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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. 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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%

2. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
Sum: Average x Number of Terms
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.

3. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.

4. Characteristics of a Rectangle
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Isolate the radical expression and use the standard rules of algebra.
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.

5. If (Square Root: x-1)+5=12 - what is the value of x/2?
Find a common denominator - then add or subtract the numerators.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
-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.
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.

6. Expressing the Union and Intersection of Sets
Use the units to keep things straight - Snowfall inches/hours
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.
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 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

7. Counting the Total Number of Possibilities for Several Events to Occur
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.

8. If the average of a - b - and 48 is 48 - what is the value of a + b?
Find a common denominator - then add or subtract the numerators.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

9. What is a Function and how do you Evaluate one?

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10. If 3(3x)=9(x+2) - what is the value of x?
Use the distributive property then combine the like terms.
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
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.

11. Dividing Expressions with Exponents that Have a Common Base
Use the formula distance=rate*time and its variations to help in this question.
2(pie)r
The value that appears the most often.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

12. Knowing if an Integer is a Multiple of 5 or 10
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.
-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.
The whole number left over after division.

13. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Average the smallest and largest number
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. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.

15. What Does Solving In Terms of Mean?
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Cancel factors common to the numerator and denominator.

16. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
The whole number left over after division.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

17. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the exponents - (x^3)^4=x^3*4=x^12

18. Finding the Circumference of a Circle
Multiply the exponents - (x^3)^4=x^3*4=x^12
2(pie)r
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the formula distance=rate*time and its variations to help in this question.

19. Finding the Surface Area of a Rectangular Solid
Use simple numbers like 1 and 2 and see what happens.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms

20. Calculating Negative Exponents and Radical Exponents
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Cross multiply.

21. If 4(x(2)-10x+25) - then what is the value of x?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

22. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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

23. What value of x is not in the domain of the function f(x)=x-2/x-3?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the formula distance=rate*time and its variations to help in this question.

24. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Express them with a common denominator.

25. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

26. Finding the Rate of Speed
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Use the formula distance=rate*time and its variations to help in this question.
Cancel factors common to the numerator and denominator.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

27. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

28. Finding the Area of a Sector

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29. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Just add or subtract the coefficients in front of the radicals.
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.

30. Finding the Slope When Given an Equation of a Line
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Adjacent angles are supplementary - Vertical angles are equal
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.

31. Finding a Term in a Geometric Sequence
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Get the absolute value equation by itself. Solve.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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.

32. Counting Consecutive Integers
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.

33. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Part=Percent x Whole
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The whole number left over after division.

34. Definition of Remainder
The whole number left over after division.
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.
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.
Use the formula distance=rate*time and its variations to help in this question.

35. Finding the Distance Between Two Points on a Coordinate Graph
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.
Switch the numerator and denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

36. Solving a Linear Equation
Do whatever is necessary to both sides to isolate the variable.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Get the absolute value equation by itself. Solve.

37. Setting Up a Ratio
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
(x1+x2)/2 -(y1+y2)/2
(pie)r(squared)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.

38. Prime Factorization of a Number
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.
Use the formula distance=rate*time and its variations to help in this question.
2(pie)r
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.

39. If r#t=t(r)-r(t) - then what is 4#3?
Plug in the given values for the unknowns and calculate according to PEMDAS.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Express them with a common denominator.
Adjacent angles are supplementary - Vertical angles are equal

40. Finding the GCF of Two or More Numbers
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number

41. Definition of an Irrational Number
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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.

42. Converting from an Improper Fraction to a Mixed Number
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.
Sum: Average x Number of Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the exponents - (x^3)^4=x^3*4=x^12

43. How do you know if an integer is a multiple of 3 or 9?
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.
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
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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

44. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Factor out and cancel all factors the numerator and denominator have in common.
(pie)r(squared)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.

45. Solving a Proportion
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Part=Percent x Whole
Cross multiply.

46. Finding the Sum of the Average of a Series of Numbers
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.

47. Finding the Missing Number in a Series When You are Given the Average
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
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

48. Definition of an Integer
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.
The whole number left over after division.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.

49. Number of Groups - +1 Each Time
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

50. Finding the Slope of a Line When Given Two Points on the Line
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A(2)+b(2)=c(2)
Slope=change in y/change in x
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2