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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. 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
Combined Percent Increase and Decrease
Rate
Average Rate
The 3-4-5 Triangle
2. 1. Re-express them with common denominators 2. Convert them to decimals
Characteristics of a Square
Interior and Exterior Angles of a Triangle
Characteristics of a Parallelogram
Comparing Fractions
3. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Solving a System of Equations
Area of a Sector
Parallel Lines and Transversals
Number Categories
4. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
Mixed Numbers and Improper Fractions
Area of a Circle
Greatest Common Factor
Intersection of sets
5. 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
Using Two Points to Find the Slope
Triangle Inequality Theorem
Simplifying Square Roots
The 5-12-13 Triangle
6. To divide fractions - invert the second one and multiply
Characteristics of a Rectangle
Counting the Possibilities
Intersecting Lines
Dividing Fractions
7. 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
Area of a Triangle
Length of an Arc
Exponential Growth
Multiplying/Dividing Signed Numbers
8. Sum=(Average) x (Number of Terms)
Exponential Growth
(Least) Common Multiple
Using the Average to Find the Sum
Characteristics of a Parallelogram
9. Add the exponents and keep the same base
Multiplying and Dividing Powers
Intersecting Lines
Combined Percent Increase and Decrease
Counting Consecutive Integers
10. Volume of a Cylinder = pr^2h
Factor/Multiple
Volume of a Cylinder
Finding the Original Whole
Pythagorean Theorem
11. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Finding the Distance Between Two Points
Solving an Inequality
The 3-4-5 Triangle
The 5-12-13 Triangle
12. 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
Volume of a Cylinder
Isosceles and Equilateral triangles
Multiplying/Dividing Signed Numbers
Adding and Subtraction Polynomials
13. 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
Percent Formula
Percent Increase and Decrease
Exponential Growth
14. 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
Intersection of sets
Factor/Multiple
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
15. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Isosceles and Equilateral triangles
Multiples of 2 and 4
Using an Equation to Find the Slope
Percent Increase and Decrease
16. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Greatest Common Factor
Finding the Missing Number
Remainders
Intersecting Lines
17. Combine like terms
Adding and Subtraction Polynomials
Pythagorean Theorem
Circumference of a Circle
Length of an Arc
18. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
Union of Sets
Exponential Growth
Number Categories
Area of a Sector
19. The whole # left over after division
Remainders
Using an Equation to Find an Intercept
Adding/Subtracting Fractions
Evaluating an Expression
20. 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
Reciprocal
Union of Sets
Direct and Inverse Variation
Characteristics of a Square
21. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Multiplying/Dividing Signed Numbers
Setting up a Ratio
Mixed Numbers and Improper Fractions
Average Formula -
22. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Solving a System of Equations
Average Formula -
Multiplying and Dividing Roots
Direct and Inverse Variation
23. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Average Rate
Multiplying Fractions
Median and Mode
Even/Odd
24. Surface Area = 2lw + 2wh + 2lh
Using Two Points to Find the Slope
Surface Area of a Rectangular Solid
Adding/Subtracting Fractions
Setting up a Ratio
25. 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
Factor/Multiple
Percent Increase and Decrease
Area of a Triangle
Similar Triangles
26. Subtract the smallest from the largest and add 1
Dividing Fractions
Identifying the Parts and the Whole
Adding and Subtracting monomials
Counting Consecutive Integers
27. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Domain and Range of a Function
Probability
Percent Formula
Multiplying Monomials
28. 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
Rate
Negative Exponent and Rational Exponent
Interior Angles of a Polygon
Solving a Quadratic Equation
29. 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)
Solving a Quadratic Equation
Direct and Inverse Variation
Length of an Arc
Tangency
30. 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
Mixed Numbers and Improper Fractions
Adding/Subtracting Fractions
Remainders
Counting the Possibilities
31. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Interior and Exterior Angles of a Triangle
Percent Increase and Decrease
Interior Angles of a Polygon
Raising Powers to Powers
32. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Solving a Proportion
Length of an Arc
Median and Mode
33. 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
Interior Angles of a Polygon
Mixed Numbers and Improper Fractions
Probability
Part-to-Part Ratios and Part-to-Whole Ratios
34. 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
Prime Factorization
The 5-12-13 Triangle
Reducing Fractions
Domain and Range of a Function
35. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Greatest Common Factor
Similar Triangles
Area of a Circle
Tangency
36. 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
Triangle Inequality Theorem
Intersecting Lines
Average of Evenly Spaced Numbers
37. To solve a proportion - cross multiply
Counting the Possibilities
Factor/Multiple
Intersection of sets
Solving a Proportion
38. The smallest multiple (other than zero) that two or more numbers have in common.
Finding the Distance Between Two Points
(Least) Common Multiple
Direct and Inverse Variation
Determining Absolute Value
39. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Adding/Subtracting Signed Numbers
Determining Absolute Value
Negative Exponent and Rational Exponent
Finding the Original Whole
40. 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
Volume of a Cylinder
The 3-4-5 Triangle
Pythagorean Theorem
Finding the Original Whole
41. 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
Dividing Fractions
Using an Equation to Find an Intercept
Even/Odd
Negative Exponent and Rational Exponent
42. 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
Repeating Decimal
Adding and Subtraction Polynomials
Simplifying Square Roots
Length of an Arc
43. Domain: all possible values of x for a function range: all possible outputs of a function
Interior and Exterior Angles of a Triangle
Domain and Range of a Function
Median and Mode
Exponential Growth
44. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Area of a Triangle
Average of Evenly Spaced Numbers
Solving a Proportion
Finding the midpoint
45. 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
Area of a Sector
Adding/Subtracting Signed Numbers
Circumference of a Circle
Identifying the Parts and the Whole
46. 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 and Dividing Powers
Counting Consecutive Integers
Multiplying Fractions
47. 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
Factor/Multiple
Finding the Original Whole
Relative Primes
Direct and Inverse Variation
48. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Even/Odd
Using an Equation to Find the Slope
Using Two Points to Find the Slope
Area of a Triangle
49. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Greatest Common Factor
Part-to-Part Ratios and Part-to-Whole Ratios
Combined Percent Increase and Decrease
Volume of a Rectangular Solid
50. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Characteristics of a Rectangle
Tangency
Pythagorean Theorem
Evaluating an Expression