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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.
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. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
A(2)+b(2)=c(2)
Get the absolute value equation by itself. Solve.

2. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
The value that falls in the middle of the set.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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.

3. What are Two Special Pythagorean Triples?

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4. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Part=Percent x Whole
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

5. Solving a Problem Involving Rates
VofaRS=lwh
Cross multiply.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Use the units to keep things straight - Snowfall inches/hours

6. Finding the Mode of a Set of Numbers
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
The value that appears the most often.

7. Average Rate and How Do You Find It
(pie)r(squared)
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Put each number in the original ratio over the sum of the numbers.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

8. Solving a Linear Equation
Use the units to keep things straight - Snowfall inches/hours
Do whatever is necessary to both sides to isolate the variable.
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.
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

9. Raising a Power to a Power
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the exponents - (x^3)^4=x^3*4=x^12

10. Finding the Rate of Speed
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 value that appears the most often.
Use the formula distance=rate*time and its variations to help in this question.
-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.

11. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Use the formula distance=rate*time and its variations to help in this question.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a

12. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Subtract the smallest from the largest and add 1
Average the smallest and largest 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.
The value that falls in the middle of the set.

13. Finding the Domain and Range of a Function
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
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.

14. Solving a System of Equations
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.
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

15. Convert From a Fraction to a Decimal - Vice Versa
-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.
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
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.
VofaRS=lwh

16. Finding the Slope of a Line When Given Two Points on the Line
-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.
Slope=change in y/change in x
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the numerators and multiply the denominators.

17. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Get the absolute value equation by itself. Solve.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.

18. If x(2)=7x+18 - what is the positive value of x?
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Multiply the numerators and multiply the denominators.
Use the distributive property then combine the like terms.

19. If (Square Root: x-1)+5=12 - what is the value of x/2?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Average the smallest and largest number
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.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25

20. Finding the Area of a Sector

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21. Dividing Expressions with Exponents that Have a Common Base
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 formula distance=rate*time and its variations to help in this question.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Slope=change in y/change in x

22. Scalene - Isosceles - and Equilateral Triangles
Express them with a common denominator.
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
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.
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.

23. Adding and Subtracting Monomials
Use the units to keep things straight - Snowfall inches/hours
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.

24. Solving an Inequality
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.
Four equal acute angles and four equal obtuse angles.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.

25. 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?
Use simple numbers like 1 and 2 and see what happens.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Use the formula distance=rate*time and its variations to help in this question.

26. Formula Used to Find Percent
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Part=Percent x Whole

27. Formula to Find Average
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms
Just add or subtract the coefficients in front of the radicals.
-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.

28. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
(pie)r(squared)

29. Setting Up a Ratio
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.

30. Finding the GCF of Two or More Numbers
Factor out and cancel all factors the numerator and denominator have in common.
-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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Subtract the smallest from the largest and add 1

31. Simplifying an Algebraic Equation
Sum: Average x Number of Terms
Cancel factors common to the numerator and denominator.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.

32. Properties of the Interior and Exterior Angles of a Triangle
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.
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
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

33. Definition of Remainder
The whole number left over after division.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
-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.
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.

34. Properties of a 45-45-90 Triangle
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Sum: Average x Number of Terms
Check the multiples of the larger number until you find one that's also a multiple of the smaller.

35. Characteristics of a Rectangle
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
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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
Sum: Average x Number of Terms

36. 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
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

37. Numbers that are Relatively Prime
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
Two relatively prime numbers are integers that have no common factor other than 1.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.

38. Finding the Length of an Arc in a Circle

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39. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The value that falls in the middle of the set.
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.

40. Difference Between a Factor and a Multiple
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
-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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
(pie)r(squared)

41. Converting from an Improper Fraction to a Mixed Number
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

42. Multiplying Binomials
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
Subtract the smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes
FOIL: First - Outer - Inner - Last... Combine Like Terms

43. Number of Groups - +1 Each Time
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value

44. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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45. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Combine like terms.

46. Definition of an Integer
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.

47. What Does Solving In Terms of Mean?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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 one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.

48. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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(2)+b(2)=c(2)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

49. If r#t=t(r)-r(t) - then what is 4#3?
2(pie)r
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
VofaC: (pie)r(2)h
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

50. Knowing if an Integer is a Multiple of 2 or 4
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
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.
-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.