Math Entrance Exam

• The sum of the length of 2 sides in the triangle must be more than the third side Ex. 1, 12, and 12
• The sum and the product of the roots of quadratic equations can be acquired by using the formula which are: sum- -b/a and for product- c/a. Example 2x^2 + 10x + 20 the sum is -5 and the product is 10.
• in the equation 3x^2+9x+18, what is the sum and product of the roots?

  sum: -b/a -9/3= -3

  product: c/a 18/3= 6
• the length of the sides of the triangle are: 3,4,5

  is this a correct sides of a triangle? yes
• the triangle ABC has a sides of 1,2,1.

  is this a proper length sides for a triangle? no
• if the quadratic equation x^2-3x+15 has a sum and products of roots 3 and 15 respectively, what is the factor that fits this roots? -5 and 3
• LCM of 22 and 30 is 330. NOTE: do the table method
• Derivatives of (sin x) is (cos x)
• Derivatives of (cos x) is (-sin x)
• Derivatives of (tan x) is (sec^2 x)
• Derivatives of (cot x) is (-csc^2 x)
• Derivatives of (csc x) is (-csc x cot x)
• Derivatives of (sec x) is (sec x tan x)
• what are the dimension(length and width) of a rectangle with a perimeter of 26 units and an area of 40 units?

  NOTE: Get the half of the perimeter then input it and the area as quadratic equation ex. x^2+13x+40

  length: 8 width: 5
• Heron's formula for finding triangle area without a given height is:

  √s(s-a)(s-b)(s-c), where s is perimeter x 1/2
• A triangle has a sides of 3,4, and 5 respectively. what is the area of the triangle?

  6
• log100=2, there is a number 10 between log and 100 which is NOT stated if it's 10 because it is a common one
• The formula of arithmetic sequence is an=a1+(n-1)d
• The formula of geometric sequence is an=a1(r)^n-1
• e^2=x in logarithm form is ln x=2
• How many ways can we arrange the word Math?

  24
• How many ways can we arrange the word alabama?

  210
• Log2(5)+Log2(x)= log2(5x)
• log2(1/8)= log2(1)-log2(8)

  =0-log2(2^3)

  =-3log2(2)

  =-3
• The formula for circular permutation is P=(n-1)!
• possible ways to form a group of 5 from 6 people. what kind of problem is this? (combination or permutation)

  Combination
• Electing a 4 officers from a class of 20 students. what kind of problem is this? (combination or permutation)

  permutation
• A 6 digits lock code have numbers from 0 to 5, what is the formula in permutation to find the code and also what is the answer?

  6P6 and 720
• How many possible ways can we form a group of 3 from the 6 people in the room. Give the formula and the answer

  6C3 and 20
• In how many ways can we arrange 9 person in a round table?

  formula: (n-1)!

  40,320
• Divide the equation using synthetic division.

  $x^2+$$7x+$$12/x+$$3$

  The picture below shows the process. The answer is x+4

  
• The formula for polygons with sides more than 4 is 180(n-2)

  Meanwhile, The size of each exterior angle can be found using the formula 360/n

  180(n-2)
• Find the arithmetic sequence of the following given number sequence:

  96+89+82+75.....+12

  d=-7

  given below is the formula

  702

  
• Find the sum of the arithmetic sequence of the following given number sequence:

  4+7+10+13+16..........+58

  d=3

  given below is the formula

  589

  
• Find the sum of the finite geometric sequence given:

  3,6,12,24,48,96

  given the formula below

  189

  
• Find the sum of the infinite geometric sequence

  8+4+2+1+1/2+1/4......

  r=1/2

  given the formula below

  16

  
• Mass=density x volume

  density=mass/volume

  volume=mass/density

  volume and density is inversely proportional to each other
• 0.444... in fraction is 4/10 while 0.282828... in fraction is 28/100 or 14/50
• The ratio of the two complimentary angle is 5:13. what is the measure of the smaller angle?

  the total of ratio when combined is 18

  25
• The inequality 3x-6 lesser than or equal to 4(x+2) is equivalent to?

  NOTE: IF NEGATIVE X AND TATANGGALIN PALIT DIRECTION NG BUNGANGA

  x is greater than or equal to -14