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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. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Simplifying Square Roots
Greatest Common Factor
Parallel Lines and Transversals
Multiples of 2 and 4
2. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Adding and Subtraction Polynomials
Greatest Common Factor
Reducing Fractions
Multiples of 2 and 4
3. pr^2
Simplifying Square Roots
Area of a Circle
Average Rate
Surface Area of a Rectangular Solid
4. Subtract the smallest from the largest and add 1
Probability
Surface Area of a Rectangular Solid
Multiples of 2 and 4
Counting Consecutive Integers
5. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Average Formula -
Remainders
Volume of a Rectangular Solid
Function - Notation - and Evaulation
6. 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
Isosceles and Equilateral triangles
Comparing Fractions
Similar Triangles
7. 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
Identifying the Parts and the Whole
Comparing Fractions
Isosceles and Equilateral triangles
Union of Sets
8. 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
Identifying the Parts and the Whole
Solving a Proportion
Intersecting Lines
Percent Formula
9. 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
Using an Equation to Find the Slope
Finding the Missing Number
Isosceles and Equilateral triangles
Greatest Common Factor
10. 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
Solving a Quadratic Equation
Combined Percent Increase and Decrease
Even/Odd
Multiplying and Dividing Roots
11. 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
Raising Powers to Powers
Negative Exponent and Rational Exponent
Solving a Proportion
Adding/Subtracting Signed Numbers
12. 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
The 5-12-13 Triangle
Relative Primes
Using an Equation to Find the Slope
Multiples of 2 and 4
13. 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
Multiplying and Dividing Roots
Adding and Subtracting Roots
Solving a Quadratic Equation
Solving an Inequality
14. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
The 5-12-13 Triangle
Tangency
Adding/Subtracting Fractions
Intersecting Lines
15. 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
Negative Exponent and Rational Exponent
Characteristics of a Rectangle
Characteristics of a Parallelogram
Dividing Fractions
16. 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
Repeating Decimal
Median and Mode
Volume of a Rectangular Solid
17. To find the reciprocal of a fraction switch the numerator and the denominator
Identifying the Parts and the Whole
Reciprocal
Length of an Arc
Negative Exponent and Rational Exponent
18. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Surface Area of a Rectangular Solid
Prime Factorization
Using an Equation to Find the Slope
Direct and Inverse Variation
19. For all right triangles: a^2+b^2=c^2
Solving an Inequality
The 5-12-13 Triangle
Multiplying and Dividing Powers
Pythagorean Theorem
20. 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
Using an Equation to Find the Slope
Part-to-Part Ratios and Part-to-Whole Ratios
Repeating Decimal
Solving a Proportion
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
Characteristics of a Square
Combined Percent Increase and Decrease
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
22. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Average Rate
Using the Average to Find the Sum
Determining Absolute Value
Prime Factorization
23. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Average Formula -
Union of Sets
PEMDAS
Finding the midpoint
24. 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
Relative Primes
Area of a Circle
Adding/Subtracting Signed Numbers
Probability
25. The whole # left over after division
Volume of a Cylinder
Remainders
Average Formula -
Identifying the Parts and the Whole
26. 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 midpoint
(Least) Common Multiple
Domain and Range of a Function
Multiplying and Dividing Roots
27. 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
Using an Equation to Find the Slope
Direct and Inverse Variation
Solving a Quadratic Equation
Average Rate
28. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior Angles of a Polygon
Finding the Original Whole
Median and Mode
Negative Exponent and Rational Exponent
29. Combine like terms
Adding and Subtraction Polynomials
Rate
Using Two Points to Find the Slope
Exponential Growth
30. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Solving a Proportion
Intersection of sets
Average of Evenly Spaced Numbers
Similar Triangles
31. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Comparing Fractions
Length of an Arc
Rate
32. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
Dividing Fractions
Median and Mode
Relative Primes
Negative Exponent and Rational Exponent
33. 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
Rate
Even/Odd
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
34. Change in y/ change in x rise/run
Even/Odd
Using Two Points to Find the Slope
Remainders
Percent Formula
35. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Average of Evenly Spaced Numbers
Solving an Inequality
Probability
(Least) Common Multiple
36. 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
(Least) Common Multiple
Factor/Multiple
Remainders
37. Factor out the perfect squares
Reciprocal
Solving a Quadratic Equation
Adding and Subtracting Roots
Simplifying Square Roots
38. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Area of a Circle
Interior and Exterior Angles of a Triangle
Tangency
Finding the Distance Between Two Points
39. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Relative Primes
Using an Equation to Find the Slope
Area of a Triangle
Multiples of 3 and 9
40. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Using an Equation to Find an Intercept
Relative Primes
Volume of a Cylinder
Parallel Lines and Transversals
41. 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
Remainders
Domain and Range of a Function
Probability
Rate
42. 2pr
Finding the Missing Number
Multiples of 3 and 9
Area of a Circle
Circumference of a Circle
43. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).
Negative Exponent and Rational Exponent
Factor/Multiple
PEMDAS
Part-to-Part Ratios and Part-to-Whole Ratios
44. Probability= Favorable Outcomes/Total Possible Outcomes
Finding the Distance Between Two Points
Probability
Intersecting Lines
Number Categories
45. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Simplifying Square Roots
Median and Mode
Counting the Possibilities
Finding the Missing Number
46. 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
Solving a Quadratic Equation
Multiplying/Dividing Signed Numbers
Average Formula -
Adding/Subtracting Signed Numbers
47. 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
Function - Notation - and Evaulation
Interior and Exterior Angles of a Triangle
Volume of a Cylinder
Percent Increase and Decrease
48. 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.
Number Categories
Finding the midpoint
Dividing Fractions
Determining Absolute Value
49. To multiply fractions - multiply the numerators and multiply the denominators
Negative Exponent and Rational Exponent
Factor/Multiple
Multiplying Fractions
Using an Equation to Find an Intercept
50. Multiply the exponents
Finding the Missing Number
Area of a Circle
Reciprocal
Raising Powers to Powers