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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. 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
Raising Powers to Powers
Interior and Exterior Angles of a Triangle
Adding and Subtraction Polynomials
Reciprocal
2. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Multiplying Fractions
Dividing Fractions
Mixed Numbers and Improper Fractions
3. A square is a rectangle with four equal sides; Area of Square = side*side
Solving a Proportion
Characteristics of a Square
Remainders
Solving an Inequality
4. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of
Area of a Triangle
Exponential Growth
Intersecting Lines
Length of an Arc
5. To multiply fractions - multiply the numerators and multiply the denominators
Rate
Simplifying Square Roots
Area of a Sector
Multiplying Fractions
6. Domain: all possible values of x for a function range: all possible outputs of a function
Dividing Fractions
Domain and Range of a Function
Identifying the Parts and the Whole
Multiplying Monomials
7. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Pythagorean Theorem
Median and Mode
Reducing Fractions
Multiplying Monomials
8. 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
Interior Angles of a Polygon
Pythagorean Theorem
Mixed Numbers and Improper Fractions
9. (average of the x coordinates - average of the y coordinates)
Adding and Subtraction Polynomials
Finding the midpoint
Interior and Exterior Angles of a Triangle
Solving an Inequality
10. 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
Multiples of 2 and 4
Solving a System of Equations
Function - Notation - and Evaulation
Raising Powers to Powers
11. 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.
Solving an Inequality
Number Categories
Probability
Finding the midpoint
12. 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
Interior Angles of a Polygon
Negative Exponent and Rational Exponent
Adding/Subtracting Signed Numbers
Solving an Inequality
13. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Median and Mode
Finding the midpoint
Characteristics of a Rectangle
Greatest Common Factor
14. 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
Multiplying and Dividing Powers
Repeating Decimal
Multiplying/Dividing Signed Numbers
Using Two Points to Find the Slope
15. Volume of a Cylinder = pr^2h
Percent Increase and Decrease
Adding/Subtracting Fractions
Adding and Subtracting Roots
Volume of a Cylinder
16. Change in y/ change in x rise/run
Using Two Points to Find the Slope
Using an Equation to Find the Slope
Average Rate
Multiplying Fractions
17. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Factor/Multiple
Surface Area of a Rectangular Solid
Solving a System of Equations
Area of a Triangle
18. Combine equations in such a way that one of the variables cancel out
Adding and Subtracting Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a System of Equations
Parallel Lines and Transversals
19. 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
Length of an Arc
Volume of a Rectangular Solid
Negative Exponent and Rational Exponent
20. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Remainders
Counting the Possibilities
Evaluating an Expression
Even/Odd
21. 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
Adding/Subtracting Fractions
Counting the Possibilities
Volume of a Rectangular Solid
Setting up a Ratio
22. 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
Volume of a Rectangular Solid
Domain and Range of a Function
Using Two Points to Find the Slope
Identifying the Parts and the Whole
23. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Average of Evenly Spaced Numbers
PEMDAS
Multiples of 2 and 4
Adding and Subtracting monomials
24. 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
Adding/Subtracting Fractions
Direct and Inverse Variation
Area of a Triangle
Characteristics of a Rectangle
25. you can add/subtract when the part under the radical is the same
Adding and Subtracting Roots
Counting the Possibilities
Triangle Inequality Theorem
Adding and Subtraction Polynomials
26. Add the exponents and keep the same base
The 5-12-13 Triangle
Multiplying and Dividing Powers
Finding the midpoint
Function - Notation - and Evaulation
27. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Intersecting Lines
Area of a Circle
Average of Evenly Spaced Numbers
Repeating Decimal
28. Factor out the perfect squares
Simplifying Square Roots
Counting the Possibilities
Volume of a Cylinder
The 3-4-5 Triangle
29. To find the reciprocal of a fraction switch the numerator and the denominator
Using Two Points to Find the Slope
Domain and Range of a Function
Reciprocal
Characteristics of a Parallelogram
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
Multiplying Monomials
Direct and Inverse Variation
Average Rate
Mixed Numbers and Improper Fractions
31. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Identifying the Parts and the Whole
Characteristics of a Square
Multiples of 3 and 9
32. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Intersecting Lines
Average Formula -
Comparing Fractions
Adding and Subtracting Roots
33. 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
Parallel Lines and Transversals
Rate
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
34. pr^2
Negative Exponent and Rational Exponent
Isosceles and Equilateral triangles
Area of a Circle
The 3-4-5 Triangle
35. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying and Dividing Powers
Counting Consecutive Integers
Finding the Distance Between Two Points
Negative Exponent and Rational Exponent
36. The largest factor that two or more numbers have in common.
Solving a System of Equations
The 3-4-5 Triangle
Greatest Common Factor
Adding/Subtracting Fractions
37. 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
Characteristics of a Parallelogram
Using the Average to Find the Sum
Adding and Subtracting Roots
38. 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
Using an Equation to Find an Intercept
Evaluating an Expression
Adding and Subtracting monomials
Average of Evenly Spaced Numbers
39. 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
Isosceles and Equilateral triangles
Prime Factorization
Part-to-Part Ratios and Part-to-Whole Ratios
Adding/Subtracting Signed Numbers
40. Surface Area = 2lw + 2wh + 2lh
Finding the Original Whole
Characteristics of a Square
Surface Area of a Rectangular Solid
Direct and Inverse Variation
41. 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
Volume of a Cylinder
Similar Triangles
Repeating Decimal
42. The whole # left over after division
Counting Consecutive Integers
Remainders
Adding and Subtracting monomials
Interior and Exterior Angles of a Triangle
43. 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
Pythagorean Theorem
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Identifying the Parts and the Whole
44. 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
Solving a System of Equations
Percent Formula
Average Formula -
45. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Finding the Distance Between Two Points
Multiplying and Dividing Roots
Intersection of sets
Counting the Possibilities
46. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Multiplying and Dividing Roots
Finding the midpoint
Tangency
Multiplying/Dividing Signed Numbers
47. Sum=(Average) x (Number of Terms)
Negative Exponent and Rational Exponent
Union of Sets
Average Formula -
Using the Average to Find the Sum
48. 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
Rate
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
Area of a Sector
49. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Domain and Range of a Function
Reciprocal
Setting up a Ratio
Exponential Growth
50. 2pr
Circumference of a Circle
Multiplying and Dividing Roots
Function - Notation - and Evaulation
Reciprocal