Test your basic knowledge |

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. An Important Property of a Line Tangent to a Circle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
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.
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.
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.

2. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
-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.
Switch the numerator and denominator.
Plug in the given values for the unknowns and calculate according to PEMDAS.

3. Convert From a Fraction to a Decimal - Vice Versa
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
The whole number left over after division.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.

4. 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
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Adjacent angles are supplementary - Vertical angles are equal

5. Evaluating an Algebraic Expression
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I

6. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
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.
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

7. Solving a Proportion
Isolate the radical expression and use the standard rules of algebra.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Cross multiply.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time

8. Finding the Slope of a Line When Given Two Points on the Line
Switch the numerator and denominator.
Slope=change in y/change in 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.
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.

9. Solving a Linear Equation
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Do whatever is necessary to both sides to isolate the variable.

10. Definition of an Irrational Number
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Put the equation into y=mx+b-- in which case b is the y-intercept.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

11. Scalene - Isosceles - and Equilateral Triangles
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.
Cross multiply.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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

12. Dividing Expressions with Exponents that Have a Common Base
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
Slope=change in y/change in x
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Plug in the given values for the unknowns and calculate according to PEMDAS.

13. What is the Triangle Inequality Theorem?
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2

14. Characteristics of a Rectangle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72

15. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Find a common denominator - then add or subtract the numerators.
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.

16. Formula Used to Find Percent
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
(pie)r(squared)
Part=Percent x Whole
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.

17. What types of angles are formed when two lines intersect?
Use the formula distance=rate*time and its variations to help in this question.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Isolate the radical expression and use the standard rules of algebra.
Adjacent angles are supplementary - Vertical angles are equal

18. Finding the y-intercept When Given an Equation of a Line
(pie)r(squared)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Factor out and cancel all factors the numerator and denominator have in common.
Put the equation into y=mx+b-- in which case b is the y-intercept.

19. How do you know if an integer is a multiple of 3 or 9?
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
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.
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

20. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Adjacent angles are supplementary - Vertical angles are equal
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.
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

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

22. What is the Pythagorean Theorem?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
A(2)+b(2)=c(2)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.

23. Finding the Rate of Speed
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
Use the formula distance=rate*time and its variations to help in this question.
Find a common denominator - then add or subtract the numerators.
Use simple numbers like 1 and 2 and see what happens.

24. Finding the Missing Number in a Series When You are Given the Average
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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 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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.

25. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal

26. Factoring the Difference of Two Squares
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the smallest from the largest and add 1
(pie)r(squared)
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)

27. Finding the Mode of a Set of Numbers
Find a common denominator - then add or subtract the numerators.
Just add or subtract the coefficients in front of the radicals.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The value that appears the most often.

28. 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?
-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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
Slope=change in y/change in x

29. If x(2)=7x+18 - what is the positive value of x?
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.

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

31. Converting From a Mixed Number to an Improper Fraction
Subtract the smallest from the largest and add 1
Do whatever is necessary to both sides to isolate the variable.
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 whole number part by the denominator - then add the numerator. Keep the same denominator.

32. Number of Groups - +1 Each Time
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
2(pie)r
Put the equation into the slope-intercept form: y=mx+b. The slope is m.

33. 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.
(x1+x2)/2 -(y1+y2)/2
Use simple numbers like 1 and 2 and see what happens.
Put the equation into y=mx+b-- in which case b is the y-intercept.

34. Calculating the Probability that an Event will Take Place
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average the smallest and largest number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)

35. Dividing Fractions
A(2)+b(2)=c(2)
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Isolate the radical expression and use the standard rules of algebra.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5

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

37. Finding the Circumference of a Circle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
2(pie)r
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.

38. 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?
(pie)r(squared)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
VofaRS=lwh

39. Finding the Distance Between Two Points on a Coordinate Graph
Get the absolute value equation by itself. Solve.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds

40. Simplifying a Fraction to Lowest Terms
Multiply the exponents - (x^3)^4=x^3*4=x^12
-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 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.

41. Knowing if an Integer is a Multiple of 2 or 4
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.
-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.
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.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7

42. Finding the Midpoint Between Two Points
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.
(x1+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.
Four equal acute angles and four equal obtuse angles.

43. Comparing the values of two or more Fractions
Part=Percent x Whole
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
Express them with a common denominator.

44. Finding the Sum of the Interior Angles of a Polygon
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Four equal acute angles and four equal obtuse angles.

45. Finding the Area of a Circle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
(pie)r(squared)
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.

46. Multiplying Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
The whole number left over after division.
Multiply the numerators and multiply the denominators.
Use the distributive property then combine the like terms.

47. Finding a Term in a Geometric Sequence
Use the formula distance=rate*time and its variations to help in this question.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
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.

48. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The value that appears the most often.
-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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2

49. Finding the Area of a Sector

50. Properties of the Interior and Exterior Angles of a Triangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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 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.