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Test your basic knowledge |
SAT Math: Concepts And Tricks
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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. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Evaluating an Expression
Prime Factorization
Using an Equation to Find the Slope
Counting Consecutive Integers
2. pr^2
Surface Area of a Rectangular Solid
Characteristics of a Parallelogram
Remainders
Area of a Circle
3. 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
Solving a Proportion
Even/Odd
Area of a Circle
Setting up a Ratio
4. 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
Identifying the Parts and the Whole
Characteristics of a Rectangle
Characteristics of a Square
Percent Increase and Decrease
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
Average Rate
Solving an Inequality
Rate
Using an Equation to Find an Intercept
6. 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
Characteristics of a Parallelogram
Triangle Inequality Theorem
Even/Odd
Finding the Distance Between Two Points
7. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Relative Primes
Circumference of a Circle
Average Rate
Using an Equation to Find an Intercept
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
Even/Odd
Function - Notation - and Evaulation
Characteristics of a Rectangle
Setting up a Ratio
9. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Multiplying and Dividing Powers
Intersection of sets
Solving an Inequality
Identifying the Parts and the Whole
10. 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
Dividing Fractions
Multiplying/Dividing Signed Numbers
(Least) Common Multiple
Number Categories
11. The largest factor that two or more numbers have in common.
Raising Powers to Powers
Volume of a Cylinder
Average Formula -
Greatest Common Factor
12. 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
Finding the Distance Between Two Points
Mixed Numbers and Improper Fractions
Greatest Common Factor
Using an Equation to Find an Intercept
13. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Multiplying/Dividing Signed Numbers
Dividing Fractions
Intersecting Lines
Negative Exponent and Rational Exponent
14. The smallest multiple (other than zero) that two or more numbers have in common.
Union of Sets
(Least) Common Multiple
Function - Notation - and Evaulation
Surface Area of a Rectangular Solid
15. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Dividing Fractions
Using an Equation to Find the Slope
The 5-12-13 Triangle
Factor/Multiple
16. (average of the x coordinates - average of the y coordinates)
Remainders
Adding/Subtracting Signed Numbers
Using an Equation to Find an Intercept
Finding the midpoint
17. 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
Prime Factorization
Direct and Inverse Variation
Number Categories
Characteristics of a Parallelogram
18. 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
Solving an Inequality
Union of Sets
The 3-4-5 Triangle
Percent Formula
19. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Adding and Subtraction Polynomials
Average of Evenly Spaced Numbers
Reciprocal
Average Formula -
20. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Even/Odd
Parallel Lines and Transversals
Finding the Missing Number
Finding the midpoint
21. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Interior and Exterior Angles of a Triangle
Reducing Fractions
Percent Increase and Decrease
Multiplying and Dividing Roots
22. 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
Function - Notation - and Evaulation
Repeating Decimal
Identifying the Parts and the Whole
Raising Powers to Powers
23. Part = Percent x Whole
Volume of a Rectangular Solid
Percent Formula
Median and Mode
PEMDAS
24. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Reciprocal
Volume of a Rectangular Solid
Interior Angles of a Polygon
Comparing Fractions
25. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Combined Percent Increase and Decrease
Volume of a Rectangular Solid
Interior Angles of a Polygon
Part-to-Part Ratios and Part-to-Whole Ratios
26. 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
Identifying the Parts and the Whole
Finding the Original Whole
Triangle Inequality Theorem
Adding/Subtracting Signed Numbers
27. 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
Average of Evenly Spaced Numbers
Percent Formula
Interior Angles of a Polygon
Negative Exponent and Rational Exponent
28. 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
Evaluating an Expression
Median and Mode
The 5-12-13 Triangle
Greatest Common Factor
29. A square is a rectangle with four equal sides; Area of Square = side*side
Using Two Points to Find the Slope
Area of a Circle
Characteristics of a Square
Multiplying Fractions
30. 2pr
Number Categories
Circumference of a Circle
Tangency
The 5-12-13 Triangle
31. To divide fractions - invert the second one and multiply
Probability
Using an Equation to Find an Intercept
Dividing Fractions
Finding the Original Whole
32. To find the reciprocal of a fraction switch the numerator and the denominator
Percent Increase and Decrease
Rate
Reciprocal
Multiplying and Dividing Roots
33. 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.
Finding the Missing Number
Solving a System of Equations
Percent Increase and Decrease
Number Categories
34. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Tangency
Setting up a Ratio
Solving an Inequality
Factor/Multiple
35. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Rate
Interior Angles of a Polygon
Raising Powers to Powers
36. 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
Multiplying and Dividing Powers
Using Two Points to Find the Slope
Prime Factorization
Adding/Subtracting Signed Numbers
37. 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
Rate
Factor/Multiple
Length of an Arc
Pythagorean Theorem
38. The whole # left over after division
Mixed Numbers and Improper Fractions
Average of Evenly Spaced Numbers
Remainders
Using Two Points to Find the Slope
39. 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
Evaluating an Expression
Interior and Exterior Angles of a Triangle
Relative Primes
Area of a Triangle
40. 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
Solving an Inequality
Comparing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
41. Change in y/ change in x rise/run
Factor/Multiple
Rate
Using Two Points to Find the Slope
PEMDAS
42. Factor out the perfect squares
Average of Evenly Spaced Numbers
Simplifying Square Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Sector
43. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Counting the Possibilities
Multiples of 2 and 4
Adding and Subtracting Roots
Solving a Quadratic Equation
44. 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
Using the Average to Find the Sum
Using an Equation to Find the Slope
Interior and Exterior Angles of a Triangle
Multiples of 3 and 9
45. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Raising Powers to Powers
Parallel Lines and Transversals
Finding the Missing Number
Adding/Subtracting Fractions
46. Probability= Favorable Outcomes/Total Possible Outcomes
Adding/Subtracting Fractions
Exponential Growth
Remainders
Probability
47. Volume of a Cylinder = pr^2h
Counting Consecutive Integers
Volume of a Cylinder
Multiplying and Dividing Powers
Reciprocal
48. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Reducing Fractions
Finding the Original Whole
Multiplying Monomials
Factor/Multiple
49. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Even/Odd
Finding the Missing Number
Multiplying Monomials
Median and Mode
50. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Volume of a Cylinder
Remainders
Multiples of 2 and 4