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SAT Math

Subjects : sat, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. Adding and Subtracting Polynomials
Use the formula distance=rate*time and its variations to help in this question.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
Combine like terms.

2. Quickly Finding the Average of a Series of Evenly Spaced Numbers
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average the smallest and largest number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

3. Definition of a Rational Number
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the formula distance=rate*time and its variations to help in this question.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

4. PEMDAS
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction

5. Counting Consecutive Integers
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B

6. Finding the GCF of Two or More Numbers
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.

7. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Sum: Average x Number of Terms
Switch the numerator and denominator.
(pie)r(squared)

8. Definition of an Irrational Number
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Combine like terms.
Subtract the smallest from the largest and add 1

9. Factoring a Polynomial ('FOIL in Reverse')
The whole number left over after division.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

10. Expressing the Union and Intersection of Sets
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

11. Simplifying a Fraction to Lowest Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Sum: Average x Number of Terms
Factor out and cancel all factors the numerator and denominator have in common.

12. Multiplying Monomials
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the numerators and multiply the denominators.

13. Characteristics of a Rectangle
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

14. Finding the LCM of Two or More Numbers

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15. Knowing if an Integer is a Multiple of 5 or 10
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
Part=Percent x Whole
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.

16. Properties of a 45-45-90 Triangle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
2(pie)r
Sum: Average x Number of Terms

17. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

18. Converting from part-to-part ratios to part-to-whole ratios
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
VofaRS=lwh
Put each number in the original ratio over the sum of the numbers.
Put the equation into y=mx+b-- in which case b is the y-intercept.

19. If x(2)=7x+18 - what is the positive value of x?
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Slope=change in y/change in x

20. Solving an Inequality
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.

21. Factoring the Difference of Two Squares
Four equal acute angles and four equal obtuse angles.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the exponents - (x^3)^4=x^3*4=x^12
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

22. Finding the Volume of a Rectangular Solid
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
VofaRS=lwh
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

23. Raising a Power to a Power
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
Express them with a common denominator.
Multiply the exponents - (x^3)^4=x^3*4=x^12

24. Finding the y-intercept When Given an Equation of a Line
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put the equation into y=mx+b-- in which case b is the y-intercept.

25. Evaluating an Algebraic Expression
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Plug in the given values for the unknowns and calculate according to PEMDAS.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Do whatever is necessary to both sides to isolate the variable.

26. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Plug in the given values for the unknowns and calculate according to PEMDAS.
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.

27. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
A(2)+b(2)=c(2)
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.

28. Finding the Rate of Speed
The whole number left over after division.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Use the formula distance=rate*time and its variations to help in this question.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives

29. Characteristics of a Parallelogram
A(2)+b(2)=c(2)
The value that appears the most often.
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

30. Finding the Circumference of a Circle
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
2(pie)r
VofaC: (pie)r(2)h
Express them with a common denominator.

31. Finding the Midpoint Between Two Points
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
(x1+x2)/2 -(y1+y2)/2
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle

32. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.

33. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.

34. How do you know if an integer is a multiple of 3 or 9?
Find a common denominator - then add or subtract the numerators.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.

35. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
Two relatively prime numbers are integers that have no common factor other than 1.

36. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.

37. Finding the Reciprocal of a Fraction
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Switch the numerator and denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

38. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use the formula distance=rate*time and its variations to help in this question.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Average the smallest and largest number

39. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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40. Difference Between a Factor and a Multiple
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.
Use the distributive property then combine the like terms.

41. Finding the Area of a Circle
Express them with a common denominator.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
(pie)r(squared)
Use the units to keep things straight - Snowfall inches/hours

42. General Procedure for Multiplying Polynomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Get the absolute value equation by itself. Solve.
Use the distributive property then combine the like terms.
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.

43. Solving a Proportion
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
Cross multiply.

44. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Combine like terms.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

45. Calculating Negative Exponents and Radical Exponents
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.

46. Finding the Area of a Sector

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47. What are Two Special Pythagorean Triples?

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48. Solving a Problem Involving Rates
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the units to keep things straight - Snowfall inches/hours

49. Prime Factorization of a Number
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

50. Knowing if an Integer is a Multiple of 2 or 4
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.