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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. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Multiples of 3 and 9
Median and Mode
Surface Area of a Rectangular Solid
Solving a Proportion
2. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Volume of a Rectangular Solid
Circumference of a Circle
Relative Primes
Average of Evenly Spaced Numbers
3. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Comparing Fractions
Average of Evenly Spaced Numbers
Using an Equation to Find an Intercept
4. 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
Multiplying/Dividing Signed Numbers
Mixed Numbers and Improper Fractions
Surface Area of a Rectangular Solid
Relative Primes
5. # 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 an Inequality
Determining Absolute Value
Percent Formula
6. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Using Two Points to Find the Slope
Prime Factorization
Using an Equation to Find the Slope
Relative Primes
7. 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
Direct and Inverse Variation
Similar Triangles
Factor/Multiple
Using an Equation to Find an Intercept
8. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Multiplying/Dividing Signed Numbers
Greatest Common Factor
Intersecting Lines
9. The largest factor that two or more numbers have in common.
Intersection of sets
Greatest Common Factor
Characteristics of a Rectangle
Adding and Subtraction Polynomials
10. Subtract the smallest from the largest and add 1
Finding the Distance Between Two Points
The 5-12-13 Triangle
Length of an Arc
Counting Consecutive Integers
11. 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
Determining Absolute Value
Multiplying and Dividing Powers
Solving an Inequality
12. Factor out the perfect squares
Area of a Circle
Simplifying Square Roots
Multiples of 2 and 4
Prime Factorization
13. 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
Pythagorean Theorem
Adding and Subtraction Polynomials
Exponential Growth
Isosceles and Equilateral triangles
14. 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
Domain and Range of a Function
Area of a Triangle
Direct and Inverse Variation
Adding and Subtracting Roots
15. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS
Adding and Subtraction Polynomials
Simplifying Square Roots
Evaluating an Expression
Interior Angles of a Polygon
16. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Finding the Distance Between Two Points
Average of Evenly Spaced Numbers
Multiplying and Dividing Roots
Comparing Fractions
17. 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
Median and Mode
Part-to-Part Ratios and Part-to-Whole Ratios
Area of a Triangle
18. 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
Average of Evenly Spaced Numbers
The 5-12-13 Triangle
Adding/Subtracting Signed Numbers
Interior Angles of a Polygon
19. Domain: all possible values of x for a function range: all possible outputs of a function
Domain and Range of a Function
Solving a System of Equations
Adding/Subtracting Fractions
Tangency
20. 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
Multiples of 3 and 9
Interior and Exterior Angles of a Triangle
Percent Increase and Decrease
Volume of a Cylinder
21. 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
Finding the Missing Number
Multiplying and Dividing Roots
Combined Percent Increase and Decrease
Intersecting Lines
22. 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
Pythagorean Theorem
Area of a Triangle
Circumference of a Circle
The 5-12-13 Triangle
23. 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
Simplifying Square Roots
Counting the Possibilities
Exponential Growth
Length of an Arc
24. 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
Adding and Subtraction Polynomials
Using an Equation to Find the Slope
Counting the Possibilities
25. pr^2
Multiples of 3 and 9
Reducing Fractions
Area of a Circle
Remainders
26. 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
Part-to-Part Ratios and Part-to-Whole Ratios
Average Rate
Isosceles and Equilateral triangles
27. 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
Average Formula -
Simplifying Square Roots
Part-to-Part Ratios and Part-to-Whole Ratios
Multiplying/Dividing Signed Numbers
28. Change in y/ change in x rise/run
Characteristics of a Rectangle
Area of a Sector
Identifying the Parts and the Whole
Using Two Points to Find the Slope
29. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Parallel Lines and Transversals
Multiplying/Dividing Signed Numbers
Mixed Numbers and Improper Fractions
Multiplying and Dividing Roots
30. To multiply fractions - multiply the numerators and multiply the denominators
Area of a Circle
Multiplying Fractions
Greatest Common Factor
Adding/Subtracting Signed Numbers
31. 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
Using Two Points to Find the Slope
Greatest Common Factor
Factor/Multiple
The 5-12-13 Triangle
32. 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
Solving an Inequality
Median and Mode
Function - Notation - and Evaulation
The 3-4-5 Triangle
33. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Area of a Circle
Adding/Subtracting Fractions
Even/Odd
Finding the midpoint
34. 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
Even/Odd
Number Categories
Part-to-Part Ratios and Part-to-Whole Ratios
Rate
35. 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
Greatest Common Factor
PEMDAS
Average Rate
36. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Greatest Common Factor
Even/Odd
Isosceles and Equilateral triangles
Solving an Inequality
37. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Part-to-Part Ratios and Part-to-Whole Ratios
Combined Percent Increase and Decrease
Using an Equation to Find an Intercept
Intersection of sets
38. The whole # left over after division
Remainders
Adding and Subtracting Roots
Multiples of 3 and 9
Reducing Fractions
39. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
(Least) Common Multiple
Adding and Subtracting Roots
Repeating Decimal
Similar Triangles
40. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Reciprocal
PEMDAS
Reducing Fractions
41. Sum=(Average) x (Number of Terms)
Probability
Using the Average to Find the Sum
Finding the Original Whole
Solving an Inequality
42. To divide fractions - invert the second one and multiply
Using an Equation to Find an Intercept
Dividing Fractions
Area of a Triangle
Surface Area of a Rectangular Solid
43. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Number Categories
Factor/Multiple
Intersection of sets
Domain and Range of a Function
44. 1. Re-express them with common denominators 2. Convert them to decimals
Mixed Numbers and Improper Fractions
Solving a System of Equations
Adding and Subtraction Polynomials
Comparing Fractions
45. Combine equations in such a way that one of the variables cancel out
Pythagorean Theorem
Combined Percent Increase and Decrease
Solving a System of Equations
Finding the midpoint
46. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
(Least) Common Multiple
Multiplying and Dividing Powers
Multiplying Fractions
47. To solve a proportion - cross multiply
Solving a Proportion
Area of a Sector
Solving an Inequality
Negative Exponent and Rational Exponent
48. 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
Characteristics of a Rectangle
Counting the Possibilities
Intersection of sets
Average Rate
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
Rate
Solving an Inequality
Remainders
Dividing Fractions
50. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Multiples of 2 and 4
(Least) Common Multiple
Intersection of sets
Interior Angles of a Polygon