Mock Battle 1

Mechanics

• The questions will be flashed on the screen, which will be read by the quiz master/s twice.

• There will be a total of thirty (30) multiple choice questions, wherein ten (10) questions are allotted for each round.

• All contestants will be given thirty (30) seconds for the Easy Round; one (1) minute for the average round; and one (1) minute and thirty (30) seconds for the difficult round.

• Each correct answer shall be equivalent to one (1) point for the Easy Round, two (2) points for Average, three (3) points for the Difficult Round, while zero (0) for incorrect or wrong answers.

EASY ROUND

Multiple Choice

Simplify the expression: (4x²y³z)²

• $$16x^4y^6z^2$$

• $$16x^4y^5z^2$$  

• $$4^2x^4y^6z^2$$  

• None of the choices
  

Multiple Choice

Simplify:

(5x + 6y - 3z) + (3x - 8y + z)

• 8x - 2y - 2z

• 8x - 14y - 4z

• 8x - 14y - 2z

• 8x + 2y + 2z

Multiple Choice

Solve for x in the equation: x² - 36 = 0

• x = 6

• x = 6 and – 6

• x = -6

• x = 18

Multiple Choice

Which of the following factors give a product of x² + 5x + 4?

• (x+1)(x+4)

• (x+2)(x+2)

• (x+5)(x-1)

• (x-4)(x-1)

Multiple Choice

Solve the equation:

$$5^{\left(x+7\right)}=25^x.$$  

• $$x=2$$  

• $$x=-2$$  

• $$x=-7$$  

• $$x=7$$  

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Multiple Choice

What is the domain of the function shown?

• All real numbers

• $$y>0$$  

• All real numbers greater than 1

• $$y<0$$  

Multiple Choice

Using the parent function y = log₃x,  what transformation is applied to obtain the graph of y = log₃(x+5)?

• Horizontal shift left 5 units

• Horizontal shift right 5 units

• Vertical shift up 5 units

• Vertical shift down 5 units

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Multiple Choice

Use multiple log properties to write as a single log:
3log₂x -  log₂y + log₂z

• log₂(x/(yz))
• log₂(x³yz)
• log₂(x³z/y)
• log₂(x³/(yz))

Multiple Choice

Expand completely: log(2x⁵) 

• log 2 + 5log x
• 5log 2 + 5log x
• 5log 2 + log x
• log 10 + log x

Multiple Choice

What are the dimensions of this matrix?

• 2 x 3
• 3 x 2
• 6 x 1
• 1 x 6

Multiple Choice

If A is a 2 × 3 matrix, and B is a 3 × 4 matrix, how many columns does AB have?

• 2

• 3

• 4

• AB is not defined

Multiple Choice

What is the determinant of this matrix?

• 5

• -5

• 0

• -12

Multiple Choice

Add

• 11    8
  -4     2
• 3     2
  -6    -6
• -3    2
  -4    -6
• 10    8
  -6    2

AVERAGE ROUND

Multiple Choice

Simplify: $$\left(\frac{5xy^{-3}}{2x^{-4}y}\right)^{-2}$$  

• 4y⁸

• 25x¹⁰

• 4y⁸/25x¹⁰

• 25x¹⁰/4y⁸

Multiple Choice

Factor completely: $$27x^5y^5+12x^3y^7$$

• $$3x^2y^5\left(9x^2+4y^4\right)$$

• $$3x^5y^7\left(9x^2-4y^4\right)$$

• $$3x^5y^7\left(4x^2+9y^4\right)$$

• $$3x^2y^5\left(9x^2+4y^4\right)$$

Multiple Choice

Solve for x in the equation: $$\frac{7x}{3}-\frac{5x}{4}=13$$

• 12

• 13

• 14

• 15

Multiple Choice

Find the equation of the line with slope 2 and passing through (-2, 1).

• y = 2x + 5

• y = 3x + 5

• y = 2x - 1

• y = 3x - 1

Multiple Choice

Give the inverse of the function f(x) = 12x + 3.

• $$f^{-1}\left(x\right)=3+12x$$

• $$f^{-1}\left(x\right)=\frac{12}{x-3}$$

• $$f^{-1}\left(x\right)=\frac{x-3}{12}$$

• $$f^{-1}\left(x\right)=12x-3$$

Multiple Choice

Determine the discriminant of x² - 9x + 15 = 0.

• 0

• 21

• 51

• 141

Multiple Choice

What is the remainder if we divide: $$\left(x^3-14x^2+51x-54\right)\ by\ \left(x+2\right)$$  

• -220

• 220

• 22

• 20

Multiple Choice

What is the product of the roots of the equation $$3x^2\ +\ 5x\ +\ 4\ =\ 0$$ ?

• $$\frac{4}{3}$$

• $$\frac{3}{4}$$

• $$-\frac{4}{3}$$

• $$-\frac{3}{4}$$

Multiple Choice

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

Multiple Choice

Solve .
$$2^{2x+3}=128$$  

• -2

• $$-\frac{3}{2}$$  

• $$\frac{3}{2}$$  

• 2

Multiple Choice

Find the value of x for

$$5^{\left(2x+3\right)}=\frac{1}{125}.$$  

• $$x=-2$$  

• $$x=-3$$  

• $$x=2$$  

• $$x=3$$  

Multiple Choice

Multiply

• 20     15    -10
  30     -5         0
• -20      15     -10
  30     -5          0
• 1        8       3
  11     4        5
• 20     -15     10
  -30         5        0  

Multiple Choice

Sam borrowed $4,500 for 2 years and had to pay $630 simple interest at the end of that time. What rate of interest did he pay?

• 6%
• 7%
• 8%
• 9%

Multiple Choice

Christian opened a savings account with $3250. His account will earn 5.2% simple interest. How much money will be in his account after 6 years?

• $4,264.00
• $1,104.00
• $1,100.00
• $4,400.00

Multiple Choice

Peter earned Php 15,000 last summer. If he deposited the money in a bank account that earns 5% interest compounded quarterly, how much money will he have after five years?

• Php 19,230.56

• Php 18,634.85

• Php 17,411.32

• Php 16,984.06

DIFFICULT ROUND

Multiple Choice

Multiply: $$\left(x^2+2x-7\right)\left(x^2-5\right)$$  

• $$x^4+2x^3-12x^2-10x+35$$

• $$x^4-2x^3-12x^2-10x+35$$

• $$x^4-2x^3-12x^2-10x-35$$

• $$4x^3-2x^2+x-10$$

Multiple Choice

If (a + b)² = 81, and a² + b² = 41, then what is ab?

• 40

• 20

• 15

• 10

Multiple Choice

The sum of the ages of Antonio and his cousin is 38. Seven years ago, Antonio was thrice as old as his cousin. Find Antonio's present age.

• 25 years old

• 26 years old

• 13 years old

• 12 years old

Multiple Choice

What should be the value of m if the value of 2x² - mx + 2 is 15 when x = -2?

• 5/2
• 3/2

• 3

• -3

Multiple Choice

Find the values of x when

$$49^{5x}=343^{\left(2x+1\right)}.$$  

• $$x=-\frac{1}{2}$$  

• $$x=\frac{1}{4}$$  

• $$x=\frac{3}{4}$$  

• $$x=\frac{5}{4}$$  

Multiple Choice

$$125^x\cdot25^{2x+1}=\left(\frac{1}{5}\right)^{x+6}$$  

Solve.

• $$-\frac{18}{6}$$  

• -1

• 1

• $$\frac{18}{6}$$  

Multiple Choice

Perform the indicated operation.  If it’s not possible, select Not Possible. 

• 7
  -7
  -6
  20
• 7 
  -9
  -6
  20
• Not Possible
• 7
  -9
  2
  20

Multiple Choice

find: B*A

• 47     30
  9     5
• 17     15
  42     35
• 10     25
  7     1
• not possible because rows do not match columns

Multiple Choice

Find the product of the two matrices.

• undefined
• -3   16
  17   12
  8   -10
• 3   12 
  -15  -8
  -1   -3
• -3   16 
  -7   -28
  -10 -10

Multiple Choice

Find the determinant of the given matrix.

• det = 2

• det = -2

• det = -64

• det = 64

Multiple Choice

Find the inverse of the given matrix.

Multiple Choice

Henry deposits P750 into a college savings account that is compounded annually when his parents received a stimulus package. If Henry lets the money sit in the account without adding or removing any and receives an 8.5% interest rate, how much money will he have total after 5 years?

• P1127.74

• P1535.24

• P2345.67

• P850.76

Multiple Choice

Marcie Mays plans to have ₱350,000 in a retirement fund 30 years from now. What monthly ordinary annuity payment should she make if the investment she has selected earns 7.2% annual interest?

• ₱3,129.09

• ₱871.29

• ₱275.76

• ₱2,757.59

Multiple Choice

An ordinary annuity was purchased 5 years ago. The annuity pays 8% compounded quarterly. The quarterly payments have been ₱500. What is the total value of the annuity to date?

• ₱12,148.68

• ₱2,602.02

• ₱2,933.30

• ₱22,880.98

Multiple Choice

You plan to retire in 30 years and want to accumulate Php 500,000 in your retirement account. How much must you invest each year to reach the goal? Assume end of the year investments and an earning rate of 12%.

• Php 2,072

• Php 8,443

• Php 14,896

• Php 20,365