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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 find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Prime Factorization
Area of a Circle
Rate
Using the Average to Find the Sum
2. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Setting up a Ratio
Solving a Quadratic Equation
Surface Area of a Rectangular Solid
Part-to-Part Ratios and Part-to-Whole Ratios
3. The smallest multiple (other than zero) that two or more numbers have in common.
Solving a System of Equations
(Least) Common Multiple
Comparing Fractions
Probability
4. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Even/Odd
Tangency
Length of an Arc
Volume of a Cylinder
5. To solve a proportion - cross multiply
Solving a Proportion
Reciprocal
Average Formula -
Union of Sets
6. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Average of Evenly Spaced Numbers
Determining Absolute Value
Even/Odd
Using an Equation to Find the Slope
7. 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
Characteristics of a Square
Counting the Possibilities
Adding and Subtraction Polynomials
8. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Multiplying Fractions
Characteristics of a Rectangle
Area of a Sector
Factor/Multiple
9. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Using an Equation to Find the Slope
Using Two Points to Find the Slope
Parallel Lines and Transversals
Multiplying/Dividing Signed Numbers
10. 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
Multiplying and Dividing Roots
Finding the midpoint
Multiples of 2 and 4
Percent Increase and Decrease
11. For all right triangles: a^2+b^2=c^2
Adding/Subtracting Signed Numbers
Pythagorean Theorem
Mixed Numbers and Improper Fractions
Determining Absolute Value
12. To divide fractions - invert the second one and multiply
Dividing Fractions
Function - Notation - and Evaulation
Greatest Common Factor
Similar Triangles
13. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Parallel Lines and Transversals
Factor/Multiple
Multiplying and Dividing Roots
Pythagorean Theorem
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Repeating Decimal
Isosceles and Equilateral triangles
Exponential Growth
Adding/Subtracting Fractions
15. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Area of a Sector
Comparing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Adding and Subtracting monomials
16. pr^2
Area of a Circle
Solving a System of Equations
Solving an Inequality
Domain and Range of a Function
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Direct and Inverse Variation
Determining Absolute Value
Domain and Range of a Function
Combined Percent Increase and Decrease
18. Surface Area = 2lw + 2wh + 2lh
Probability
Finding the midpoint
Isosceles and Equilateral triangles
Surface Area of a Rectangular Solid
19. Combine like terms
Interior Angles of a Polygon
Mixed Numbers and Improper Fractions
Finding the Original Whole
Adding and Subtraction Polynomials
20. 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
Setting up a Ratio
Multiplying and Dividing Powers
Identifying the Parts and the Whole
21. 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
Multiplying and Dividing Roots
Multiplying/Dividing Signed Numbers
Using an Equation to Find an Intercept
Average Rate
22. 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
Factor/Multiple
Intersecting Lines
Counting the Possibilities
23. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Solving a Proportion
Finding the Original Whole
Finding the Distance Between Two Points
Area of a Circle
24. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Identifying the Parts and the Whole
Intersection of sets
Domain and Range of a Function
Part-to-Part Ratios and Part-to-Whole Ratios
25. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12
The 5-12-13 Triangle
Reciprocal
Interior Angles of a Polygon
Finding the Missing Number
26. 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
The 5-12-13 Triangle
Isosceles and Equilateral triangles
Volume of a Cylinder
Area of a Triangle
27. Add the exponents and keep the same base
Multiplying and Dividing Powers
Multiples of 3 and 9
Simplifying Square Roots
Volume of a Cylinder
28. (average of the x coordinates - average of the y coordinates)
Volume of a Rectangular Solid
Finding the midpoint
Adding/Subtracting Signed Numbers
Using an Equation to Find the Slope
29. 1. Re-express them with common denominators 2. Convert them to decimals
Combined Percent Increase and Decrease
Using the Average to Find the Sum
Comparing Fractions
Using Two Points to Find the Slope
30. Part = Percent x Whole
Solving a Quadratic Equation
Percent Formula
Setting up a Ratio
PEMDAS
31. Multiply the exponents
The 3-4-5 Triangle
Similar Triangles
Using an Equation to Find the Slope
Raising Powers to Powers
32. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Comparing Fractions
Combined Percent Increase and Decrease
Average of Evenly Spaced Numbers
33. A square is a rectangle with four equal sides; Area of Square = side*side
Average Rate
Circumference of a Circle
Characteristics of a Square
Volume of a Cylinder
34. To multiply fractions - multiply the numerators and multiply the denominators
Using Two Points to Find the Slope
Solving a Quadratic Equation
Multiplying Fractions
Characteristics of a Rectangle
35. 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
Factor/Multiple
Reducing Fractions
Adding and Subtracting monomials
Interior and Exterior Angles of a Triangle
36. 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
Exponential Growth
Using an Equation to Find an Intercept
Direct and Inverse Variation
Volume of a Rectangular Solid
37. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Adding and Subtraction Polynomials
Adding/Subtracting Signed Numbers
Simplifying Square Roots
Interior Angles of a Polygon
38. 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)
Adding and Subtracting Roots
Length of an Arc
Multiples of 2 and 4
Average Formula -
39. The largest factor that two or more numbers have in common.
Multiplying and Dividing Roots
Remainders
Solving a Quadratic Equation
Greatest Common Factor
40. 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
Exponential Growth
(Least) Common Multiple
Volume of a Rectangular Solid
Multiples of 2 and 4
41. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Area of a Triangle
Area of a Circle
Counting Consecutive Integers
Similar Triangles
42. Subtract the smallest from the largest and add 1
Counting Consecutive Integers
Percent Formula
Average Formula -
Intersecting Lines
43. 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
Greatest Common Factor
Multiplying/Dividing Signed Numbers
Solving an Inequality
Percent Formula
44. 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
Probability
Triangle Inequality Theorem
Dividing Fractions
Combined Percent Increase and Decrease
45. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Using Two Points to Find the Slope
Multiplying Monomials
Tangency
Percent Increase and Decrease
46. 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
Interior and Exterior Angles of a Triangle
Median and Mode
Characteristics of a Square
47. 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
Finding the Original Whole
Combined Percent Increase and Decrease
Adding/Subtracting Signed Numbers
Counting the Possibilities
48. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Counting Consecutive Integers
Surface Area of a Rectangular Solid
Multiples of 3 and 9
Area of a Circle
49. you can add/subtract when the part under the radical is the same
Tangency
Adding and Subtracting Roots
(Least) Common Multiple
Direct and Inverse Variation
50. 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
Combined Percent Increase and Decrease
Intersecting Lines
Reciprocal
Rate