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92 Cards in this Set
- Front
- Back
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Will the number of equations equal the number of variables always?
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NO. Never assume this. It is depends.
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How should absolute value equations be solved?
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They should be solved for both positive and negative values of the variable/number/expression inside the absolute value symbols
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What about equations with even exponents?
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They have two solutions as they hide the sign of the base. e.g. x square has value of +x and -x
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What about equations with odd exponents?
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They only have one solution.
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What are the 3 basic means of solving exponential equations?
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1. Square both sides
2. Make the base the same 3. Make the exponent the same. |
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Can you solve quadratic equations that has zero in the denominator?
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NO. x2+x-12/x-2 = 0; x = 2 is not a solution.
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How to solve problems involving sequence?
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You must identify the rule of the sequence.
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What if the rule of sequence is not provided. How to identify the rule?
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1. Information about the form of the sequence should be given.
2. A few consecutive numbers in the sequence should be given |
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What is the formula if the difference of successive terms are the same in a sequence?
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kn+x. k is the difference and x is the first term
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What is the formula if the difference of the difference of successive terms are the same in a sequence?
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an2 + bn + c.
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How do you solve equations with large exponents?
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You write out a few of the sequences till a pattern is found. e.g. what is the units digit of 3 to the power 365.
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What is the domain of function graph?
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It is the input values or the x coordinate
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What is the range of a function graph?
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It is the output values or y coordinate
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The would the inequality sign flip for an equation?
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When you multiply or divide the inequality with a negative number
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Can you multiply or divide inequalities with variables?
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NO. this is because the sign of the variable is not known. You have to take it to one side and factor it out.
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For what type of equations will you have a range of values
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For equations that have even exponents and absolute values.
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What steps do you follow to solve questions with multiple inequalities?
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1. Simplify the equations
2. Arrange them together with the inequality in one direction 3. Arrange it to line up the common variable. 4. Take the extreme values out. |
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What are the rules involved in solving VICS?
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1. Never pick 1 or 0
2. Pick small numbers 3. Pick different numbers 4. Test all answer choices till only one correct answer is found. If there is more than one correct answer then solve for different numbers those common answers. |
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What are the sides of common right angle triangles?
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3-4-5; 5-12-13;8-15-17
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What is the ratio of the sides of an isosceles triangle?
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1:1:root2
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What is the ratio of the sides of an equilateral triangle?
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1:root3:2
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What is the rule governing the sum of the sides of a triangle?
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Sum of any two sides of a triangle is greater than the third side.
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What is the formula of the diagonal of a square?
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d= sroot2; where s is the length of the side
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What is the formula of the diagonal of a cube?
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d= sroot3; where s is the length of the side
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How do you find the diagonal of a rectangle?
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Use Pythagorean theorem
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How do you find the diagonal of a rectangular solid?
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Use Pythagorean theorem twice.
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What is the relationship between the angles of similar triangles?
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The corresponding angles are the same
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What is the relationship between the angles of similar triangles?
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The corresponding sides will be proportional
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How to solve complex polygon questions?
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Break them up into small triangles or extend the lines to get the angles in view.
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What is the circumference of a circle?
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2(pi)r
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What is the circumference of a cylinder?
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2(pi)r(r+h)
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What is the circumference of a square?
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4s
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What is the circumference of a cube?
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6s
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What is the circumference of a sphere?
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??
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What is the circumference of a cone?
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??
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What is the area of a circle?
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pi(r)square
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What is the area of a square?
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(s)quare
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What is the volume of cylinder?
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Pi r square h
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What is the length of an arc?
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x/360 * pi r square. where x is the angle of the sector.
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What is the perimeter of a sector?
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x/360(2pir) + 2r.
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What is the area of a sector?
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x/360*pi(r)square
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What type of triangle is an inscribed triangle with one side as the diagonal?
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A right angled triangle.
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What is the surface area of a cylinder?
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2(pi(r)square + 2pi(r)h. This is the surface are of the 2 circles plus the rectangle that forms the body of the cylinder.
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What is the volume of a cylinder?
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pi(r)square(h)
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What is the perimeter of a sector?
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x/360(2pir) + 2r.
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What is the area of a sector?
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x/360*pi(r)square
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What type of triangle is an inscribed triangle with one side as the diagonal?
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A right angled triangle.
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What is the surface area of a cylinder?
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2(pi(r)square + 2pi(r)h. This is the surface are of the 2 circles plus the rectangle that forms the body of the cylinder.
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What is the volume of a cylinder?
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pi(r)square(h)
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What is one technique to solve line angle questions?
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Extend the parallel lines to get the transverse angles to solve the problem.
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What is the slope of a line?
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rise/run. Or (y2 - y1)/(x2- x1)
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What are the 4 types of slopes?
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+ve, -ve, zero(y=0), undefined(x=0)
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What is a y intercept?
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It is the point the coordinate plane where the line intersects the y - axis where x = 0.
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What is the x axis?
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It is the point on the coordinate plane where the line intersects the x axis and y=0.
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What is the equation of a line?
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y = mx+b, where m is the slope, b is the y intercept.
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What is the point on the coordinate plane for the y intercept of a line?
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(0, b).
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What is the first thing to be done on seeing a line question?
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Form the line equation if not already provided.
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What are the steps to form a line equation given two points?
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1) Find the slope
2) Form the equation with the slope. 3) Plug in b with one of the points y coordinate. |
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How to find the distance between two points?
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1) Draw a right triangle with the two points and the coordinate axis.
2) Find the length of the two shorter sides which the difference of the points(x2 - x1) etc 3) Use pythagoras theorem to find the longer side. |
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How to identify what quadrants a line passes through?
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1) Rewrite eqn as y=mx+b.
2) Find the x and y intercept. 3) Draw the line. |
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What is the relationship between the slopes of two lines that bisect each other?
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they are the inverse negative relationship.
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How to find the mid point of a line given its points?
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Find the average. Add the points and divide by 2.
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What is the area of a Rhombus?
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(d1*d2)/2
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What is the area of a parallelogram?
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b*h
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What is the area of a trapezoid?
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(b1+b2)*h/2
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What is the sum of the interior angles of a polygon?
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(n-2)*180
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Name the sides proportion of 3 common right angled triangles?
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1) 3-4-5
2) 5-12-13 3) 8-15-17 |
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What is the difference between two numbers that have the same integers in reverse order?
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9
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How to find the units digit of a sum or product of numbers?
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The units digit doesnt change so ignore the other places and add or multiply the units place alone.
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How to simply division with large divisors?
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Bring the divisor to a single digit. e.g. 1530798/314988 ~= 15/3
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What are proper fractions?
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Fractions that fall between 0 and 1. Or the numerator is lesser than the denominator.
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Are mixed fractions proper?
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No. They are improper fractions as the numerator is greater than one.
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What is the result of adding the same number to both numerator and denominator of a proper fraction?
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It brings the number closer to one.
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When you multiple two proper fractions, is the resultant proper fraction greater or smaller?
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Smaller
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When you divide two proper fractions, is the resultant proper fraction greater or smaller?
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Greater
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When you add two proper fractions, is the resultant proper fraction greater or smaller?
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greater
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When you subtract two proper fractions, is the resultant proper fraction greater or smaller?
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smaller
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What steps do you take to compare to proper fractions as being greater or smaller with respect to each other?
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Cross-multiply the numbers and write the answer on top of each respective numerator to compare.
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What technique to use when solving large fractions?
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Use bench mark rounded values. eg. What is 10/22 of 5/18 of 2000 can be simplified as 1/2 of 1/4 of 2000
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When do you pick smart numbers for word problems?
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When no quantities or totals are given
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How to pick a smart number?
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Try to pick the least common denominator
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How to solve for unknowns for part whole questions?
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Use the % table.
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What steps do you take to compare to proper fractions as being greater or smaller with respect to each other?
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Cross-multiply the numbers and write the answer on top of each respective numerator to compare.
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What technique to use when solving large fractions?
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Use bench mark rounded values. eg. What is 10/22 of 5/18 of 2000 can be simplified as 1/2 of 1/4 of 2000
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When do you pick smart numbers for word problems?
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When no quantities or totals are given
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How to pick a smart number?
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Try to pick the least common denominator
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How to solve for unknowns for part whole questions?
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Use the % table.
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How to calculate increase or decrease in quantity?
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Original(1 +- %change/100) = new
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Successive increase or decrease formula?
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original(x/100)(y/100) = new
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What is the formula for calculating simple interest?
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P*R*T
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What is the formula for calculating compound interest?
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P(1+ r/n) raised to the power of nt
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What table to use to solve mixture problems?
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Original Change New
M1 M1 Total |
