UPCAT Math Challenge

The average of 7 numbers is 24. The smallest of the numbers is 2 and the largest of the numbers is 31. What is the average of the middle 5 numbers?

• 25

• 26

• 27

• 28

Two side lengths of a triangle are 5 and 6, which of the following CANNOT be the length of the third side?

• 3

• 6

• 9

• 12

Eric wishes to shift the graph of the function ƒ(x) = x² four places to the right and six places down from the origin (0,0). Which equation represents this translation?

• $ƒ(x)=x–\ 4^2+6$

• $ƒ(x)=(x−4)^2−6$

• $ƒ(x)=(x^2−4)^2−6$

• $ƒ(x)=x+4^2–6$

What is the slope intercept form of $(13x−5x)+12−2y=6$  ?

•  $y=3x–9$  

•  $y=4x+3$  

•  $y=6x+2$  

•  $y=-2x+5$  

The coordinates (−3, 5) and (3, 5) designate the diameter of a circle, what is its circumference?

• 2π

• 4π

• 6π

• 8π

What is the solution set of | 2(x – 1) – 15 | = 7?

• { 5 }

• { 12 }

• { 5,12 }

• { -5,12 }

A and B are reciprocals (when multiplied together their product is 1). If A < −1, then B must be which of the following?

• 0 < B < 1

• -1 < B < 0

• B < -1

• B < 0

Which of these is true for all real numbers x and y such that x > 0 and y < 0?

• xy > 0

• x + y > 0

• $x^2+y^2>0$

• x – y < 0

At what point on the Cartesian plane do the following two lines intersect?

 $\frac{y}{3}-\frac{7}{3}=x$  and $\frac{y}{3}+\frac{4}{3}=x$  

• (4, 3)

• (6, 2)

• The lines do not intersect.

• (5, -2)

The slope of the line represented by the equation 2(x − 3) − 6y = 10 is equal to what?

• – 1/2

• 1/3

• 1/3

• 2