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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. 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
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.

2. Characteristics of a Square
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
Isolate the radical expression and use the standard rules of algebra.

3. Properties of Similar Triangles
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Cancel factors common to the numerator and denominator.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the formula distance=rate*time and its variations to help in this question.

4. Finding the Length of an Arc in a Circle

5. Finding the Slope When Given an Equation of a Line
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Factor out and cancel all factors the numerator and denominator have in common.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

6. Multiplying Binomials
Average the smallest and largest number
FOIL: First - Outer - Inner - Last... Combine Like Terms
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Switch the numerator and denominator.

7. Finding the LCM of Two or More Numbers

8. Converting From a Mixed Number to an Improper Fraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
A(2)+b(2)=c(2)
Plug in the given values for the unknowns and calculate according to PEMDAS.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

9. Numbers that are Relatively Prime
Use the distributive property then combine the like terms.
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
Two relatively prime numbers are integers that have no common factor other than 1.

10. Finding the Rate of Speed
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Use the formula distance=rate*time and its variations to help in this question.
-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.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.

11. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Do whatever is necessary to both sides to isolate the variable.

12. Factoring a Polynomial ('FOIL in Reverse')
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

13. What value of x is not in the domain of the function f(x)=x-2/x-3?
Factor out and cancel all factors the numerator and denominator have in common.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
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.

14. Simplifying an Algebraic Equation
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Cancel factors common to the numerator and denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

15. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put each number in the original ratio over the sum of the numbers.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle

16. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Multiply the exponents - (x^3)^4=x^3*4=x^12
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.

17. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Factor out and cancel all factors the numerator and denominator have in common.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.

18. Finding the Mode of a Set of Numbers
The value that appears the most often.
The whole number left over after division.
2(pie)r
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.

19. Knowing if an Integer is a Multiple of 5 or 10
-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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
2(pie)r
Sum: Average x Number of Terms

20. Setting Up a Ratio
Multiply the exponents - (x^3)^4=x^3*4=x^12
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.

21. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Slope=change in y/change in x

22. Solving a System of Equations
The value that appears the most often.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
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.
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.

23. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

24. What types of angles are formed when a transversal cross parallel lines?
Four equal acute angles and four equal obtuse angles.
-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.
(pie)r(squared)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

25. Dividing Fractions
Use the units to keep things straight - Snowfall inches/hours
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

26. Finding the Sum of the Interior Angles of a Polygon
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the formula distance=rate*time and its variations to help in this question.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)

27. Calculating Negative Exponents and Radical Exponents
Slope=change in y/change in x
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

28. If the average of a - b - and 48 is 48 - what is the value of a + b?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Average: Sum of the Terms/Number of the Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96

29. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
Put each number in the original ratio over the sum of the numbers.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

30. Finding the y-intercept When Given an Equation of a Line
Use the formula distance=rate*time and its variations to help in this question.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12

31. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
-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.
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.

32. How do you know if an integer is a multiple of 3 or 9?
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Do whatever is necessary to both sides to isolate the variable.
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.
A(2)+b(2)=c(2)

33. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
The value that falls in the middle of the set.
Four equal acute angles and four equal obtuse angles.
Get the absolute value equation by itself. Solve.

34. Formula to Find Average
Cross multiply.
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.
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: Sum of the Terms/Number of the Terms

35. Multiplying Fractions
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the units to keep things straight - Snowfall inches/hours
Multiply the numerators and multiply the denominators.

36. Finding the Volume of a Cylinder
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaC: (pie)r(2)h
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

37. If (Square Root: x-1)+5=12 - what is the value of x/2?
Use simple numbers like 1 and 2 and see what happens.
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

38. Determining Absolute Value of a Number
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.

39. Counting the Total Number of Possibilities for Several Events to Occur
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.
Isolate the radical expression and use the standard rules of algebra.
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

40. Formula Used to Find Percent
VofaC: (pie)r(2)h
Part=Percent x Whole
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

41. Counting Consecutive Integers
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
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.
Subtract the smallest from the largest and add 1
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

42. Solving an Inequality
Part=Percent x Whole
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average: Sum of the Terms/Number of the Terms

43. Comparing the values of two or more Fractions
Express them with a common denominator.
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
Sum: Average x Number of Terms
Average: Sum of the Terms/Number of the Terms

44. Direct Variation and Inverse Variation
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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
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

45. Expressing the Union and Intersection of Sets
Adjacent angles are supplementary - Vertical angles are equal
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
-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.
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

46. If 4(x(2)-10x+25) - then what is the value of x?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

47. Finding the Area of a Circle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
(pie)r(squared)

48. Characteristics of a Rectangle
Get the absolute value equation by itself. Solve.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
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.

49. Finding the Area of a Triangle

50. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.