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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. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Average Formula -
Prime Factorization
Determining Absolute Value
Triangle Inequality Theorem
2. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Similar Triangles
Multiplying Monomials
Solving a Proportion
Average of Evenly Spaced Numbers
3. For all right triangles: a^2+b^2=c^2
Median and Mode
Pythagorean Theorem
Counting the Possibilities
Domain and Range of a Function
4. 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
Probability
The 3-4-5 Triangle
Intersecting Lines
Adding and Subtraction Polynomials
5. Probability= Favorable Outcomes/Total Possible Outcomes
Direct and Inverse Variation
Determining Absolute Value
Characteristics of a Square
Probability
6. 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
Adding and Subtracting Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Triangle
Characteristics of a Parallelogram
7. Change in y/ change in x rise/run
Adding and Subtraction Polynomials
Average Rate
Using Two Points to Find the Slope
Characteristics of a Square
8. To multiply fractions - multiply the numerators and multiply the denominators
Multiplying Fractions
Counting Consecutive Integers
Interior Angles of a Polygon
Repeating Decimal
9. 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
Remainders
Pythagorean Theorem
Prime Factorization
Rate
10. 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
Domain and Range of a Function
The 5-12-13 Triangle
Isosceles and Equilateral triangles
Characteristics of a Parallelogram
11. 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
Combined Percent Increase and Decrease
Adding/Subtracting Fractions
Factor/Multiple
The 5-12-13 Triangle
12. To divide fractions - invert the second one and multiply
Counting Consecutive Integers
Using an Equation to Find an Intercept
Surface Area of a Rectangular Solid
Dividing Fractions
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)
Interior and Exterior Angles of a Triangle
Area of a Sector
Combined Percent Increase and Decrease
Counting Consecutive Integers
14. Multiply the exponents
Characteristics of a Square
Raising Powers to Powers
Intersecting Lines
Length of an Arc
15. 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
Area of a Triangle
Identifying the Parts and the Whole
Adding/Subtracting Fractions
Characteristics of a Parallelogram
16. 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
Solving a Proportion
Union of Sets
Multiples of 3 and 9
Triangle Inequality Theorem
17. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Length of an Arc
Adding/Subtracting Fractions
Similar Triangles
18. 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
Adding and Subtracting monomials
Solving a Quadratic Equation
Simplifying Square Roots
19. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Evaluating an Expression
Volume of a Rectangular Solid
Multiples of 2 and 4
Combined Percent Increase and Decrease
20. 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
Length of an Arc
Function - Notation - and Evaulation
Even/Odd
Union of Sets
21. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Adding/Subtracting Fractions
Function - Notation - and Evaulation
Adding and Subtracting Roots
Intersecting Lines
22. Add the exponents and keep the same base
Determining Absolute Value
Multiplying and Dividing Powers
Direct and Inverse Variation
Multiplying/Dividing Signed Numbers
23. Combine like terms
Adding and Subtraction Polynomials
Function - Notation - and Evaulation
Average Rate
Median and Mode
24. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Circumference of a Circle
Multiplying Fractions
Function - Notation - and Evaulation
Determining Absolute Value
25. The smallest multiple (other than zero) that two or more numbers have in common.
Factor/Multiple
Using Two Points to Find the Slope
Function - Notation - and Evaulation
(Least) Common Multiple
26. Combine equations in such a way that one of the variables cancel out
Characteristics of a Rectangle
Solving a System of Equations
Volume of a Rectangular Solid
Raising Powers to Powers
27. To find the reciprocal of a fraction switch the numerator and the denominator
Multiples of 2 and 4
(Least) Common Multiple
Raising Powers to Powers
Reciprocal
28. 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
Area of a Triangle
Counting the Possibilities
Finding the Distance Between Two Points
Percent Formula
29. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Rate
Number Categories
Characteristics of a Rectangle
Adding/Subtracting Signed Numbers
30. 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
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Mixed Numbers and Improper Fractions
Similar Triangles
31. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Multiplying Monomials
Dividing Fractions
Solving a Proportion
Area of a Circle
32. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Rate
Reciprocal
Using the Average to Find the Sum
33. 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
The 5-12-13 Triangle
Evaluating an Expression
Using Two Points to Find the Slope
Characteristics of a Parallelogram
34. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Dividing Fractions
Factor/Multiple
Volume of a Cylinder
Using Two Points to Find the Slope
35. 2pr
Circumference of a Circle
Even/Odd
Area of a Circle
Average of Evenly Spaced Numbers
36. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Adding and Subtracting Roots
Prime Factorization
Function - Notation - and Evaulation
Area of a Triangle
37. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Rate
Adding/Subtracting Fractions
Tangency
Multiplying Fractions
38. 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
Percent Formula
Even/Odd
Factor/Multiple
Solving an Inequality
39. 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
Adding/Subtracting Signed Numbers
Using Two Points to Find the Slope
Comparing Fractions
Percent Increase and Decrease
40. Volume of a Cylinder = pr^2h
Area of a Sector
Pythagorean Theorem
Remainders
Volume of a Cylinder
41. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Tangency
Volume of a Rectangular Solid
Similar Triangles
42. 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
Intersection of sets
Adding/Subtracting Signed Numbers
Reciprocal
Finding the Original Whole
43. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Rate
Solving a Proportion
Adding and Subtracting monomials
Median and Mode
44. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Formula -
Finding the Missing Number
Relative Primes
Average Rate
45. 1. Re-express them with common denominators 2. Convert them to decimals
Average Formula -
Solving a System of Equations
Comparing Fractions
Exponential Growth
46. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Counting the Possibilities
Counting Consecutive Integers
Using an Equation to Find the Slope
Characteristics of a Rectangle
47. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Comparing Fractions
Evaluating an Expression
Factor/Multiple
Finding the midpoint
48. 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
Comparing Fractions
Using an Equation to Find the Slope
Using an Equation to Find an Intercept
Finding the Distance Between Two Points
49. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Dividing Fractions
Multiples of 3 and 9
Percent Increase and Decrease
50. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Factor/Multiple
Finding the Missing Number
Union of Sets
Intersection of sets