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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. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Adding/Subtracting Signed Numbers
Raising Powers to Powers
Area of a Circle
Average of Evenly Spaced Numbers
2. 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
Multiplying/Dividing Signed Numbers
Finding the Distance Between Two Points
Characteristics of a Parallelogram
Characteristics of a Rectangle
3. 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)
Intersection of sets
Length of an Arc
Solving a Proportion
Determining Absolute Value
4. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Percent Formula
Solving a Proportion
Using an Equation to Find an Intercept
5. 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
Intersection of sets
Using an Equation to Find the Slope
Solving an Inequality
Characteristics of a Square
6. 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
Multiplying/Dividing Signed Numbers
Prime Factorization
Multiplying Monomials
Determining Absolute Value
7. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Area of a Circle
Characteristics of a Square
Finding the Distance Between Two Points
Multiples of 2 and 4
8. 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
Multiples of 2 and 4
Finding the Missing Number
Adding/Subtracting Signed Numbers
Volume of a Rectangular Solid
9. Multiply the exponents
Finding the Distance Between Two Points
Average Formula -
Isosceles and Equilateral triangles
Raising Powers to Powers
10. Combine like terms
Adding and Subtraction Polynomials
Percent Formula
Finding the Original Whole
Area of a Triangle
11. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Interior and Exterior Angles of a Triangle
Volume of a Rectangular Solid
Intersecting Lines
12. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Triangle
Multiplying Fractions
Finding the Original Whole
13. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Multiples of 3 and 9
Mixed Numbers and Improper Fractions
Function - Notation - and Evaulation
Reducing Fractions
14. 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
(Least) Common Multiple
Characteristics of a Parallelogram
Adding and Subtracting monomials
15. 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
Solving an Inequality
Using Two Points to Find the Slope
Reciprocal
Repeating Decimal
16. 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
Direct and Inverse Variation
Identifying the Parts and the Whole
Number Categories
Average Rate
17. 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
Area of a Circle
Relative Primes
Characteristics of a Parallelogram
Evaluating an Expression
18. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Prime Factorization
Area of a Triangle
Factor/Multiple
Reducing Fractions
19. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Factor/Multiple
PEMDAS
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
20. To solve a proportion - cross multiply
Exponential Growth
Factor/Multiple
Solving a Proportion
Multiplying and Dividing Roots
21. 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
Negative Exponent and Rational Exponent
Determining Absolute Value
Length of an Arc
Finding the Original Whole
22. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Solving a Quadratic Equation
Median and Mode
Using an Equation to Find the Slope
Multiples of 3 and 9
23. For all right triangles: a^2+b^2=c^2
Solving an Inequality
Characteristics of a Square
Reducing Fractions
Pythagorean Theorem
24. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Evaluating an Expression
Setting up a Ratio
Parallel Lines and Transversals
Surface Area of a Rectangular Solid
25. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Characteristics of a Rectangle
Area of a Sector
Circumference of a Circle
Multiples of 3 and 9
26. pr^2
Multiplying/Dividing Signed Numbers
Area of a Circle
Average Formula -
Adding/Subtracting Signed Numbers
27. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Intersecting Lines
Function - Notation - and Evaulation
Multiples of 3 and 9
Counting Consecutive Integers
28. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Adding and Subtracting monomials
Tangency
Adding/Subtracting Fractions
Finding the midpoint
29. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Percent Formula
Finding the Missing Number
Evaluating an Expression
30. Domain: all possible values of x for a function range: all possible outputs of a function
Using an Equation to Find the Slope
Intersection of sets
Domain and Range of a Function
Direct and Inverse Variation
31. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Relative Primes
Similar Triangles
Finding the Distance Between Two Points
Characteristics of a Square
32. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Similar Triangles
Adding/Subtracting Fractions
Median and Mode
Solving an Inequality
33. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Domain and Range of a Function
Parallel Lines and Transversals
Counting Consecutive Integers
Probability
34. A square is a rectangle with four equal sides; Area of Square = side*side
Union of Sets
Characteristics of a Square
Direct and Inverse Variation
Domain and Range of a Function
35. 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.
Even/Odd
Dividing Fractions
Intersection of sets
Number Categories
36. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
The 3-4-5 Triangle
Counting the Possibilities
Finding the Distance Between Two Points
Dividing Fractions
37. The whole # left over after division
Tangency
Remainders
Characteristics of a Rectangle
Similar Triangles
38. 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
Probability
Percent Increase and Decrease
Evaluating an Expression
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
Percent Increase and Decrease
Number Categories
Using an Equation to Find the Slope
Counting Consecutive Integers
40. 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
Finding the Missing Number
Interior and Exterior Angles of a Triangle
Parallel Lines and Transversals
41. To divide fractions - invert the second one and multiply
Dividing Fractions
Interior Angles of a Polygon
Tangency
Adding and Subtracting monomials
42. 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
Adding and Subtracting Roots
Direct and Inverse Variation
Interior and Exterior Angles of a Triangle
Rate
43. 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
Adding/Subtracting Fractions
Raising Powers to Powers
Combined Percent Increase and Decrease
44. To multiply fractions - multiply the numerators and multiply the denominators
Isosceles and Equilateral triangles
Multiplying Fractions
Solving an Inequality
Simplifying Square Roots
45. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Rate
Area of a Triangle
Using an Equation to Find the Slope
Average Rate
46. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Even/Odd
Adding and Subtraction Polynomials
Finding the midpoint
47. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Finding the Original Whole
Using an Equation to Find an Intercept
Even/Odd
48. you can add/subtract when the part under the radical is the same
Probability
Adding and Subtracting Roots
Even/Odd
Using an Equation to Find an Intercept
49. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Parallel Lines and Transversals
Negative Exponent and Rational Exponent
Remainders
50. Factor out the perfect squares
Simplifying Square Roots
Volume of a Cylinder
Characteristics of a Rectangle
Average Rate