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Test your basic knowledge |
SAT Math: Concepts And Tricks
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Subjects
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sat
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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. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is
Simplifying Square Roots
Reducing Fractions
Repeating Decimal
Average of Evenly Spaced Numbers
2. you can add/subtract when the part under the radical is the same
Simplifying Square Roots
Exponential Growth
Adding and Subtracting Roots
Solving a Proportion
3. The smallest multiple (other than zero) that two or more numbers have in common.
(Least) Common Multiple
Multiplying and Dividing Powers
Identifying the Parts and the Whole
Intersecting Lines
4. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation
Average Formula -
Function - Notation - and Evaulation
Reducing Fractions
Solving a Quadratic Equation
5. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.
Multiplying/Dividing Signed Numbers
Factor/Multiple
Number Categories
Characteristics of a Rectangle
6. 1. Re-express them with common denominators 2. Convert them to decimals
Comparing Fractions
Reciprocal
Mixed Numbers and Improper Fractions
Repeating Decimal
7. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the
PEMDAS
Negative Exponent and Rational Exponent
Dividing Fractions
Mixed Numbers and Improper Fractions
8. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x
Mixed Numbers and Improper Fractions
Probability
Using an Equation to Find an Intercept
Comparing Fractions
9. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact
Characteristics of a Parallelogram
Average of Evenly Spaced Numbers
Similar Triangles
Tangency
10. To divide fractions - invert the second one and multiply
Repeating Decimal
Dividing Fractions
Number Categories
Area of a Triangle
11. (average of the x coordinates - average of the y coordinates)
Counting the Possibilities
Multiplying and Dividing Powers
Area of a Circle
Finding the midpoint
12. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)
Characteristics of a Rectangle
Length of an Arc
Dividing Fractions
Remainders
13. The whole # left over after division
Combined Percent Increase and Decrease
Remainders
Finding the Distance Between Two Points
Rate
14. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive
Percent Formula
Solving an Inequality
Determining Absolute Value
Adding/Subtracting Signed Numbers
15. Part = Percent x Whole
Mixed Numbers and Improper Fractions
Using the Average to Find the Sum
Function - Notation - and Evaulation
Percent Formula
16. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)
Union of Sets
Average Formula -
Repeating Decimal
Remainders
17. To add or subtract fraction - first find a common denominator - then add or subtract the numerators
Repeating Decimal
Adding/Subtracting Fractions
Median and Mode
Evaluating an Expression
18. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4
Volume of a Rectangular Solid
Reducing Fractions
Multiples of 2 and 4
Part-to-Part Ratios and Part-to-Whole Ratios
19. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²
Counting Consecutive Integers
PEMDAS
Finding the Distance Between Two Points
Multiples of 2 and 4
20. Change in y/ change in x rise/run
Triangle Inequality Theorem
The 3-4-5 Triangle
Solving a Quadratic Equation
Using Two Points to Find the Slope
21. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)
Identifying the Parts and the Whole
Relative Primes
Average Rate
Area of a Sector
22. 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
Counting the Possibilities
Length of an Arc
Characteristics of a Parallelogram
Circumference of a Circle
23. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional
Characteristics of a Square
Solving a System of Equations
Median and Mode
Similar Triangles
24. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds
Relative Primes
Finding the Original Whole
Average Rate
Even/Odd
25. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees
Interior and Exterior Angles of a Triangle
Part-to-Part Ratios and Part-to-Whole Ratios
Solving a Proportion
Function - Notation - and Evaulation
26. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520
Finding the Original Whole
Characteristics of a Square
Reducing Fractions
Adding/Subtracting Signed Numbers
27. The largest factor that two or more numbers have in common.
Relative Primes
Greatest Common Factor
Adding/Subtracting Signed Numbers
Intersecting Lines
28. 2pr
Greatest Common Factor
(Least) Common Multiple
Relative Primes
Circumference of a Circle
29. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side
Median and Mode
Pythagorean Theorem
Intersection of sets
The 3-4-5 Triangle
30. To multiply fractions - multiply the numerators and multiply the denominators
Average Formula -
PEMDAS
Simplifying Square Roots
Multiplying Fractions
31. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr
Adding/Subtracting Signed Numbers
Adding and Subtracting monomials
Combined Percent Increase and Decrease
Multiplying and Dividing Powers
32. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50
Determining Absolute Value
Circumference of a Circle
Finding the Missing Number
Percent Increase and Decrease
33. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3
Multiplying and Dividing Roots
Volume of a Rectangular Solid
Surface Area of a Rectangular Solid
Volume of a Cylinder
34. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet
Surface Area of a Rectangular Solid
Direct and Inverse Variation
Multiplying and Dividing Roots
Rate
35. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height
Characteristics of a Parallelogram
Setting up a Ratio
Number Categories
Negative Exponent and Rational Exponent
36. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110
Adding/Subtracting Fractions
Combined Percent Increase and Decrease
Adding and Subtraction Polynomials
Rate
37. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them
Even/Odd
Prime Factorization
Using Two Points to Find the Slope
Simplifying Square Roots
38. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign
Multiplying and Dividing Roots
Intersecting Lines
Even/Odd
Surface Area of a Rectangular Solid
39. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a
Exponential Growth
Identifying the Parts and the Whole
Adding and Subtracting monomials
Number Categories
40. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3
Adding/Subtracting Fractions
Comparing Fractions
Part-to-Part Ratios and Part-to-Whole Ratios
Interior and Exterior Angles of a Triangle
41. Combine like terms
Adding and Subtraction Polynomials
Area of a Triangle
Rate
Solving a System of Equations
42. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex
Area of a Circle
Raising Powers to Powers
Finding the Original Whole
Area of a Triangle
43. Probability= Favorable Outcomes/Total Possible Outcomes
Probability
Raising Powers to Powers
Remainders
Area of a Circle
44. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions
Number Categories
Domain and Range of a Function
Solving a Quadratic Equation
Average Rate
45. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common
Reducing Fractions
Average Formula -
Setting up a Ratio
Finding the midpoint
46. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign
Intersecting Lines
Relative Primes
Multiples of 2 and 4
Multiplying/Dividing Signed Numbers
47. To solve a proportion - cross multiply
Average Rate
Solving a Proportion
Simplifying Square Roots
Percent Formula
48. Factor out the perfect squares
Solving a System of Equations
Characteristics of a Parallelogram
Adding/Subtracting Fractions
Simplifying Square Roots
49. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b
Using an Equation to Find the Slope
Finding the Original Whole
Function - Notation - and Evaulation
Volume of a Cylinder
50. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle
Percent Formula
The 5-12-13 Triangle
Pythagorean Theorem
Relative Primes