 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

Go Through The Test Twice 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

ALL PROBLEMS ON THE ACT CAN BE SOLVED WITHOUT USING A CALCULATOR 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

Check Your Answer 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 CORRECT ANSWER: A 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 CORRECT ANSWER: A

BACKSOLVE (cont) F. 0 G. 2 4 J. 8 K. 10

BACKSOLVE (cont) F. 0 G. 2 4 J. 8 K. 10 Correct Answer:J

GUESSTIMATE 60 x 0.02 = 1.2 CORRECT ANSWER: C 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 CORRECT ANSWER: C 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 CORRECT ANSWER: K

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? 5° 30° 40° 55° 60° x 125° 85°

CORRECT ANSWER: B EYEBALL (cont.) In the figure below, what is the value of x? x 5° 30° 40° 55° 60° 125° 85° 55° 95° 180 –125 = 55 180 - 85 = 95 180 – 55 – 95 = 30 CORRECT ANSWER: B

By looking at the figure: A looks larger than 99°– eliminate answer F 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

CORRECT ANSWER: G EYEBALL (cont.) Total number of students = 720 Total number of freshmen = 240 Total number of degrees in a circle = 360° CORRECT ANSWER: G

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 -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

CORRECT ANSWER:B PICK NUMBERS (cont.) If kx + k = 0, and k>1, then x = ? -1 1 -k k kx + k = 0 k(x+1) = 0 k= 0 OR x+1 = 0 k= 0 OR x = -1 CORRECT ANSWER:B

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?

CORRECT ANSWER: F 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? CORRECT ANSWER: F

Practice Questions

Question 1 D C 13 17 19 24 25 4 12 A 3 B

ABC is a 3-4-5 right triangle and BCD is a 5-12-13 right triangle CORRECT ANSWER: A 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

CORRECT ANSWER: A 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 CORRECT ANSWER: A

CORRECT ANSWER: D 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 CORRECT ANSWER: D 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

y = mx + b CORRECT ANSWER: A What is the slope of the line x = 2y +3? Question 4 What is the slope of the line x = 2y +3? CORRECT ANSWER: A 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 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? CORRECT ANSWER: C B 180 – 30 – 60 = 90 90 30 60 120 A C D 180 – 120 = 60

CORRECT ANSWER: D Areacircle = r2 Circumference = 2r 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 CORRECT ANSWER: D

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? CORRECT ANSWER: B 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 CORRECT ANSWER: C

For all y, 26y – (-10y) – 3y(-y+3) = ? 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 CORRECT ANSWER: E

Question 10 C 65 70 75 80 85 D 100 30 A B

CORRECT ANSWER: D C D 65 70 75 80 85 80° 100 50 50 30 A B 180 – 30 – 50 = 100 180 – 100= 80 m BDC = 80 CORRECT ANSWER: D

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

RST is a 3-4-5 right triangle 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 CORRECT ANSWER: C 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

CORRECT ANSWER: C AreaTriangle = ½ base x height 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 CORRECT ANSWER: C

Question 13 A 6  2 6 12 36 O 60 B

CORRECT ANSWER: B Circumference = 2r C = 26 C = 12 degrees = arc 60(12) = 360 x 720 = 360 x 2 = x A 6 O 60 CORRECT ANSWER: B B

Question 14 A 13 C 12 B

CORRECT ANSWER: A a2 + b2 = c2 122 + b2 = 132 144 + b2 = 169 b2 = 25

Question 15 CORRECT ANSWER: E

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? 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 CORRECT ANSWER: E

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

Areapiece = Areasquare - Areacircle 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 CORRECT ANSWER: C

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 CORRECT ANSWER: E

Question 19 Find the last number in the series: 8, 4, 12, 6, 18, 9,? 84 8-4=4 or 82=4 412 4+8=12 or 4x3=12 126 12-6=6 or 122 = 6 6 18 6+12=18 or 6x3=18 189 18-9=9 or 182 = 9 19 20 22 24 27 9x3=27 CORRECT ANSWER: E

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? 82 83 84 85 86 Let x = the fifth test score (91 + 88 + 86 + 78 + x )  5 = 85 343 + x = 425 x = 82 CORRECT ANSWER: A

CORRECT ANSWER: C 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° CORRECT ANSWER: C

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? Probability of drawing a green jelly bean CORRECT ANSWER: D

CORRECT ANSWER: C c < a < b 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 CORRECT ANSWER: C

Question 24 B A 1 C CORRECT ANSWER: C

Question 25 B E C D A

CORRECT ANSWER: E 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 Answer every question Check your work Work for the whole 60 minutes