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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. Combine like terms
Using an Equation to Find an Intercept
Characteristics of a Parallelogram
Adding and Subtraction Polynomials
Multiplying Monomials
2. Change in y/ change in x rise/run
Multiplying Monomials
Using Two Points to Find the Slope
Percent Increase and Decrease
Parallel Lines and Transversals
3. Sum=(Average) x (Number of Terms)
Percent Increase and Decrease
Using the Average to Find the Sum
Area of a Circle
Multiplying Fractions
4. 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
Domain and Range of a Function
Counting the Possibilities
Finding the Missing Number
5. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Greatest Common Factor
Relative Primes
Union of Sets
Evaluating an Expression
6. 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
Number Categories
Finding the Missing Number
Median and Mode
The 5-12-13 Triangle
7. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Reciprocal
Adding and Subtracting monomials
The 3-4-5 Triangle
Intersecting Lines
8. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Number Categories
Counting the Possibilities
Similar Triangles
Adding and Subtraction Polynomials
9. To solve a proportion - cross multiply
Mixed Numbers and Improper Fractions
Finding the Distance Between Two Points
Percent Increase and Decrease
Solving a Proportion
10. 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
Average Formula -
Interior and Exterior Angles of a Triangle
Solving a System of Equations
Multiplying Monomials
11. (average of the x coordinates - average of the y coordinates)
Determining Absolute Value
PEMDAS
Finding the midpoint
Relative Primes
12. To multiply fractions - multiply the numerators and multiply the denominators
Volume of a Rectangular Solid
Domain and Range of a Function
Multiplying Monomials
Multiplying Fractions
13. 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
Tangency
Area of a Triangle
Factor/Multiple
Simplifying Square Roots
14. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Volume of a Rectangular Solid
Setting up a Ratio
Multiples of 2 and 4
15. 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.
Mixed Numbers and Improper Fractions
Number Categories
Multiplying Monomials
Identifying the Parts and the Whole
16. 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
Negative Exponent and Rational Exponent
Mixed Numbers and Improper Fractions
Surface Area of a Rectangular Solid
Finding the midpoint
17. 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
Isosceles and Equilateral triangles
Rate
Union of Sets
Using the Average to Find the Sum
18. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Finding the Original Whole
Simplifying Square Roots
Greatest Common Factor
Adding and Subtracting monomials
19. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Tangency
Prime Factorization
Isosceles and Equilateral triangles
Volume of a Rectangular Solid
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
Median and Mode
Area of a Triangle
Function - Notation - and Evaulation
Similar Triangles
21. 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
Using an Equation to Find an Intercept
Identifying the Parts and the Whole
Raising Powers to Powers
Simplifying Square Roots
22. 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
Dividing Fractions
Repeating Decimal
Adding and Subtracting Roots
23. 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
Greatest Common Factor
Surface Area of a Rectangular Solid
Repeating Decimal
Multiplying Fractions
24. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Solving a Quadratic Equation
Multiplying Fractions
Factor/Multiple
Evaluating an Expression
25. pr^2
Interior Angles of a Polygon
Area of a Triangle
Area of a Circle
Probability
26. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Area of a Sector
Triangle Inequality Theorem
Using the Average to Find the Sum
Multiplying Monomials
27. 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)
Length of an Arc
Area of a Sector
Probability
Simplifying Square Roots
28. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Determining Absolute Value
Using the Average to Find the Sum
Characteristics of a Square
Repeating Decimal
29. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Adding and Subtracting monomials
Adding/Subtracting Signed Numbers
Union of Sets
Reciprocal
30. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Probability
Direct and Inverse Variation
Finding the Distance Between Two Points
Adding/Subtracting Fractions
31. Combine equations in such a way that one of the variables cancel out
Solving a System of Equations
Multiplying Fractions
Remainders
Triangle Inequality Theorem
32. The whole # left over after division
Volume of a Cylinder
Number Categories
Remainders
Intersecting Lines
33. For all right triangles: a^2+b^2=c^2
Solving an Inequality
PEMDAS
Pythagorean Theorem
Adding and Subtracting Roots
34. The largest factor that two or more numbers have in common.
Greatest Common Factor
Relative Primes
Mixed Numbers and Improper Fractions
Finding the Distance Between Two Points
35. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Solving a System of Equations
Setting up a Ratio
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Circle
36. 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
Intersection of sets
Identifying the Parts and the Whole
The 3-4-5 Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
37. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Isosceles and Equilateral triangles
Parallel Lines and Transversals
Determining Absolute Value
Intersection of sets
38. 2pr
Intersection of sets
Finding the Original Whole
Circumference of a Circle
Identifying the Parts and the Whole
39. To find the reciprocal of a fraction switch the numerator and the denominator
The 3-4-5 Triangle
Reciprocal
The 5-12-13 Triangle
(Least) Common Multiple
40. 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
Similar Triangles
Finding the Original Whole
Volume of a Rectangular Solid
41. 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
Simplifying Square Roots
Surface Area of a Rectangular Solid
Multiples of 3 and 9
42. Domain: all possible values of x for a function range: all possible outputs of a function
Similar Triangles
Using an Equation to Find an Intercept
Domain and Range of a Function
Characteristics of a Rectangle
43. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Number Categories
Surface Area of a Rectangular Solid
Solving a System of Equations
44. Part = Percent x Whole
Percent Formula
Tangency
Exponential Growth
Comparing Fractions
45. To divide fractions - invert the second one and multiply
Dividing Fractions
The 5-12-13 Triangle
Adding and Subtraction Polynomials
Prime Factorization
46. 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
Setting up a Ratio
Combined Percent Increase and Decrease
Determining Absolute Value
Remainders
47. 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
Intersecting Lines
Multiplying/Dividing Signed Numbers
Characteristics of a Square
Triangle Inequality Theorem
48. Surface Area = 2lw + 2wh + 2lh
Combined Percent Increase and Decrease
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
Surface Area of a Rectangular Solid
49. 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)
(Least) Common Multiple
Area of a Sector
Multiplying/Dividing Signed Numbers
Counting Consecutive Integers
50. 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
Solving a Proportion
Adding/Subtracting Signed Numbers
Solving an Inequality
Average of Evenly Spaced Numbers