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Points N and J have coordinates (-1, -1) and (3,3) respectively.

What is the length of line NJ?

(the distance between 1 1 2 2( , ) ( , )x y and x y )

Distance Formula = 2 22 1 2 1( ) ( )x x y y

. 4

. 8

. 6

. 8

. 4 2

A

B

C

D

E

2 2

2 2

(3(1)) (3(1))

4 4

32 16242

CORRECT ANSWER: E

Question 15

2x5 3x4y6

Calculator or Zoom?

34 53

Calculator or Zoom?

73 54

25 (33 – 43)

7x2y4 (2x2 – 7xy4 + 3xy)

(3x – 5y2)2

What is the value of x in the solution for the system of equations below?

2x + 5y = 20

6x – ½ y = 29

A. 4

B. 5

C. 6

D. 15

E. 20

Question 7

ZOOM?

What is the value of x in the solution for the system of equations below?

2x + 5y = 20

6x – ½ y = 29

2x + 5y = 20

6x – ½ y = 29 multiply by 10

solve for x x = 5

2x + 5y = 20

60x - 5y = 290

add equations together 62x = 310

What is the value of x in the solution for the system of equations below?

2x + 5y = 20

6x – ½ y = 29

12x – y = 58

-y = 58 – 12x

y = -58 + 12x

2x + 5(-58+12x) = 20

solve for y

substitute into 1st equation

solve for x

2x + -290 + 60x = 20

62x + -290 = 20

62x = 310

x = 5

CORRECT ANSWER: B

2x – 4 = 8

2x – 4 < 8

2x – 4 > 8

√576

4√1296

6√64

A

B C

3

4

5

Cos A= Sin A=Tan A=Cos C=Sin C=Tan C=

Will you be asked for Sin B?

A

B C

3

4

5

Use Sin to findAngle A

Use Cos to findAngle A

A

B C

5

12

13

Use Sin to findAngle C

Use Cos to findAngle C

A

B C

5

12

13

Use Sin to findAngle A

Use Cos to findAngle A

Imaginary Numbers

1. i14 Calculator or zoom?

2. i7

3. i20

1. i21

1. i(2 + i)

2. 6i(5 – 4i)

3. (2 + 8i) + (-3 – 9i)

4. (6 – 5i) – (3 + 12i)

5. (2 – i)(4 + 3i)

If the area of a circle is , what is the length of its circumference?

Areacircle = r2 Circumference = 2r = r2

1 = r2

1 = r

C = 2(1)

C = 2

A. 1

B. 2

C.

D. 2

E. 3

CORRECT ANSWER: D

Question 6

GUESSTIMATE (cont.)

A

B 3 meters C

? 4 meters

F. 12 G. 7 H. 5 J. 3 K. 7

12, 7, and 5 are longer than the hypotenuse – eliminate answers F, G, and H

In the right triangle below, how many meters long is AB?

GUESSTIMATE (cont.)

A

B 3 meters C

? 4 meters

F. 12 G. 7 H. 5 J. 3 K. 7

2 2 2

2 2 2

2

2

3 4

9 16

7

7

a b c

b

b

b

b

CORRECT ANSWER: K

In the right triangle below, how many meters long is AB?

EYEBALLOne the ACT, the diagrams are “not necessarily” drawn to scale, but usually they’re quite accurate, so you could eliminate certain answer choices by sizing things up with your eyes

In the figure below, what is the value of x?

125° 85°

xA. 5°

B. 30°

C. 40°

D. 55°

E. 60°

By looking at the figure:

X looks too big to be 5°- eliminate answer A

X looks too small to be either 60° or 55° - eliminate answers E and D

EYEBALL (cont.)

In the figure below, what is the value of x?

125° 85°

xA. 5°

B. 30°

C. 40°

D. 55°

E. 60° 180 –125 = 55

55°

180 - 85 = 95

95°

180 – 55 – 95 = 30

CORRECT ANSWER: B

C

A

D

B

412

3

A. 13

B. 17

C. 19

D. 24

E. 25

Question 1

In the figure below, CA is perpendicular to AB and CB isperpendicular to BD; AB is 3 units long, AC is 4 units long,and BD is 12 units long. How many units long is CD?

C

A

D

B

412

3

222

222

2

2

34

916

25

5

abc

CB

CB

CB

CB

22 2

2

2

5 12

25 144

169

13

CD

CD

CD

CD

CORRECT ANSWER: A

ABC is a 3-4-5 right triangle and BCD is a 5-12-13 right triangle

5

13

In the figure below, line m is parallel to line n, and line t is a transversal crossing both m and n. Which of the following lists has 3 angles that are all equal in measure?

t

a m

n

b c

d

e

A. a,b,d

B. a,c,d

C. a,c,e

D. b,c,d

E. b,c,e

CORRECT ANSWER: A

Question 2

A shirt that originally cost $35 is on sale at 20% off. If the sales tax on shirts is 5% of the purchase price, how much would it cost to buy the shirt at its sale price?

A. $ 7.35

B. $20.00

C. $26.60

D. $29.40

E. $29.75

35 (.20) = 7

35 – 7 = 28

28 (.05) = 1.40

28 + 1.40 = 29.40

35 (.80) = 28

28 (1.05) = 29.40

CORRECT ANSWER: D

Question 3

What is the slope of the line x = 2y +3?

x = 2y + 3 x – 3 = 2y 3

23

2213

22

xy

xy

xy

y = mx + b

1

23

2

m

b

CORRECT ANSWER: A1

. 2

. 1

3.

2. 2

. 3

A

B

C

D

E

Question 4

In the figure below, A, C, and D are collinear. If the measure of A is 30 and the measure ofBCD is 120, what is the measure of B?

A

B

C D

A. 30

B. 60

C. 90

D. 120

E. 150

Question 5

In the figure below, A, C, and D are collinear. If the measure of A is 30 and the measure of BCD is 120, what is the measure of B?

A

B

C D

30

120

180 – 120 = 60

60

180 – 30 – 60 = 9090

CORRECT ANSWER: C

123 45

234 56

?

CORRECT

ANSWER: C

1. 617. 2713. 187. 95. 6

A

B

C

D

E

1 2 3 20

2 3 4 30

1 2 4 4

2 3 3 6

1 8 2

2 9 3

1 8 6

2 9 9

1 2

2 99 4 13

18 18 18

Question 8

Regular calculator or ZOOM?

For all y, 26y – (-10y) – 3y(-y+3) = ?

A. 10y

B. -3y2 + 25y

C. 3y2 + 7y

D. 3y2 + 25y

E. 3y2 + 27y

26y – (-10y) – 3y(-y+3)

26y +10y +3y2 – 9y

3y2 +27y

CORRECT ANSWER: E

Question 9

A B30

100

DCA. 65

B. 70

C. 75

D. 80

E. 85

Question 10

In shown below, BD bisects ABC. The measure of ABC

is 100 , and A measures 30 . What is the measure of BDC?

ABC

A B30 50

DC

A. 65

B. 70

C. 75

D. 80

E. 85

50100

180 – 100= 80

m BDC = 80

180 – 30 – 50 = 100

80°

CORRECT ANSWER: D

In shown below, BD bisects ABC. The measure of ABC

is 100 , and A measures 30 . What is the measure of BDC?

ABC

In the figure below, S is a right angle, RS is 3 units long, and ST is 4 units long. If the measure of R is x, then sin x = ?

x

R 3 S

4

T 3.53.44.55.45.3

A

B

C

D

E

Question 11

In the figure below, S is a right angle, RS is 3 units long, and ST is 4 units long. If the measure of R is x, then sin x = ?

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = cx

R 3 S

4

T

5

sinoppositexhypotenuse

4

sin5x

RST is a 3-4-5 right triangle

CORRECT ANSWER: C

In the figure below, the lengths of DE, EF, and FG are given, in units. What is the area, in square units, of triangle DEG?

D 12 E 7 F

G

10

.29

.47.5

.60

.6 149

.120

A

B

C

D

E

Question 12

In the figure below, the lengths of DE, EF, and FG are given, in units. What is the area, in square units, of triangle DEG?

D 12 E 7 F

G

10

AreaTriangle = ½ base x height

= ½ (12) (10)

= 60CORRECT ANSWER: C

O

6

A

60

B

A.

B. 2

C. 6

D. 12

E. 36

Question 13

In the figure below, A and B lie on the circle centered at O,OA is 6 units long, and the measure of AOB is 60°. Howmany units long is minor arc AB?

Circumference = 2r

C = 26

C = 12

O

6

A

60

B

60

36012

arc x

circle

degrees = arc

60(12) = 360 x

720 = 360 x

2 = x

CORRECT ANSWER:

B

A

C 12 B

13

12. 513. 1212. 135. 125. 13

A

B

C

D

E

Question 14

In the right triangle below, the length of AB is 13 units and the length of CB is 12 units. What is the tangent of A?

A

C 12 B

13

a2 + b2 = c2

122 + b2 = 132

144 + b2 = 169

b2 = 25

b = 5

5

tanoppositexadjacent

12tan5x

CORRECT ANSWER: A

CORRECT ANSWER: E

Question 16What is the cost in dollars to carpet a room x yards long and y yards wide if the carpet costs two dollars per square foot?

A. xy

B. 2xy

C. 3xy

D. 6xy

E. 18xy

y yards = 3y feet

x yards = 3x feet

Arearectangle= length x width

= 3x(3y) = 9xy square feetTotal Cost = area x price

= 9xy (2) = 18xy

Question 17In the figure below, the largest possible circle is cut out of a square piece of tin. The area of the remaining piece of tin is approximately (in square inches)

A. 0.14

B. 0.75

C. 0.86

D. 1.0

E. 3.14

2 inches

CORRECT ANSWER: C

Question 17In the figure below, the largest possible circle is cut out of a square piece of tin. The area of the remaining piece of tin is approximately (in square inches)

A. 0.14

B. 0.75

C. 0.86

D. 1.0

E. 3.14

2 inchesAreacircle = r2

12 = = 3.14Areasquare = s2

22 = 4

Areapiece = Areasquare - Areacircle 4 – 3.14 =

0.86

1

CORRECT ANSWER: E

Question 18

Which of the following is equal to 3.14 x 106?

A. 314

B. 3140

C. 31,400

D. 314,000

E. 3,140,000

3.1400000000

3140000.0000

Regular calculator or ZOOM or NEITHER?

CORRECT ANSWER: E

Question 19

Find the last number in the series: 8, 4, 12, 6, 18, 9,?

A. 19

B. 20

C. 22

D. 24

E. 27

84 8-4=4 or82=4

412 4+8=12 or 4x3=12

126 12-6=6 or 122 = 6

6 18 6+12=18 or 6x3=18

189 18-9=9 or 182 = 9

9x3=27

CORRECT ANSWER: A

Question 20 Lyndsey receives grades of 91, 88, 86, and

78 on four tests. What grade must she receive on her fifth test to have an average test score of 85?

A. 82

B. 83

C. 84

D. 85

E. 86

Let x = the fifth test score

(91 + 88 + 86 + 78 + x ) 5 = 85

343 + x = 425

x = 82

CORRECT ANSWER: C

Question 21

One angle, A, has 3 times the measure of its supplement, B. What is the degree measure of A?

A. 112 ½°

B. 120°

C. 135°

D. 150°

E. 157 ½°

Let x = the measure of B

then 3x = the measure of A

x + 3x = 180°

4x = 180°

x = 45°

B = 45°

A = 135°

CORRECT ANSWER: D

Question 22

A bag contains 4 red jelly beans, 5 green jelly beans, and 3 white jelly beans. If a jelly bean is selected at random from the bag, what is the probability that the jelly bean selected is green?

1A.

121

B. 55

C. 235

D. 125

E. 7

Probability of drawing a green jelly bean

number of green jelly beans 5total number of jelly beans 12

CORRECT ANSWER: C

Question 23For all positive values of a, b, and c with a<b

and a>c, which of the following MUST be true?

I. a+b>c

II. 2a>c

III. a+c>b

A. I only

B. II only

C. I and II only

D. II and III only

E. I, II, and III

I. a and b are both greater than c, so their sum will also be – TRUE

III. If c=2, a=4, and b=10, then a+c<b - FALSE

II. a>c, so 2a>c – TRUE

c < a < b

CORRECT ANSWER: C

Question 24The scales on both axes of the standard (x,y) coordinate

plane below are the same. Of the following, which is

the best estimate for the slope of AB?

A. 4

3B.

41

C. 41

D. -4

E. -4

B

A

riseslope =

run

1

C

14

Question 25In the figure below, D is a point on AB and E is a point

on BC such that DE AC. If DB = 4, AB = 10, BC = 20,

what is the length of EC?

A. 4

B. 6

C. 8

D. 10

E. 12

B

E

C

D

A

4 1020-x 204 20 10(20 )

80 200 10

120 10

12

x

x

x

x

B

20-x

E

x

C

4

D

6

A

CORRECT ANSWER: E

10

20

ABC and DBE are similar triangles,

so their sides are in proportion

Things to Remember on the Math ACT

Don’t read the directions

Bring a calculator that you know how to use

Read the question carefully

Pay attention to what the question asks you to find

Watch for unnecessary information

Draw a picture

Pace yourself (60 questions/60 minutes)

Things to Remember on the Math ACT

Do the easy questions first, then try the hard ones

Show some work and circle your answers in your test booklet

Don’t waste too much time on one problem

Eliminate wrong answers before guessing

Answer every question

Check your work

Work for the whole 60 minutes