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SAT Math

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.
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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 Circumference of a Circle
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Average the smallest and largest number
2(pie)r

2. Formula to Find Average
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
FOIL: First - Outer - Inner - Last... Combine Like Terms
Average: Sum of the Terms/Number of the Terms

3. Prime Factorization of a Number
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Average the smallest and largest number
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
VofaC: (pie)r(2)h

4. Determining Absolute Value of a Number
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
2(pie)r
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

5. 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.
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.
The value that falls in the middle of the set.
Find a common denominator - then add or subtract the numerators.

6. What are Two Special Pythagorean Triples?

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7. Definition of a Rational Number
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaRS=lwh

8. Finding a Term in a Geometric Sequence
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

9. What Does Solving In Terms of Mean?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the equation into y=mx+b-- in which case b is the y-intercept.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.

10. Comparing the values of two or more Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
-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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Express them with a common denominator.

11. Characteristics of a Rectangle
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cancel factors common to the numerator and denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
2(pie)r

12. Number of Groups - +1 Each Time
Get the absolute value equation by itself. Solve.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

13. Simplifying a Fraction to Lowest Terms
(pie)r(squared)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.
Factor out and cancel all factors the numerator and denominator have in common.

14. Solving a Radical Equation
Isolate the radical expression and use the standard rules of algebra.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Switch the numerator and denominator.

15. General Procedure for Multiplying Polynomials
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distributive property then combine the like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

16. Multiplying Monomials
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Subtract the smallest from the largest and add 1
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.

17. An Important Property of a Line Tangent to 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.
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.
Do whatever is necessary to both sides to isolate the variable.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

18. Finding the Median of a Set of Numbers
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
-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.
The value that falls in the middle of the set.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.

19. Finding the Area of a Sector

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20. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

21. Dividing Fractions
Find a common denominator - then add or subtract the numerators.
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Change the division sign to a multiplication sign - invert the second fraction - and multiply.

22. If 3(3x)=9(x+2) - what is the value of x?
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4

23. Multiply and Divide Positive and Negative Numbers
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
Cancel factors common to the numerator and denominator.
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.

24. Adding and Subtracting Fractions
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Find a common denominator - then add or subtract the numerators.

25. Solving a Problem Involving Rates
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use the units to keep things straight - Snowfall inches/hours
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Sum: Average x Number of Terms

26. Finding the Surface Area of a Rectangular Solid
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
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
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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

27. Finding the Slope of a Line When Given Two Points on the Line
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Slope=change in y/change in x
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

28. Solving a Linear Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Do whatever is necessary to both sides to isolate the variable.
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.

29. If r#t=t(r)-r(t) - then what is 4#3?
(x1+x2)/2 -(y1+y2)/2
The whole number left over after division.
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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.

30. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
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
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.

31. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Two relatively prime numbers are integers that have no common factor other than 1.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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.

32. Converting from part-to-part ratios to part-to-whole ratios
Multiply the exponents - (x^3)^4=x^3*4=x^12
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put each number in the original ratio over the sum of the numbers.

33. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Plug in the given values for the unknowns and calculate according to PEMDAS.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 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.

34. Solving an Inequality
Switch the numerator and denominator.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

35. Raising a Power to a Power
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Multiply the exponents - (x^3)^4=x^3*4=x^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

36. Finding the y-intercept When Given an Equation of a Line
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.

37. Finding the Domain and Range of a Function
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Use the distributive property then combine the like terms.

38. Direct Variation and Inverse Variation
Subtract the smallest from the largest and add 1
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

39. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put each number in the original ratio over the sum of the numbers.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

40. If x(2)=7x+18 - what is the positive value of x?
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.

41. Multiplying Expressions with Exponents that Have a Common Base
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
The value that falls in the middle of the set.
Use the distributive property then combine the like terms.
Subtract the smallest from the largest and add 1

42. 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.
The value that appears the most often.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.

43. Finding the Missing Number in a Series When You are Given the Average
-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.
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

44. If 2+l6-xl=10 and x>0 - what is the value of 2x?
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
Factor out and cancel all factors the numerator and denominator have in common.
Get the absolute value equation by itself. Solve.

45. Finding the Area of a Triangle

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46. 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
Average the smallest and largest number
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

47. 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 value that falls in the middle of the set.
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.
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.

48. Finding the Sum of the Interior Angles of a Polygon
Express them with a common denominator.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides

49. If 4(x(2)-10x+25) - then what is the value of x?
Slope=change in y/change in x
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.
Cancel factors common to the numerator and denominator.
FOIL: First - Outer - Inner - Last... Combine Like Terms

50. Finding the Volume of a Cylinder
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Average the smallest and largest number
VofaC: (pie)r(2)h