Act Math Practice

Front 1

Back 1

E. 100

Front 2

The first term is 1 in the geometric sequence1, −3, 9, −27, .... What is the SEVENTH term of thegeometric sequence?

A. −243

B. −30

C. 81

D. 189

E. 729

Back 2

E. 729

Front 3

Students studying motion

observed a cart rolling at a

constant rate along a straight line. The table belowgives the distance, d feet, the cart was from a referencepoint at

1-second intervals from t = 0

seconds tot = 5 seconds.

Which of the following equations represents thisrelationship

between d and t ?

A. d=00t+14

B. d=06t+08

C. d=06t+14

D. d=14t+06

E. d=34t

Back 3

C. d=06t+14

Front 4

This month, Kami sold 70 figurines in 2 sizes. Thelarge figurines sold for $12 each, and the smallfigurines sold for $8 each. The amount of money hereceived from the sales of the large figurines was equal to the amount of money he received from the sales ofthe small

figurines. How many large figurines did

Kami sell this month?

A. 20

B. 28

C. 35

D. 42

E. 50

Back 4

B. 28

Front 5

If a, b, and c are positive integers such that a^b =x and c^b=y, then xy=?

Back 5

Front 6

The equation y=ax^2 +bx+c is graphed in thestandard (x,y)

coordinate plane below for real values ofa, b, and c. When

y = 0, which of the following best

describes the solutions for x ?

F) 2 distinct positive real solutions

G) 2 distinct negative real solutions

H) 1 positive real solution and 1 negative real solution

J) 2 real solutions that are not distinct

K) 2 distinct solutions that are not real

Back 6

H) 1 positive real solution and 1 negative real solution

Front 7

What is the product of the complex numbers (−3i + 4) and (3i + 4) ?

Back 7

C. 25

Front 8

Which of the following is the graph of the region1 < x + y < 2 in the

standard (x,y) coordinate plane?

Back 8

Front 9

Which of the following describes a true relationship between the

functions f(x) = (x − 3)^2 + 2

and g(x) = (1/2) x + 1 graphed below in the standard (x,y)

coordinate plane?

F) f(x) = g(x) for

exactly 2 values of x

G) f(x) = g(x) for exactly 1 value of x

H) f(x) < g(x) for all x

J) f(x) > g(x) for all x

K) f (x) is the inverse of g(x)

Back 9

F) f(x) = g(x) for exactly 2 values of x

Front 10

What is the slope of CD ?

A)−3

B) −1

C) 1

D) 5/21

E) 3/2

Back 10

B) −1

Front 11

When ABCD is reflected over the y-axis to A′B′C′D′,what are the

coordinates of D′ ?

F. (−12, 1)

G. (−12,−1)

H. ( 12,−1)

J. (1,12)

K. (1,−12)

Back 11

F. (−12, 1)

Front 12

Given f(x) = x - (1/x) and g(x) = 1/x What is f(g(1/2))?

F) -4

G) -3/2

H) -2/3

J) 0

K) 3/2

Back 12

Front 13

A formula to estimate the

monthly payment, p dollars, on a

short-term loan (given to the left) where a dollars is the amount of the loan, r is the annual interest rate expressed as a decimal, and y years is the length of the loan. When a is multiplied by 2,what is the effect on p ?

A) p is divided by 6

B) p is divided by 2

C) p does not change

D) p is multiplied by 2

E) p is multiplied by 4

Back 13

D) p is multiplied by 2

Front 14

The points E(6,4) and F(14,12) lie in the standard (x,y) coordinate plane shown below. Point D lies on line segment EF between point E and point F such that the length of line segment EF is 4 times the length of line segment DE . What are the coordinates of point D ?

F. ( 7, 5)

G.( 8, 6)

H.( 8, 8)

J.(10, 8)

K.(12,10)

Back 14

G.( 8, 6)

Front 15

Back 15

D. 27

Front 16

The shaded region in the graph

below represents thesolution set to which of the following systems of

−5 < 1 − 3x < 10 inequalities?

Back 16

Front 17

Which of the following is the

solution statement forthe inequality shown below?

−5 < 1 − 3x < 10

Back 17

Front 18

After completing the poll, Kelly wondered how manyof the

students polled had skied both cross-country anddownhill. How many of the students polled

indicated that they had skied both cross-country and downhill?

A. 73

B. 65

C. 47

D. 18

E. 8

Back 18

E. 8

Front 19

Which of the following number line graphs shows thesolution set to the inequality

⎪x − 5⎪ < −1 ?

Back 19

Front 20

Back 20

Front 21

The sum of the real numbers x and y is 11. Their difference is 5. What is the value of xy ?

F.3

G.5

H.8

J. 24

K. 55

Back 21

J. 24

Front 22

What is the slope of the line through (–5,2) and (6,7) inthe standard (x,y) coordinate plane?

F. 9

G. 5

H. –5

J. 5/11

K. -5/11

Back 22

J. 5/11

Front 23

The diameter, d centimeters, of the metal polesGoodpole Manufacturing produces must satisfy theinequality |d – 3| ≤ 0.001. What is the

maximumdiameter, in centimeters, such a metal pole may have?

F . 1.4995

G. 1.5005

H. 2.999

J. 3.000

K. 3.001

Back 23

K. 3.001

Front 24

The slope of the line with equation y = ax + b is greaterthan the slope of the line with equation

y = cx + b.Which of the following statements must be true aboutthe relationship between

a and c ?

Back 24

Front 25

Two hoses are used to fill the pool. Twice as many gal-lons of water per minute flow through one of the hosesas through the other. Both hoses had been on for12 hours and had filled the pool to the 4-foot markwhen the hose with the faster flow stopped working.The hose with the

slower flow then finished filling thepool to the 5-foot mark.

Which of the following graphsshows the relationship between the time spent fillingthe pool and the height of the water in the pool?

Back 25

Front 26

The inequality 3(x + 2) > 4(x – 3) is equivalent towhich of the following

inequalities?

F) x<–6

G) x<5

H) x< 9

J) x<14

K) x<18

Back 26

K) x<18

Front 27

In the standard (x,y) coordinate plane, the midpoint of line segment AB is (4,–3) and A is located at (1,–5). If (x,y) are thecoordinates of B, what is the value of x + y ?

A. 19

B. 8

C. 6

D. –1.5

E. –3

Back 27

C. 6

Front 28

Back 28

Front 29

Tickets for the Senior Talent Show at George Washing-ton Carver High School are $3 for adults and $2 forstudents. To cover

expenses, a total of $600 must becollected from ticket sales for the show. One of the fol-lowing graphs in the standard (x,y)

coordinate plane,where x is the number of adult tickets sold and y is thenumber of student tickets sold, represents all the poss-ible combinations of ticket sales that cover at least$600 in expenses. Which graph is it?

Back 29

Front 30

Back 30

Front 31

The point (2,5) is shown in the standard (x,y) coordinate plane below. Which of the following is another point on the line through the point (2,5) with a slope of -2/3?

A) (-1,3)

B) ( 0, 8)

C) (4,2)

D) (5,3)

E) (5,7)

Back 31

D) (5,3)

Front 32

The number line graph below is the graph of which ofthe

following inequalities?

A. –1 ≤ x and 3 ≤ x

B. –1 ≤ x and 3 ≥ x

C. –1 ≤ x or 3 ≤ x

D. –1 ≥ x or 3 ≤ x

E. –1 ≥ x or 3 ≥ x

Back 32

D. –1 ≥ x or 3 ≤ x

Front 33

All of the following graphs have equal scales on theaxes. One of the graphs shows only points for which they-coordinate is 1 less than the square of the

x-coordinate.Which one?

Back 33

Front 34

A) -70

B) -36

C) 0

D) 36

E) 70

Back 34

A) -70

Front 35

Back 35

A) 8

Front 36

A function f is an odd function if and only iff(–x) = –f(x) for every value of x in the domain of f.One of the functions graphed in the standard (x,y)coordinate plane below is an odd function. Which one?

Back 36

Front 37

Back 37

J) 125