UPCAT TEST - MATH

If f(x)= 2x³/3 , and f(x+2)=18, then x=?
1. Replace x with x + 2

1

How many sides is triangle

3

How many sides is quadrilateral

4

How many sides is Pentagon

5

How many sides is Hexagon

6

How many sides is Heptagon/Septagon

7

How many sides is Octagon

8

How many sides is Enneagon

9

How many sides is Decagon

10

Sum° of triangle

180

Sum° of Quadrilateral

360

Sum° of Pentagon

540

Sum° of Hexagon

720

Sum° of Heptagon/Septagon

900

Sum° of Octagon

1080

Sum° of Enneagon

1160

Sum° of Decagon

1440

Regular Individual Angle Formula

Sum/Sides of Polygon

Individual Angle of Decagon

144

i¹

i

i²

-1

i³

-i

i⁴

1

i²¹⁶

1

The expression x³yz/xy⁵z is equal to?
1. Write them as powers:
2. Subtract exponents (same base rule)

x²/y^-4

Pedro can finish painting a wall in 6 hours. Juan can finish painting the same in wall in 3 hours. How long will it take them to finish painting the wall together?
1. Get work rates (make a fraction)
2. Combine rates to get wall/hour

2

Perfect Square Trinomial

a² ± 2ab + b² = (a ± b)²

The expression x²−8x+16 can be factored as?
1. Make it a perfect trinomial square
2. Know what is a and b

(x - 4)²

Fractional exponent rule

x^m/n = n√x^m​= (n√x​)^m

The expression x^2/3 is equivalent to:

∛x²

Company A invested 10,000 pesos in a bond that yields 10% per year. How much more do they need to invest in another bond that yields 5% if they want to earn 1,500 pesos in a year?
1. Get Earnings and Total Desired Earnings
2. Find how much to invest in Company B

10,000

Earnings Formula

Investment x Interest Rate

A certain car dealer offers customizable cars. It offers 3 different colors, 2 different transmissions, and 5 different seat covers for every car. How many different customizations are possible?

30

If 5^x/5⁷ = 125, what is x?

10

Formula of m₂

-1/m₁

Point-Slope Form

y−y₁​ = m₂ ​(x−x₁​)

The line y = 4x + 6 is perpendicular to line l, which intersects it at point (0, 6). What is the equation of line l?
1. Find m₁, y_1, m₂
2. Use Point-Slope Form

y = -1/4x + 6

Average Formula

x + y + z/3

If the sum of the values x and y is z, what is the average of the three values?
1. Get Average Formula

2z/3

The number of ice cream cones eaten is directly proportional to the amount of burgers available. If 10 ice cream cones were eaten when there were 50 burgers available, how many ice cream cones will be eaten if 75 burgers are available?
1. Make it a fraction
2. Make x and equalize first fraction

15

In the following equation, x = z^3 for all integers y. What is y in terms of z?

y = 2 + x^2
Put value of x in fraction

2 + z⁶

What is the probability that you will pick a green marble out of a bag with 3 red marbles, 4 blue marbles and 7 green marbles?
1. Add all marbles and make it a denominator

1/2

You blindly guessed the last five multiple-choice items of an UPCAT practice test. What is the probability that you will answer all five questions correctly?
1. Make fraction of possible correct answer and the number of choices
2. Make it to the 5th power

1/1024

If x+4/8 − 2x+8/16 = x+4/4 then x=?
1. Gawing mong magkakamukha
2. Reduce smallest terms

-4

If x² + 8x + 16 = 30, (x+4) is equal to?

±√30

Given the series 1, 5, 13, 29, ... What is the 6th term?
1. Know the differences

125

nth term formula

a_n = a₁ + (n - 1)d

Find the sum of the arithmetic series 1, 5, 9, 13, ... , 45.
1. Find nth term

276

Formula for Sum of series

S_n = n/2 (a₁ + a_n)

x′

2h - x

y′

2k − y

A circle with the equation (x - 2)² + (y - 2)² = 4 is on the xy-coordinate plane. What is the point on the circle opposite the point (0, 2), which is also on the circle?
1. Know value of Center (h, k), point and radius
2. Know value of x’ and y’

(4, 2)

Odd ± Even
Odd x Odd
Odd²
Odd³

Odd

Odd ± Odd
Odd x Even

Even

x is an odd number. Which of the following numbers are odd numbers too?

4x + 1

Theo is x years old and Julian is 5 years younger. In 3 years, Theo’s age will be double that of Julian’s. How old is Theo now?
1. Make age of theo x
2. Don’t forget the double

7

A_square

s²

P_square

4s

A_rectangle

Lw

P_rectangle

2L + 2w

A_circle

πr²

P_circle

πd

A_triangle

a + b + c

P_triangle

½ bh

Given the figure above with a square attached to a triangle, what its perimeter?
1. Know values of each side

18 + 6√3

What is the area of figure 3 given in item 101?
1. Get area of square and triangle
2. Combine

36 + 6√3

What is the radius of the biggest cylinder you can fit in a prism that has a length and width of 5, and a height of 21?
1. List terms

2.5

A_cube

6s²

V_cube

5³

A_{rectangular prism}

2Lw + 2hw + 2Lh

V_{rectangular prism}

Lwh

A_sphere

4πr²

V_sphere

4/3πr³

A_cylinder

2πrh + πr²

V_cylinder

πr²h

6y (2x + 7) = 36. What is the value of xy in the equation above?
1. Get rid of 6

6 - 7y/2

If x + 7y = −8, and 2x + 6y = 6, what is (x − y) equal to?
1. Get value of x
2. Solve eq. 2 and get y
3. Solve eq. 1 and get x

14

If x² (x³) = y¹⁰ what is x in terms of y?
1. Combine x exponents

y²

Distance Formula

speed x time

Two runners started running from the same area. Runner A ran with a speed of 3 m/s, and runner B ran with a speed of 5 m/s. By how many meters does runner B lead after 15 seconds?

30

Δ > 0

2 real roots

Δ = 0

1 real root

Δ < 0

no real roots

How many real roots does the quadratic equation x² − 4x +12 have?
1. Look for values of a, b, c
2. Define if what root

0

Discriminant Δ

b² - 4ac

Full Circle in degrees

360

Full circle in radians

2πrad

Convert π/3 to radians.

60

What is the next term in this series? 1, 3, 7, 17, _____ (mas mataas sa 17 at 17 + 10)

41

Solve for x: x/x² + 6x + 8 = √576/x + 2
1. Simplify Terms
2. Factor denominator
3. Eliminate common factor

- 96/23

PQRS is a positive, even integer with its digits represented by the respective variables P, Q, R & S. How many possible number combinations are there if no digits can repeat?

1. Understand that the whole needs to be even, not each number. PQRS like 1000 is even as a whole.

2520

Given the equation 2x² + 7x + 6 = 0, what are possible values of the variable x?
1. Know values of a, b, c
2. Multiply a to c
3. Find two numbers that when you multiply, the answer is the value of a and c, and when you add the answer is value of b
4. Replace two numbers to 7×
5. Group into terms and factor it (divide to x and 2)
6. Factor out common term

-2

Given that the population of the Philippines is 100,000,000 people, how many individuals are not Roman Catholic?
1. Subtract 100% to not roman catholic
2. Multiply the value to population in the ph

18,000,000

Given the equation, a² - b² = 9 here b is a positive integer less than 10, what is the value of a?
1. Get factors of 9 and a² - b²
2. Solve for value of a

5

Factor using difference of squares
a² - b²

(a−b)(a+b)

Midpoint of AC is equivalent to

Midpoint of BD

Midpoint Formula

M_x = B_x + D_x/2, M_y = B_y + D_y/2

Find BD Formula

√(X_B - X_D)² + (Y_B - Y_D)²

On the xy-coordinate plane, the following points are part of rhombus ABCD.

Point A: (1, 2)

Point B: (3, 2)

Point C: (2, 0)

What is the length of diagonal BD?
1. Find midpoint of BD
2. Use midpoint to find D
3. Find the length of BD

√13

In the English Premier League, there are 20 teams that go against each other twice in one season. How many games in total are played in one season?
1. Divide number of teams to number of temas in one match up
2. Multiply number of teams to number of teams they might go against with
3. Multipy the value to number of chance they might go against with

380