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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. Factor out the perfect squares
The 3-4-5 Triangle
Tangency
Multiples of 2 and 4
Simplifying Square Roots
2. (average of the x coordinates - average of the y coordinates)
Finding the midpoint
Solving a Quadratic Equation
Average of Evenly Spaced Numbers
Multiplying/Dividing Signed Numbers
3. 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
Using Two Points to Find the Slope
Combined Percent Increase and Decrease
Characteristics of a Rectangle
Characteristics of a Square
4. Probability= Favorable Outcomes/Total Possible Outcomes
The 5-12-13 Triangle
Probability
Counting the Possibilities
Counting Consecutive Integers
5. Sum=(Average) x (Number of Terms)
Using the Average to Find the Sum
Identifying the Parts and the Whole
Surface Area of a Rectangular Solid
Using Two Points to Find the Slope
6. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Tangency
Solving a Quadratic Equation
Reducing Fractions
Counting the Possibilities
7. Multiply the exponents
Multiplying/Dividing Signed Numbers
Intersecting Lines
Area of a Triangle
Raising Powers to Powers
8. 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
Reciprocal
Interior Angles of a Polygon
9. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Multiples of 3 and 9
Solving a Quadratic Equation
Using an Equation to Find the Slope
Finding the Original Whole
10. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Number Categories
Using the Average to Find the Sum
Using an Equation to Find the Slope
Multiplying and Dividing Powers
11. 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
Number Categories
Triangle Inequality Theorem
Circumference of a Circle
12. 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
Union of Sets
Function - Notation - and Evaulation
Counting Consecutive Integers
Multiplying/Dividing Signed Numbers
13. 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
Adding and Subtracting monomials
Circumference of a Circle
PEMDAS
14. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Intersection of sets
Function - Notation - and Evaulation
Determining Absolute Value
Negative Exponent and Rational Exponent
15. pr^2
Mixed Numbers and Improper Fractions
Number Categories
Area of a Circle
Finding the midpoint
16. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
The 5-12-13 Triangle
Domain and Range of a Function
Rate
Average Rate
17. Combine like terms
Relative Primes
Adding and Subtraction Polynomials
Evaluating an Expression
Prime Factorization
18. 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
Intersecting Lines
Area of a Triangle
Tangency
19. 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
Solving a Quadratic Equation
Finding the midpoint
Raising Powers to Powers
The 5-12-13 Triangle
20. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Counting Consecutive Integers
Tangency
Area of a Circle
Adding/Subtracting Fractions
21. 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
Average Formula -
Characteristics of a Square
Setting up a Ratio
Isosceles and Equilateral triangles
22. 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
Finding the Original Whole
Greatest Common Factor
Using Two Points to Find the Slope
Rate
23. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Function - Notation - and Evaulation
Average of Evenly Spaced Numbers
Intersecting Lines
Characteristics of a Rectangle
24. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Counting Consecutive Integers
Similar Triangles
Multiples of 2 and 4
Number Categories
25. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Multiplying/Dividing Signed Numbers
Prime Factorization
Counting Consecutive Integers
Finding the Distance Between Two Points
26. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Circumference of a Circle
Reciprocal
Function - Notation - and Evaulation
27. To multiply fractions - multiply the numerators and multiply the denominators
Using an Equation to Find an Intercept
Parallel Lines and Transversals
Multiplying Fractions
Isosceles and Equilateral triangles
28. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Interior Angles of a Polygon
Greatest Common Factor
Prime Factorization
Determining Absolute Value
29. Part = Percent x Whole
Finding the Missing Number
Rate
Multiples of 2 and 4
Percent Formula
30. To solve a proportion - cross multiply
Circumference of a Circle
Rate
Solving a Proportion
Area of a Triangle
31. Domain: all possible values of x for a function range: all possible outputs of a function
Multiplying and Dividing Powers
Prime Factorization
Domain and Range of a Function
Determining Absolute Value
32. 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
Negative Exponent and Rational Exponent
Triangle Inequality Theorem
PEMDAS
33. 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
Probability
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Evaluating an Expression
34. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Dividing Fractions
Average Formula -
Multiplying Monomials
Setting up a Ratio
35. To find the reciprocal of a fraction switch the numerator and the denominator
Negative Exponent and Rational Exponent
Reciprocal
Using an Equation to Find the Slope
Direct and Inverse Variation
36. Change in y/ change in x rise/run
Remainders
Characteristics of a Square
Raising Powers to Powers
Using Two Points to Find the Slope
37. A square is a rectangle with four equal sides; Area of Square = side*side
Average of Evenly Spaced Numbers
Characteristics of a Square
Using Two Points to Find the Slope
Negative Exponent and Rational Exponent
38. 1. Re-express them with common denominators 2. Convert them to decimals
Multiplying Monomials
Solving a Quadratic Equation
Comparing Fractions
Area of a Triangle
39. 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
Adding/Subtracting Fractions
Identifying the Parts and the Whole
Volume of a Rectangular Solid
Evaluating an Expression
40. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Finding the Missing Number
Intersection of sets
Domain and Range of a Function
The 3-4-5 Triangle
41. 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
Finding the midpoint
Direct and Inverse Variation
Average of Evenly Spaced Numbers
42. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Prime Factorization
Interior Angles of a Polygon
Combined Percent Increase and Decrease
Evaluating an Expression
43. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Multiples of 2 and 4
Finding the Original Whole
Multiplying Fractions
Characteristics of a Rectangle
44. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Tangency
Finding the Missing Number
Domain and Range of a Function
Intersection of sets
45. The largest factor that two or more numbers have in common.
Adding and Subtracting Roots
Volume of a Rectangular Solid
Greatest Common Factor
Solving a Proportion
46. 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
Multiples of 2 and 4
Relative Primes
Determining Absolute Value
Finding the Distance Between Two Points
47. 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
Multiplying/Dividing Signed Numbers
Area of a Circle
Combined Percent Increase and Decrease
48. Combine equations in such a way that one of the variables cancel out
Multiplying Fractions
Finding the Original Whole
Adding and Subtraction Polynomials
Solving a System of Equations
49. 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
Solving an Inequality
Triangle Inequality Theorem
Intersection of sets
Exponential Growth
50. 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
Determining Absolute Value
The 3-4-5 Triangle
Area of a Triangle
Similar Triangles