ACT Tips and Practice

14 questions dealing with Pre-Algebra10 questions from Elementary Algebra 9 questions based on Intermediate Algebra 9 questions from Coordinate Geometry14 questions from Plane Geometry 4 Trigonometry questions60 Questions Total in 60 minutes time!

The questions assume knowledge of basic formulas and computational skills but do not require memorization of complex formulas or extensive computation

60 Math questions in 60 minutes means:

Don’t waste time on any one problem, spend your time doing as many problems as you can

The questions are arranged in order of difficulty: easier questions at the beginning, harder questions at the end

Don’t PANIC: answering only half of the questions right will give you a score of 20 on the Math Section

Go Through The Test Twice

Take 45 minutes to work through the test¥Answer the questions that you know how to do¥Guess on the questions you know you’ll never get¥Mark the harder questions that you’ll come back to later

Spend the last 15 minutes going over the test again

¥Answer the questions you skipped¥Make sure you have answered every question¥Spend any remaining time checking your work

ALL PROBLEMS ON THE ACT CAN BE

SOLVED WITHOUT USING A CALCULATOR

¥You may use a four-function, scientific, or graphing calculator on the Math test

¥Calculators, such as TI-89 and TI-92 are NOT permitted (see page 4 in the ACT prep booklet)

¥Bring a calculator that you know how to use – bringing a more powerful calculator that you do not know how to use isn’t going to help you

Read the problem carefullyPay attention to what the question asks you

to findWatch for unnecessary informationLabel the figures with numbers or lettersDraw a picture

1. There’s more than one way to solve these problems

2. It’s a timed test – find a quick and reliable way to solve the problem

3. Do your work in your test booklet

4. Be careful using your calculator – it’s easy to push the wrong button

5. Don’t get involved in long, complicated, or tricky calculations

Make sure you answered the question that was asked

Each of the wrong answers represents a common mistake that you might have made

If your answer isn’t one of the choices, reread the question and check your work

Take advantage of the multiple-choice format and try each answer until you find the one that works.

WARNING: Doing it this way will take more time.

BACKSOLVE

The greatest common divisor of 84, 90, and 66 (that is, the largest exact divisor of all three numbers) is:

A. 6

B. 12

C. 18

D. 36

E. 90

90 does not go into 84 – eliminate answer E36 does not go into 84 – eliminate answer D18 does not go into 84 – eliminate answer C12 does not go into 90 – eliminate answer B

6 must be the correct answer and it checks

84 = 2٠2٠3٠7 90 = 2٠3٠3٠5 66 = 2٠3٠11

2٠3 = 6CORRECT ANSWER: A

F. 0

G. 2

H. 4

J. 8

K. 10

If (3)12x, then x = ?

Let x = 0 (3 )12

(30)12

(30)12

312

x

Let x = 2 (3 )1 2

(3 2)1 22.1012.414

x

Let x = 4 (3 )12

(34)12

(32)12

5122.2362.414

x

Let x = 8 (3 )1 2

(3 8)1 22.4142.414

x

F. 0

G. 2

H. 4

J. 8

K. 10

If (3)12x, then x = ?

Correct Answer: J

2

(3 )12

3 (12)

3 (12)(12)

3 12 22

3 322

3 3 4238

x

x

x

x

x

x

GUESSTIMATEIf you can estimate the correct answer, then you should be able to eliminate at least one or two answer choices.

What is 2% of 60?

A. 120

B. 12

C. 1.2

D. 0.12

E. 0.012

120 is greater than 60 – eliminate answer A12 is too large – eliminate answer B

0.012 is too small – eliminate answer E

60 x 0.02 = 1.2

CORRECT ANSWER: C

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?

One 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 below:X looks too big to be 5°- eliminate answer AX looks too small to be either 60° or 55° - eliminate answers E and D

In the figure to the right, what is the value of x?

125° 85°

x

A. 5°

B. 30°

C. 40°

D. 55°

E. 60° 180 –125 = 55

55°

180 - 85 = 95

95°

180 – 55 – 95 = 30CORRECT ANSWER: B

Lola is making the circle graph below showing the number of students at each grade level in her high school. What should be the measure of A?

F. 99°G. 120°H. 133°J. 167°K. 240°

A°

240 freshmen

200 sophomores

150 juniors

130 seniors

By looking at the figure below:A looks larger than 99°– eliminate answer FA looks smaller than 240° – eliminate answer K

Total number of students = 720

Total number of freshmen = 240

Total number of degrees in a circle = 360°

number of freshmen degrees in Anumber of students degrees in circle240720 360240(360) 72086400 720120

A

AA

A

CORRECT ANSWER: G

Some problems are hard because they’re general or abstract, so replace variables with specific numbers

If kx + k = 0, and k>1, then x = ?

A. 0

B. -1

C. 1

D. -k

E. k

Pick a value for k that is greater than 1

Let k = 2

kx + k = 0

2x + 2 = 0

2x = -2

x = -1

Let k = 5

kx + x = 0

5x + 5 = 0

5x = -5

x = -1

If kx + k = 0, and k>1, then x = ?

A. 0

B. -1

C. 1

D. -k

E. k

kx + k = 0

k(x+1) = 0

k= 0 OR x+1 = 0

k= 0 OR x = -1

CORRECT ANSWER: B

For all a 0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane?

. 0

.

.

.

. 2

FaGbbHabJa

K a

11 22

1 2

1 2

(,) and (,)xy xyyymxx

Let a = 1 and b = 2 (1,2) and (-1,2) 22001(1)2

Let a = -1 and b = -2 (-1,-2) and (1,-2) 2(2) 0 011 2

For all a 0, what is the slope of the line segment connecting (a,b) and (-a,b) in the usual (x,y) coordinate plane?

. 0

.

.

.

. 2

FaGbbHabJa

K a

11 22

1 2

1 2

(,) and (,)

(,) and (,)0

()2

xy xyyymxxab abbbmaaa

CORRECT ANSWER: F

Practice Questions

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

de

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 = 2828 (.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 323

221322

xy

xy

xy

Remember the equation: y = mx + b

1232

m

b

CORRECT ANSWER: A

1. 2

. 13. 2

. 2. 3

A

B

C

DE

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 D30 120 180 – 120 = 6060

180 – 30 – 60 = 9090

CORRECT ANSWER: C

and

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

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

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

To cancel the y value, multiply eqn. 2 by 10 and add to eqn. 1

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 – 12xy = -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

123 45234 56

?

CORRECT

ANSWER: C

1. 617. 2713. 187. 95. 6

A

B

C

D

E

1 2 3 202 3 4 301 2 4 42 3 3 61 8 22 9 31 8 62 9 91 22 99 4 13

18 18 18

Question 8

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

A. 10yB. -3y2 + 25yC. 3y2 + 7yD. 3y2 + 25yE. 3y2 + 27y

26y – (-10y) – 3y(-y+3) =26y +10y +3y2 – 9y =3y2 +27y

CORRECT ANSWER: E

Question 9

A B30

100

DC

A. 65

B. 70

C. 75

D. 80

E. 85

Question 10

In shown below, BD bisects ABC. The measure of ABCis 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 ABCis 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 = c x

R 3 S

4

T

5

sin oppositexhypotenuse

4sin5x

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

ABC

DE

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

O6

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

6A

60

B

6036012

arc xcircle

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

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 2

2 1 2 1( ) ( )x x y y . 4

. 8

. 6. 8

. 4 2

A

BCD

E

2 2

2 2

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

4 4

32 16242

CORRECT ANSWER: E

Question 15

CORRECT ANSWER: E

Question 16

What 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 17

In 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 17

In 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 = = 3.14

Areasquare = 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

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 or 82=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 21One angle, A, has 3 times the measure of its supplement, B. What is the degree measure of A?A. 112.5°B. 120°C. 135°D. 150°E. 157.5°

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. 121B. 55C. 235D. 12

5E. 7

Probability of drawing a green jelly bean:

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

CORRECT ANSWER: C

Question 23

For 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. 43B. 41C. 41D. - 4

E. -4

BA

riseslope = run

1C

14

Question 25

In the figure below, D is a point on AB and E is a pointon BC such that DE AC. If DB = 4, AB = 10, BC = 20,what is the length of EC?

A. 4B. 6C. 8D. 10E. 12

B

E

C

D

A

4 1020-x 204 20 10(20 )80 200 10120 10

12

xx

xx

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

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