ACT Review #5

A number, x, is decreased by 40% then increased by 25%. What is the final result in terms of x?

• 0.55x

• 0.575x

• 0.65x

• 0.7x

• 0.75x

Tags

CCSS.6.EE.B.6

 $\left(\frac{1}{3}y^{\frac{1}{2}}\right)^4\times\left(2x^2y\right)^2$  

•  $\frac{4}{81}x^4y^{\frac{10}{2}}$  

•  $\frac{1}{81}x^2y^3$  

•  $\frac{4}{81}x^5y^{\frac{9}{2}}$  

•  $\frac{1}{81}x^2y^4$  

•  $\frac{4}{27}x^4y^{\frac{8}{3}}$  

Tags

CCSS.HSA.APR.A.1

The expression  $\left(x+y\right)\left[z-\left(x-y\right)\right]$  is equivalent to which of the following?

•  $xz-x^2+2xy+y^2$  

•  $2xz+x^2-yz+y^2$  

•  $xz-x^2+yz+y^2$  

•  $xz+x^2-yz-y^2$  

•  $xyz+y^2-xy+yz+y^2$  

Tags

CCSS.HSA.APR.A.1

There are 32 marbles in a jar: 14 blue, 10 red, 5 green, and 3 yellow. Sally pulls one marble, randomly, from the jar. Without replacing the marble, she pulls another marble. What is the probability that both marbles will be red?

• $\frac{40}{426}$

• $\frac{41}{456}$

• $\frac{43}{476}$

• $\frac{44}{476}$

• $\frac{45}{496}$

If  $x+y=7$  and  $x-y=3$  , what is  $x^2-y^2=$  ?

• 4

• 21

• 25

• 36

• 40

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

The circumference of a large wedding cake is 60 inches. If the cake is divided evenly into 12 slices, what is the length of the arc, in inches, made by 5 combined slices?

• 12

• 13

• 15

• 20

• 25

Tags

CCSS.HSG.C.B.5

A rectangle measures 65 inches by 77 inches. What is the length of the diagonal of the rectangle (rounded to the nearest hundredth)?

• 100.77

• 110.77

• 125.07

• 134.67

• 137.77

Tags

CCSS.8.G.B.8

If  $f\left(x\right)=x^2+2x+2$ , what is  $f\left(x+h\right)$  ?

•  $2x^2+4hx+h^2-2x-2h$  

•  $x+h^2+2xh+2+h$  

•  $x^2+2x+2xh+2h+h^2+2$  

•  $x^2+4xh+4h^2+2x$  

•  $2x^2+2xh+2h^2+2x+2$  

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

In the figure above, lines d and f are parallel and the angle measures are as given. What is the value of x?

• 35

• 60

• 85

• 100

• 120

Tags

CCSS.8.G.A.5

Which of the following represents the equation of the line that passes through the point (2,3) with a slope of $-\frac{1}{3}$  ?

•  $y=2x+4$  

•  $y=4x+2$  

•  $y=-\frac{1}{3}x+\frac{11}{3}$  

•  $y=-3x+\frac{11}{3}$  

•  $y=-\frac{2}{3}x+\frac{11}{3}$