triangle
Relative Primes
Intersecting Lines
5. 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
Even/Odd
Combined Percent Increase and Decrease
Characteristics of a Rectangle
Average Formula -
6. 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
Simplifying Square Roots
Finding the midpoint
Relative Primes
PEMDAS
7. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
Probability
Solving an Inequality
Setting up a Ratio
Negative Exponent and Rational Exponent
8. 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
Average Rate
Repeating Decimal
Pythagorean Theorem
Adding/Subtracting Signed Numbers
9. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Repeating Decimal
Combined Percent Increase and Decrease
Factor/Multiple
Domain and Range of a Function
10. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Median and Mode
Solving a Quadratic Equation
Negative Exponent and Rational Exponent
Parallel Lines and Transversals
11. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Exponential Growth
Interior and Exterior Angles of a Triangle
Tangency
12. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Length of an Arc
Multiplying and Dividing Roots
Percent Formula
13. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Finding the midpoint
Characteristics of a Rectangle
Factor/Multiple
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.
Number Categories
Pythagorean Theorem
Characteristics of a Square
Average Rate
15. Probability= Favorable Outcomes/Total Possible Outcomes
Relative Primes
Solving a Proportion
Probability
Exponential Growth
16. To solve a proportion - cross multiply
Domain and Range of a Function
Repeating Decimal
Solving a Proportion
Prime Factorization
17. 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)
Raising Powers to Powers
Isosceles and Equilateral triangles
Length of an Arc
Relative Primes
18. Sum=(Average) x (Number of Terms)
Reducing Fractions
Using the Average to Find the Sum
Multiples of 2 and 4
Factor/Multiple
19. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Counting the Possibilities
Median and Mode
Solving a Quadratic Equation
Characteristics of a Rectangle
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
Domain and Range of a Function
Even/Odd
Solving an Inequality
Multiples of 2 and 4
21. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Median and Mode
Direct and Inverse Variation
Finding the Original Whole
Reducing Fractions
22. 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
Finding the Missing Number
Characteristics of a Square
Area of a Triangle
Interior and Exterior Angles of a Triangle
23. 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
Interior and Exterior Angles of a Triangle
Interior Angles of a Polygon
(Least) Common Multiple
Domain and Range of a Function
24. 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
Volume of a Rectangular Solid
Percent Increase and Decrease
Finding the midpoint
25. Add the exponents and keep the same base
Evaluating an Expression
Exponential Growth
Adding/Subtracting Signed Numbers
Multiplying and Dividing Powers
26. To divide fractions - invert the second one and multiply
Multiplying Fractions
Intersection of sets
Using an Equation to Find an Intercept
Dividing Fractions
27. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Using an Equation to Find an Intercept
Relative Primes
Solving a Quadratic Equation
28. 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
Finding the midpoint
Repeating Decimal
Number Categories
Characteristics of a Parallelogram
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
Tangency
Using an Equation to Find an Intercept
Exponential Growth
Solving an Inequality
30. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Number Categories
Combined Percent Increase and Decrease
Prime Factorization
31. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Mixed Numbers and Improper Fractions
Multiples of 3 and 9
Parallel Lines and Transversals
Reducing Fractions
32. The smallest multiple (other than zero) that two or more numbers have in common.
Characteristics of a Parallelogram
(Least) Common Multiple
Union of Sets
Dividing Fractions
33. For all right triangles: a^2+b^2=c^2
Even/Odd
Pythagorean Theorem
Using an Equation to Find the Slope
Multiplying/Dividing Signed Numbers
34. 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
Multiplying Fractions
Greatest Common Factor
Rate
(Least) Common Multiple
35. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Triangle Inequality Theorem
Rate
Intersecting Lines
Domain and Range of a Function
36. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a System of Equations
Reciprocal
Intersection of sets
37. Change in y/ change in x rise/run
Direct and Inverse Variation
Using Two Points to Find the Slope
Finding the Original Whole
Pythagorean Theorem
38. 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
Union of Sets
Adding and Subtracting Roots
Isosceles and Equilateral triangles
Solving a Quadratic Equation
39. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Using Two Points to Find the Slope
Adding and Subtracting monomials
Exponential Growth
40. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Repeating Decimal
Prime Factorization
Multiplying Monomials
Even/Odd
41. Factor out the perfect squares
Parallel Lines and Transversals
Surface Area of a Rectangular Solid
Intersection of sets
Simplifying Square Roots
42. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Characteristics of a Parallelogram
Adding/Subtracting Signed Numbers
Even/Odd
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
Rate
The 3-4-5 Triangle
44. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Raising Powers to Powers
Determining Absolute Value
Interior Angles of a Polygon
Domain and Range of a Function
45. The largest factor that two or more numbers have in common.
Circumference of a Circle
Solving a System of Equations
Area of a Sector
Greatest Common Factor
46. 1. Re-express them with common denominators 2. Convert them to decimals
Finding the midpoint
Simplifying Square Roots
Solving an Inequality
Comparing Fractions
47. Combine like terms
Adding and Subtraction Polynomials
Percent Formula
Reciprocal
Evaluating an Expression
48. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Adding and Subtraction Polynomials
PEMDAS
Multiplying and Dividing Roots
Intersection of sets
49. 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
Similar Triangles
The 3-4-5 Triangle
The 5-12-13 Triangle
Tangency
50. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Circumference of a Circle
Exponential Growth
Volume of a Rectangular Solid
Rate