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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
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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 solve a proportion - cross multiply
Solving a Proportion
Solving an Inequality
Using Two Points to Find the Slope
Greatest Common Factor
2. Multiply the exponents
Raising Powers to Powers
Intersecting Lines
Similar Triangles
Surface Area of a Rectangular Solid
3. 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
Solving a Proportion
Number Categories
Finding the Missing Number
Evaluating an Expression
4. 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
Using the Average to Find the Sum
Adding/Subtracting Signed Numbers
Tangency
Solving an Inequality
5. 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)
Greatest Common Factor
Length of an Arc
Finding the Original Whole
Prime Factorization
6. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Multiplying Monomials
Similar Triangles
Finding the Original Whole
Multiplying/Dividing Signed Numbers
7. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)
Interior and Exterior Angles of a Triangle
Similar Triangles
Characteristics of a Square
PEMDAS
8. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.
The 5-12-13 Triangle
Solving a Proportion
Union of Sets
Factor/Multiple
9. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Surface Area of a Rectangular Solid
Number Categories
Tangency
Circumference of a Circle
10. To find the reciprocal of a fraction switch the numerator and the denominator
Even/Odd
Negative Exponent and Rational Exponent
Tangency
Reciprocal
11. 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
Evaluating an Expression
Relative Primes
Counting Consecutive Integers
Adding/Subtracting Signed Numbers
12. Add the exponents and keep the same base
Solving a Proportion
Reciprocal
Multiplying and Dividing Powers
Similar Triangles
13. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Characteristics of a Rectangle
Adding/Subtracting Signed Numbers
Average Rate
Using Two Points to Find the Slope
14. 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
Direct and Inverse Variation
Characteristics of a Rectangle
Repeating Decimal
Adding/Subtracting Signed Numbers
15. 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
Percent Increase and Decrease
Using an Equation to Find the Slope
Finding the Distance Between Two Points
16. 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
Circumference of a Circle
Negative Exponent and Rational Exponent
Area of a Sector
Part-to-Part Ratios and Part-to-Whole Ratios
17. 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
Surface Area of a Rectangular Solid
Multiplying Monomials
Exponential Growth
18. pr^2
Counting the Possibilities
Reciprocal
Area of a Circle
Counting Consecutive Integers
19. 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
Multiplying and Dividing Roots
Adding and Subtraction Polynomials
Triangle Inequality Theorem
Identifying the Parts and the Whole
20. The largest factor that two or more numbers have in common.
Direct and Inverse Variation
Area of a Triangle
Greatest Common Factor
Finding the Distance Between Two Points
21. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Using the Average to Find the Sum
Finding the Distance Between Two Points
Relative Primes
Intersecting Lines
22. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2
Intersection of sets
Using an Equation to Find an Intercept
Multiplying Monomials
(Least) Common Multiple
23. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180
Identifying the Parts and the Whole
Adding/Subtracting Signed Numbers
Parallel Lines and Transversals
Factor/Multiple
24. you can add/subtract when the part under the radical is the same
Factor/Multiple
(Least) Common Multiple
Identifying the Parts and the Whole
Adding and Subtracting Roots
25. 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
Percent Increase and Decrease
Relative Primes
Comparing Fractions
26. 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
Average of Evenly Spaced Numbers
Area of a Circle
Interior Angles of a Polygon
Function - Notation - and Evaulation
27. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3
Reciprocal
Setting up a Ratio
Even/Odd
Area of a Sector
28. 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
Adding/Subtracting Signed Numbers
Using the Average to Find the Sum
Finding the Distance Between Two Points
29. To multiply fractions - multiply the numerators and multiply the denominators
Reciprocal
Multiplying Fractions
Remainders
Using an Equation to Find the Slope
30. 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
Area of a Circle
The 3-4-5 Triangle
Intersection of sets
Multiplying Fractions
31. 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
Interior and Exterior Angles of a Triangle
Rate
Exponential Growth
Domain and Range of a Function
32. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9
Negative Exponent and Rational Exponent
Multiplying Monomials
Circumference of a Circle
Multiples of 3 and 9
33. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime
Combined Percent Increase and Decrease
Prime Factorization
Reducing Fractions
Volume of a Cylinder
34. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides
Combined Percent Increase and Decrease
The 3-4-5 Triangle
Interior Angles of a Polygon
Dividing Fractions
35. 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 and Subtracting monomials
Using Two Points to Find the Slope
Using an Equation to Find the Slope
Multiples of 2 and 4
36. 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
Intersecting Lines
Volume of a Cylinder
Rate
Multiplying and Dividing Powers
37. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Dividing Fractions
Adding/Subtracting Fractions
Multiplying and Dividing Roots
Pythagorean Theorem
38. For all right triangles: a^2+b^2=c^2
Using Two Points to Find the Slope
Pythagorean Theorem
Raising Powers to Powers
Adding and Subtraction Polynomials
39. Volume of a Cylinder = pr^2h
Volume of a Cylinder
Using the Average to Find the Sum
Part-to-Part Ratios and Part-to-Whole Ratios
Domain and Range of a Function
40. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
PEMDAS
Multiples of 2 and 4
Reciprocal
The 3-4-5 Triangle
41. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.
The 3-4-5 Triangle
Interior and Exterior Angles of a Triangle
Identifying the Parts and the Whole
Intersection of sets
42. 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
Domain and Range of a Function
Counting the Possibilities
Factor/Multiple
Pythagorean Theorem
43. To divide fractions - invert the second one and multiply
Function - Notation - and Evaulation
Parallel Lines and Transversals
Intersecting Lines
Dividing Fractions
44. 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
Finding the Original Whole
Intersection of sets
Surface Area of a Rectangular Solid
Percent Formula
45. The median is the value that falls in the middle of the set - the mode is the value that appears most often
Evaluating an Expression
Area of a Circle
Median and Mode
Characteristics of a Square
46. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Adding and Subtracting monomials
Finding the Missing Number
Probability
Counting the Possibilities
47. 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
Repeating Decimal
Length of an Arc
Solving a System of Equations
Area of a Triangle
48. 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
Direct and Inverse Variation
Intersecting Lines
Isosceles and Equilateral triangles
Multiplying Fractions
49. 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
Characteristics of a Square
Characteristics of a Parallelogram
Factor/Multiple
Multiplying/Dividing Signed Numbers
50. The smallest multiple (other than zero) that two or more numbers have in common.
Using the Average to Find the Sum
Solving a Quadratic Equation
(Least) Common Multiple
Number Categories