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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. Subtract the smallest from the largest and add 1
Characteristics of a Square
Identifying the Parts and the Whole
Counting Consecutive Integers
The 5-12-13 Triangle
2. 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
Circumference of a Circle
Multiplying and Dividing Powers
Greatest Common Factor
Triangle Inequality Theorem
3. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
The 3-4-5 Triangle
Volume of a Cylinder
Multiplying Fractions
Setting up a Ratio
4. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal
Relative Primes
Percent Increase and Decrease
Using an Equation to Find an Intercept
Intersecting Lines
5. Part = Percent x Whole
Exponential Growth
Area of a Circle
Percent Formula
Comparing Fractions
6. 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
Determining Absolute Value
Domain and Range of a Function
Characteristics of a Parallelogram
Even/Odd
7. For all right triangles: a^2+b^2=c^2
Pythagorean Theorem
Counting the Possibilities
Percent Formula
Characteristics of a Parallelogram
8. 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
Solving a System of Equations
Finding the Original Whole
Multiplying and Dividing Powers
Adding and Subtracting Roots
9. To find the reciprocal of a fraction switch the numerator and the denominator
Reciprocal
Circumference of a Circle
Tangency
Median and Mode
10. The whole # left over after division
Solving a Proportion
Remainders
Average Rate
Intersection of sets
11. The smallest multiple (other than zero) that two or more numbers have in common.
Area of a Sector
(Least) Common Multiple
Percent Increase and Decrease
The 5-12-13 Triangle
12. 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
Even/Odd
Multiplying/Dividing Signed Numbers
Similar Triangles
Repeating Decimal
13. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Comparing Fractions
Average Formula -
Pythagorean Theorem
Dividing Fractions
14. Domain: all possible values of x for a function range: all possible outputs of a function
Characteristics of a Parallelogram
Solving a Proportion
Reciprocal
Domain and Range of a Function
15. Combine like terms
Adding and Subtraction Polynomials
Identifying the Parts and the Whole
Negative Exponent and Rational Exponent
Length of an Arc
16. (average of the x coordinates - average of the y coordinates)
Part-to-Part Ratios and Part-to-Whole Ratios
Using the Average to Find the Sum
Solving a Proportion
Finding the midpoint
17. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Factor/Multiple
Pythagorean Theorem
The 3-4-5 Triangle
Determining Absolute Value
18. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Surface Area of a Rectangular Solid
Area of a Circle
Intersection of sets
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
The 5-12-13 Triangle
(Least) Common Multiple
Part-to-Part Ratios and Part-to-Whole Ratios
Prime Factorization
20. pr^2
Area of a Circle
Interior Angles of a Polygon
Simplifying Square Roots
Solving an Inequality
21. 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
Evaluating an Expression
Multiplying Monomials
Percent Increase and Decrease
22. 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
Characteristics of a Rectangle
Adding/Subtracting Fractions
Comparing Fractions
23. Volume of a Cylinder = pr^2h
Volume of a Rectangular Solid
Interior Angles of a Polygon
Multiplying/Dividing Signed Numbers
Volume of a Cylinder
24. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45
Relative Primes
Characteristics of a Rectangle
Tangency
Average of Evenly Spaced Numbers
25. 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
Union of Sets
Average of Evenly Spaced Numbers
Part-to-Part Ratios and Part-to-Whole Ratios
26. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
PEMDAS
Length of an Arc
The 3-4-5 Triangle
Raising Powers to Powers
27. 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
Direct and Inverse Variation
Mixed Numbers and Improper Fractions
Dividing Fractions
Identifying the Parts and the Whole
28. 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
Using the Average to Find the Sum
The 3-4-5 Triangle
Multiplying/Dividing Signed Numbers
Tangency
29. 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
Percent Increase and Decrease
Average of Evenly Spaced Numbers
Adding and Subtraction Polynomials
Part-to-Part Ratios and Part-to-Whole Ratios
30. 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
Percent Formula
Comparing Fractions
Determining Absolute Value
Exponential Growth
31. 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
Volume of a Cylinder
Intersecting Lines
Raising Powers to Powers
32. 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)
Area of a Sector
Length of an Arc
Evaluating an Expression
Exponential Growth
33. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width
Volume of a Rectangular Solid
Pythagorean Theorem
Characteristics of a Rectangle
Raising Powers to Powers
34. To multiply fractions - multiply the numerators and multiply the denominators
Reciprocal
Number Categories
Multiplying Fractions
Multiplying/Dividing Signed Numbers
35. 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
Volume of a Rectangular Solid
Negative Exponent and Rational Exponent
Direct and Inverse Variation
Part-to-Part Ratios and Part-to-Whole Ratios
36. The largest factor that two or more numbers have in common.
Identifying the Parts and the Whole
Greatest Common Factor
Average Rate
Raising Powers to Powers
37. 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
Number Categories
Parallel Lines and Transversals
The 5-12-13 Triangle
38. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Counting Consecutive Integers
Area of a Circle
Prime Factorization
Parallel Lines and Transversals
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
Adding/Subtracting Fractions
Using an Equation to Find the Slope
Negative Exponent and Rational Exponent
Using an Equation to Find an Intercept
40. 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 an Intercept
Percent Formula
Solving a Proportion
Finding the Missing Number
41. Add the exponents and keep the same base
Similar Triangles
Multiplying and Dividing Powers
(Least) Common Multiple
Isosceles and Equilateral triangles
42. 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
Isosceles and Equilateral triangles
Adding and Subtracting Roots
Percent Increase and Decrease
Number Categories
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
Domain and Range of a Function
Finding the midpoint
Direct and Inverse Variation
Solving an Inequality
44. 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
Mixed Numbers and Improper Fractions
Using an Equation to Find an Intercept
Average Rate
Multiplying and Dividing Powers
45. Probability= Favorable Outcomes/Total Possible Outcomes
Even/Odd
Length of an Arc
Multiplying Fractions
Probability
46. Surface Area = 2lw + 2wh + 2lh
Intersecting Lines
Multiplying and Dividing Powers
Surface Area of a Rectangular Solid
Direct and Inverse Variation
47. To solve a proportion - cross multiply
Determining Absolute Value
Solving a Proportion
Negative Exponent and Rational Exponent
Volume of a Cylinder
48. 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
Adding and Subtraction Polynomials
Relative Primes
Evaluating an Expression
Isosceles and Equilateral triangles
49. To divide fractions - invert the second one and multiply
The 5-12-13 Triangle
Adding/Subtracting Signed Numbers
Dividing Fractions
Characteristics of a Square
50. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Greatest Common Factor
Function - Notation - and Evaulation
Multiplying Monomials
Factor/Multiple