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ACT PREP. . MATH. Educational Talent Search and Upward Bound Forward Service Corporation. Content.  14 questions dealing with Pre-Algebra  10 questions from Elementary Algebra  9 questions based on Intermediate Algebra  9 questions from Coordinate Geometry

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ACT PREP

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ACT PREP

## 

MATH

Educational Talent Search and Upward Bound

Forward Service Corporation

Content

14 questions dealing with Pre-Algebra

 10 questions from Elementary Algebra

 9 questions based on Intermediate Algebra

 9 questions from Coordinate Geometry

 14 questions from Plane Geometry

 4 Trigonometry questions

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

Pace Yourself

• 60 questions

60 minutes

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

The questions are arranged in order of difficulty

RELAX: answering only half of the questions right onwill give you a score of 20 on the Math Section

Pace Yourself

Go Through The Test Twice

• Take 45 minutes to go 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

Calculators

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

Understand the Problem

• Read the problem carefully

• Pay attention to what the question asks you to find

• Watch for unnecessary information

• Label the figures with numbers or letters

• Draw a picture

Solving the Problem

• There’s more than one way to solve these problems

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

• Do your work in your test booklet

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

• 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

When You

Get Stuck

BACKSOLVE

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.

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

• 6

• 12

• 18

• 36

• 90

84 = 2٠2٠3٠7 90 = 2٠3٠3٠5 66 = 2٠3٠11

2٠3 = 6

90 does not go into 84 – eliminate answer E

36 does not go into 84 – eliminate answer D

18 does not go into 84 – eliminate answer C

12 does not go into 90 – eliminate answer B

6 must be the correct answer and it checks

BACKSOLVE (cont)

• F. 0

• G. 2

• 4

• J. 8

• K. 10

BACKSOLVE (cont)

• F. 0

• G. 2

• 4

• J. 8

• K. 10

GUESSTIMATE

If 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?

60 x 0.02 = 1.2

• 120

• 12

• 1.2

• 0.12

• 0.012

120 is greater than 60 – eliminate answer A

12 is too large – eliminate answer B

0.012 is too small – eliminate answer E

GUESSTIMATE (cont.)

A

? 4 meters

B 3 meters C

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

GUESSTIMATE (cont.)

A

? 4 meters

B 3 meters C

EYEBALL

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

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?

• 30°

• 40°

• 55°

• 60°

x

125° 85°

EYEBALL (cont.)

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

x

• 30°

• 40°

• 55°

• 60°

125° 85°

55°

95°

180 –125 = 55

180 - 85 = 95

180 – 55 – 95 = 30

EYEBALL (cont.)

By looking at the figure:

A looks larger than 99°– eliminate answer F

A looks smaller than 240° – eliminate answer K

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°

240 freshmen

A

200 sophomores

130 seniors

150 juniors

EYEBALL (cont.)

Total number of students = 720

Total number of freshmen = 240

Total number of degrees in a circle = 360°

PICK NUMBERS

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 = ?

Pick a value for k that is greater than 1

• 0

• -1

• 1

• -k

• k

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

PICK NUMBERS (cont.)

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

• 0

• -1

• 1

• -k

• k

kx + k = 0

k(x+1) = 0

k= 0 OR x+1 = 0

k= 0 OR x = -1

PICK NUMBERS (cont.)

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?

PICK NUMBERS (cont.)

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?

Practice

Questions

Question 1

D

C

• 13

• 17

• 19

• 24

• 25

4

12

A

3

B

13

D

C

5

4

12

A

3

B

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

Question 2

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?

• a,b,d

• a,c,d

• a,c,e

• b,c,d

• b,c,e

a

m

n

b c

d

e

t

Question 3

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?

35 (.20) = 7

35 – 7 = 28

• \$ 7.35

• \$20.00

• \$26.60

• \$29.40

• \$29.75

28 (.05) = 1.40

28 + 1.40 = 29.40

35 (.80) = 28

28 (1.05) = 29.40

Question 4

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

y = mx + b

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?

• 30

• 60

• 90

• 120

• 150

B

A

C D

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?

B

180 – 30 – 60 = 90

90

30

60

120

A

C D

180 – 120 = 60

Question 6

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

• 1

• 2

• 2

• 3

Areacircle = r2 Circumference = 2r

 = r2

1 = r2

1 = r

C = 2(1)

C = 2

Question 7

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

2x + 5y = 20

6x – ½ y = 29

• 4

• 5

• 6

• 15

• 20

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

2x + 5y = 20

60x - 5y = 290

multiply by 10

add equations together 62x = 310

solve for x x = 5

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

2x + 5y = 20

6x – ½ y = 29

solve for y

12x – y = 58

-y = 58 – 12x

substitute into 1st equation

y = -58 + 12x

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

solve for x

2x + -290 + 60x = 20

62x + -290 = 20

62x = 310

x = 5

Question 8

Question 9

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

• 10y

• -3y2 + 25y

• 3y2 + 7y

• 3y2 + 25y

• 3y2 + 27y

26y – (-10y) – 3y(-y+3)

26y +10y +3y2 – 9y

3y2 +27y

Question 10

C

• 65

• 70

• 75

• 80

• 85

D

100

30

A B

C

D

• 65

• 70

• 75

• 80

• 85

80°

100

50

50

30

A B

180 – 30 – 50 = 100

180 – 100= 80

m BDC = 80

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 = ?

T

4

x

R 3 S

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 = ?

T

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = c

5

4

x

R 3 S

RST is a 3-4-5 right triangle

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?

G

10

D 12 E 7 F

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?

G

10

D 12 E 7 F

AreaTriangle = ½ base x height

= ½ (12) (10)

= 60

Question 13

A

6

• 2

• 6

• 12

• 36

O

60

B

Circumference = 2r

C = 26

C = 12

degrees = arc

60(12) = 360 x

720 = 360 x

2 = x

A

6

O

60

B

Question 14

A

13

C12 B

a2 + b2 = c2

122 + b2 = 132

144 + b2 = 169

b2 = 25

b = 5

A

13

5

C12 B

Question 15

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?

x yards = 3x feet

y yards = 3y feet

• xy

• 2xy

• 3xy

• 6xy

• 18xy

Arearectangle= length x width

= 3x(3y) = 9xy square feet

Total 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)

2 inches

• 0.14

• 0.75

• 0.86

• 1.0

• 3.14

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)

2 inches

Areacircle = r2

• 0.14

• 0.75

• 0.86

• 1.0

• 3.14

 12 =  = 3.14

1

Areasquare = s2

22 = 4

Areapiece = Areasquare - Areacircle

4 – 3.14 = 0.86

Question 18

Which of the following is equal to 3.14 x 106?

• 314

• 3140

• 31,400

• 314,000

• 3,140,000

3.1400000000

3140000.0000

Question 19

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

84 8-4=4or82=4

4124+8=12 or 4x3=12

12612-6=6 or 122 = 6

6 186+12=18 or 6x3=18

18918-9=9 or 182 = 9

• 19

• 20

• 22

• 24

• 27

9x3=27

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?

• 82

• 83

• 84

• 85

• 86

Let x = the fifth test score

(91 + 88 + 86 + 78 + x )  5 = 85

343 + x = 425

x = 82

Question 21

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

Let x = the measure of B

then 3x = the measure of A

• 112 ½°

• 120°

• 135°

• 150°

• 157 ½°

x + 3x = 180°

4x = 180°

x = 45°

B = 45°

A = 135°

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?

Probability of drawing a green jelly bean

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

c < a < b

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

• I only

• II only

• I and II only

• II and III only

• I, II, and III

II. a>c, so 2a>c – TRUE

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

Question 24

B

A

1

C

Question 25

B

E

C

D

A

B

20-x

E

x

C

20

4

D

6

A

10

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