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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. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Rate
Multiplying Fractions
Determining Absolute Value
Adding/Subtracting Fractions
2. Add the exponents and keep the same base
Solving a Quadratic Equation
Part-to-Part Ratios and Part-to-Whole Ratios
Multiples of 2 and 4
Multiplying and Dividing Powers
3. Multiply the exponents
Surface Area of a Rectangular Solid
Raising Powers to Powers
Reducing Fractions
Median and Mode
4. Factor out the perfect squares
Adding and Subtraction Polynomials
Simplifying Square Roots
Isosceles and Equilateral triangles
Multiplying Monomials
5. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Solving a System of Equations
Area of a Triangle
Using the Average to Find the Sum
Reducing Fractions
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
Percent Formula
Circumference of a Circle
Parallel Lines and Transversals
Characteristics of a Parallelogram
7. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Dividing Fractions
Adding and Subtracting Roots
Adding/Subtracting Fractions
8. 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
Solving an Inequality
Area of a Triangle
Identifying the Parts and the Whole
Average of Evenly Spaced Numbers
9. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Exponential Growth
Prime Factorization
Multiplying and Dividing Roots
Surface Area of a Rectangular Solid
10. 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
Evaluating an Expression
Using an Equation to Find an Intercept
Finding the Original Whole
Counting the Possibilities
11. 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
Greatest Common Factor
Remainders
Prime Factorization
Isosceles and Equilateral triangles
12. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Volume of a Rectangular Solid
Using an Equation to Find the Slope
Adding and Subtracting monomials
The 3-4-5 Triangle
13. you can add/subtract when the part under the radical is the same
Adding and Subtraction Polynomials
Remainders
Adding and Subtracting Roots
Factor/Multiple
14. Combine like terms
Adding and Subtraction Polynomials
Area of a Sector
Prime Factorization
Combined Percent Increase and Decrease
15. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Probability
Intersecting Lines
Simplifying Square Roots
Mixed Numbers and Improper Fractions
16. The largest factor that two or more numbers have in common.
Repeating Decimal
Greatest Common Factor
Adding and Subtracting Roots
Adding/Subtracting Signed Numbers
17. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiplying/Dividing Signed Numbers
Reciprocal
Multiples of 3 and 9
Parallel Lines and Transversals
18. 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
Rate
Average Rate
Direct and Inverse Variation
Surface Area of a Rectangular Solid
19. pr^2
Solving an Inequality
Area of a Circle
Exponential Growth
Domain and Range of a Function
20. 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
Reducing Fractions
Adding/Subtracting Signed Numbers
The 5-12-13 Triangle
Tangency
21. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
(Least) Common Multiple
PEMDAS
Identifying the Parts and the Whole
Average Rate
22. To find the reciprocal of a fraction switch the numerator and the denominator
Percent Increase and Decrease
Reciprocal
Multiplying and Dividing Roots
Multiples of 3 and 9
23. Subtract the smallest from the largest and add 1
Multiplying/Dividing Signed Numbers
Counting Consecutive Integers
Surface Area of a Rectangular Solid
Triangle Inequality Theorem
24. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Exponential Growth
Number Categories
Median and Mode
Multiples of 3 and 9
25. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Adding and Subtracting Roots
Intersecting Lines
Comparing Fractions
Setting up a Ratio
26. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Adding and Subtracting Roots
Tangency
Union of Sets
Multiples of 2 and 4
27. 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
Characteristics of a Square
Tangency
Using the Average to Find the Sum
28. 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
Dividing Fractions
Repeating Decimal
Function - Notation - and Evaulation
Remainders
29. 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
Triangle Inequality Theorem
Solving a Proportion
Area of a Triangle
30. 2pr
Repeating Decimal
Domain and Range of a Function
Circumference of a Circle
Characteristics of a Square
31. 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
Finding the Distance Between Two Points
Parallel Lines and Transversals
Rate
32. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Intersection of sets
Counting Consecutive Integers
Multiplying and Dividing Roots
Triangle Inequality Theorem
33. Combine equations in such a way that one of the variables cancel out
Multiples of 3 and 9
Solving a System of Equations
Characteristics of a Square
Direct and Inverse Variation
34. 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
Reducing Fractions
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Evaluating an Expression
35. Part = Percent x Whole
Remainders
Percent Formula
The 3-4-5 Triangle
Length of an Arc
36. Surface Area = 2lw + 2wh + 2lh
Direct and Inverse Variation
Surface Area of a Rectangular Solid
Finding the Original Whole
Using Two Points to Find the Slope
37. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Circle
Finding the Distance Between Two Points
Multiplying Monomials
38. 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.
Intersection of sets
Characteristics of a Parallelogram
Adding and Subtracting Roots
Number Categories
39. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Average Formula -
Adding and Subtracting monomials
Volume of a Cylinder
Counting Consecutive Integers
40. 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
Counting the Possibilities
Tangency
Simplifying Square Roots
41. 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
Relative Primes
Combined Percent Increase and Decrease
Adding and Subtraction Polynomials
Counting Consecutive Integers
42. A square is a rectangle with four equal sides; Area of Square = side*side
Setting up a Ratio
Interior Angles of a Polygon
Using an Equation to Find an Intercept
Characteristics of a Square
43. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Average of Evenly Spaced Numbers
Combined Percent Increase and Decrease
Reciprocal
Multiplying Monomials
44. 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
Mixed Numbers and Improper Fractions
Dividing Fractions
Volume of a Cylinder
Intersecting Lines
45. 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
Adding and Subtracting Roots
Intersection of sets
Solving an Inequality
46. 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)
Area of a Sector
Multiplying and Dividing Roots
Triangle Inequality Theorem
Rate
47. 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
Counting the Possibilities
Circumference of a Circle
Function - Notation - and Evaulation
Domain and Range of a Function
48. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Solving a Proportion
Triangle Inequality Theorem
Multiplying and Dividing Powers
49. For all right triangles: a^2+b^2=c^2
Negative Exponent and Rational Exponent
Solving a Proportion
Relative Primes
Pythagorean Theorem
50. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Simplifying Square Roots
Volume of a Cylinder
Volume of a Rectangular Solid
Multiples of 2 and 4