Exercise 20

Consider the function whose correspondence rule is ( f(x) = x^3 – x ). If the line with equation ( y = mx + n ) cuts the graph of this function at points ( ( 0, , f(0) ) ) and ( ( 1, , f(1) ) ), then we can say of ( […]

Exercise 19

The quotient of ( left( cfrac{-8}{9} right)^3 div left( cfrac{12}{27} right)^3 ) equals to: ( left( cfrac{24}{81} right)^3 ) ( -8 ) ( cfrac{24}{81} ) ( 8 ) ( (-2)^6 ) Try to solve it before checking the answer. Answer ( -8 ) Step by Step Solution [begin{aligned}&left( frac{-8}{9} right)^3 div left( frac{12}{27} right)^3\[1em]&hspace{5em}=left( frac{-8}{9} […]

Exercise 18

The following expression,   ( cfrac{ 0.hat{6} + 0.hat{3} }{ 2.hat{2} } ),   equals to: The following expression, [ cfrac{ 0.hat{6} + 0.hat{3} }{ 2.hat{2} }, ] equals to: ( cfrac{ 81 }{ 100 } ) ( cfrac{ 20 }{ 9 } ) ( cfrac{ 9 }{ 20 } ) ( cfrac{ 2 }{ […]

Exercise 17

The numeric value of the expression:   ( cfrac{ 3 x^2 y sqrt{ 2x + y } }{ sqrt{ 4x^2 + 4xy + y^2 } } )   when   ( x = 1 )   and   ( y = -1 )   is: The numeric value of the expression: [ frac{ 3 x^2 […]

Exercise 16

Mary and Peter work together on a factory night shift. Mary has one night off every 4 days and Peter has one night off every 6 days. It they go out dancing when their nights off match, how often do they go out dancing together? 4 days 6 days 8 days 12 days 24 days […]

Exercise 15

A glass has the shape of a straight circular cylinder and its capacity is of one liter. If the height of the glass is 10 cm, what is its radius? ( cfrac{100}{ pi } ) ( cfrac{1}{ sqrt{10 pi} } ) ( cfrac{1}{10pi} ) ( 10 sqrt{pi} ) ( cfrac{ 10 sqrt{pi} }{ pi } […]

Exercise 14

In an academic term, a student submits 10 evaluations, which are qualified with grades between 0 and 5 (both inclusive). The average of the first 7 evaluations is 3.75. If the student’s final grade (FG) is the average of the 10 grades, then: (2.625 leq text{FG} leq 3.75 ) (0 leq text{FG} leq 3.75 ) […]

Exercise 13

The area of the square (ABCD) in the attached figure is 16. If (O) is the center of the square, what is the area of the shaded region? 4 8 12 2 6 Try to solve it before checking the answer. Answer 4 Step by Step Solution Let (A) be the area of the shaded […]

Exercise 12

A set has (n) different elements, and an element (a), different from the others, is added to it. If an element is randomly extracted from this latter set, what is the probability that the extracted element is (a)? (1) ( cfrac{1}{n + 1} ) (n) (0) ( cfrac{1}{n} ) Try to solve it before checking […]

Exercise 11

If ( vec{v} = (-2, , 3) )   and   ( vec{w} = (3, , -1) ), then   ( -2 vec{v} – (-3) vec{w} )   equals to: ( (2, , 3) ) ( (-5, -9) ) ( (5, , 9) ) ( (13, -6) ) ( (13, -9) ) Try to solve […]