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. Multiplying Binomials
The value that appears the most often.
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.
FOIL: First - Outer - Inner - Last... Combine 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


2. PEMDAS
Cancel factors common to the numerator and denominator.
Use the units to keep things straight - Snowfall inches/hours
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.


3. Adding and Subtracting Roots
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.
Just add or subtract the coefficients in front of the radicals.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


4. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


5. Finding the Sum of the Interior Angles of a Polygon
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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.


6. Finding the LCM of Two or More Numbers

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7. Converting From a Mixed Number to an Improper Fraction
VofaC: (pie)r(2)h
Part=Percent x Whole
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


8. What are Two Special Pythagorean Triples?

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9. General Procedure for Multiplying Polynomials
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


10. What Does Solving In Terms of Mean?
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Subtract the smallest from the largest and add 1
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


11. Definition of a Rational Number
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


12. Setting Up a Ratio
(pie)r(squared)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the units to keep things straight - Snowfall inches/hours


13. Adding and Subtracting Polynomials
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Combine like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


14. Finding the Volume of a Rectangular Solid
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Adjacent angles are supplementary - Vertical angles are equal
VofaRS=lwh


15. Characteristics of a Parallelogram
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
(x1+x2)/2 -(y1+y2)/2
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


16. Knowing if an Integer is a Multiple of 5 or 10
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.
Use simple numbers like 1 and 2 and see what happens.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


17. If r#t=t(r)-r(t) - then what is 4#3?
Find a common denominator - then add or subtract the numerators.
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
Put each number in the original ratio over the sum of the numbers.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


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

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19. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


20. What is the Triangle Inequality Theorem?
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.


21. Finding the Area of a Sector

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22. If (Square Root: x-1)+5=12 - what is the value of x/2?
Adjacent angles are supplementary - Vertical angles are equal
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(pie)r(squared)


23. Finding the Circumference of a Circle
Use the units to keep things straight - Snowfall inches/hours
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
2(pie)r


24. Finding the Median of a Set of Numbers
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The value that falls in the middle of the set.
Isolate the radical expression and use the standard rules of algebra.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


25. Comparing the values of two or more Fractions
The value that falls in the middle of the set.
Cross multiply.
Express them with a common denominator.
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


26. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Use the formula distance=rate*time and its variations to help in this question.
-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.
FOIL: First - Outer - Inner - Last... Combine Like Terms


27. Increasing and Decreasing a Number by a Certain Percentage
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Multiply the numerators and multiply the denominators.
-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.


28. Difference Between a Factor and a Multiple
-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 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.
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
Switch the numerator and denominator.


29. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
Use simple numbers like 1 and 2 and see what happens.
VofaC: (pie)r(2)h
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the exponents - (x^3)^4=x^3*4=x^12


30. Solving a Linear Equation
Put each number in the original ratio over the sum of the numbers.
Do whatever is necessary to both sides to isolate the variable.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
A(2)+b(2)=c(2)


31. Formula to Find Average
Part=Percent x Whole
Average: Sum of the Terms/Number of the Terms
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.


32. 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%
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Express them with a common denominator.


33. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Average: Sum of the Terms/Number of the Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


34. Calculating the Probability that an Event will Take Place
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Adjacent angles are supplementary - Vertical angles are equal
Get the absolute value equation by itself. Solve.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


35. Converting from part-to-part ratios to part-to-whole ratios
Use simple numbers like 1 and 2 and see what happens.
Put each number in the original ratio over the sum of the numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Factor out and cancel all factors the numerator and denominator have in common.


36. 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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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.


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

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38. If x(2)=7x+18 - what is the positive value of x?
Factor out and cancel all factors the numerator and denominator have in common.
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.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


39. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Slope=change in y/change in x


40. Finding the Slope When Given an Equation of a Line
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
(x1+x2)/2 -(y1+y2)/2
Part=Percent x Whole
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


41. Adding and Subtracting Monomials
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.
-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.
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


42. Finding the Area of a Triangle

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43. Counting the Total Number of Possibilities for Several Events to Occur
(x1+x2)/2 -(y1+y2)/2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
Do whatever is necessary to both sides to isolate the variable.


44. Multiplying Expressions with Exponents that Have a Common Base
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


45. Adding a Positive Number to a Negative Number
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Four equal acute angles and four equal obtuse angles.


46. 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.
Use the distributive property then combine the like 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 value that appears the most often.


47. Finding the Surface Area of a Rectangular Solid
Use the formula distance=rate*time and its variations to help in this question.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor out and cancel all factors the numerator and denominator have in common.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


48. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
Slope=change in y/change in x
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.
Average: Sum of the Terms/Number of the Terms
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.


49. Finding the Area of a Circle
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.
(pie)r(squared)
A(2)+b(2)=c(2)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


50. Simplifying Square Roots
Average the smallest and largest number
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 the numerators and multiply the denominators.