ACT Form 71A Math Answer Explanation



Choice C

0.75(120)+20(2)=90+40=130


Choice G

15=3×5 6=2×3 4=2×2 2×2×3×5=60


Choice D

(36+24)2=120


Choice J

180°64°=116°


Choice B

14×25010=14×25=614


2012 December(71A) Math Question 6

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice F

3:12=1:4


Choice C

(1)+(3)+2 =13+2 =0


Choice G

9+3x=27 3x=279=18 x=6 2x=12


2012 December(71A) Math Question 9

Word Problems

- 1 Variable Equations


Choice A

100(5+0.10.08+0.03) =100(5+0.05) =505


2012 December(71A) Math Question 10

Word Problems

- Cost


Choice J

$32000(1+0.035) =$32000+$1120 =$33120


Choice E

13(56+112+13) =13(1012+112+412) =13(1512) =512


2012 December(71A) Math Question 12

Inequalities

- Number Line


Choice H

4x26 4x8 x2 H.


2012 December(71A) Math Question 13

Word Problems

- 1 Variable Equations


Choice C

1500+900=2400 2400÷20=120


2012 December(71A) Math Question 14

Angles

- Collinear Points & Triangles


Choice H

A=B=C=60° x°=180°60°=120°


2012 December(71A) Math Question 15

Quadratic Equations

- Factoring


Choice E

16x2=30 x2=3016 x=3016


Choice F

100(20)+30(4020) =2000+600 =2600 2600÷800=314


2012 December(71A) Math Question 17

Statistics

- Mean, Median


2012 December(71A) Math Question 18

Graphing Properties

- Create Graphs or Figures


Choice G

50 10089,96 101 150103,104,106,113 151 200160,160,161


Choice D

89x=43100 43x=8900 x=206.97


2012 December(71A) Math Question 20

Statistics

- Mean, Median


Choice K

160+1006+104+113+160+103+161+89+96=1092 1092+x+y9+2=1092+x+y11


2012 December(71A) Math Question 21

Probability

- One Event


Choice B

35=8+r8+5+11+r=8+r24+r 3(24+r)=5(8+r) 72+3r=40+5r 32=2r r=16


Choice G

(5x34x2+7x3)(3x3+4x23x+1) =2x38x2+10x4


2012 December(71A) Math Question 23

Graphing Properties

- Create Graphs or Figures


Choice E

(E)


Choice J

f(4) =5(4)22(4)+10 =5(16)+8+10 =80+8+10 =98


Choice D

612=0.5 (D)


2012 December(71A) Math Question 26

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice H

71a

tanθ=38 θ=arctan38


2012 December(71A) Math Question 27

Word Problems

- Distance, Speed, Time


Choice E

2+3d+2=22 4+3d=22


2012 December(71A) Math Question 28

Equation of a Line

- Equations that Describe a Line


Choice G

3x+5y=6 5y=3x+6 y=35+6 m=35


Choice C

3x122x+6=5x15+6 x6=5x9 6x=3 x=12


Choice H

If x=12 (12)3=18 0<18<1 $$\Rightarrow …


Choice E

(2a)6+3a45a42a =8a62a42a =4a5a3


Choice J

1.28×1043.5×103 =12.8×1033.5×103 =9.3×103


2012 December(71A) Math Question 33

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice A

AB2=32+42=52 AB=5 sinA=35


Choice H

1122:162 =1144:136=1:4 l=10×4=40


Choice C

3(2)=5 164=12 52+122=25+144=169=13 $$\pi r^{2}=\pi …


2012 December(71A) Math Question 36

Trigonometry

- Pythagorean Theorem & sin cos tan



2012 December(71A) Math Question 37

Absolute Values

- Absolute Value Expressions


Choice B

2w+7=∣2 2∣=2 2w+7=2w=2.5


Choice K

71a

(K)


2012 December(71A) Math Question 39

Equation of a Line

- Distance & Midpoint


Choice B

12+(4)2=4 18+22=10 (4,10)


2012 December(71A) Math Question 40

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice G

sin58°50=sin68°AB


2012 December(71A) Math Question 41

Conics

- Circles


Choice D

71a

0+82=4 6+02=3


2012 December(71A) Math Question 42

Angles

- Circles


Choice J

71a


4x6x2=23x

A rational number is …


2012 December(71A) Math Question 44

Algebraic & Function Expressions

- Nested Functions


Choice K

g(2)=2(2)1=5 f(5)=3(5)+2=13


Choice B

36=6×6 6×4=24


2012 December(71A) Math Question 46

Word Problems

- Distance, Speed, Time


Choice F

Distance=V×Time $$1 segment:2 …


Choice C

180°43°32°=105°=B AC>BC>AB


2012 December(71A) Math Question 48

Absolute Values

- Graphing Absolute Values


Choice F

y=∣x12 (1,2)2=02


2012 December(71A) Math Question 49

Conics

- Ellipse


Choice E

71a

h>0,k>0 16=42 4=22


2012 December(71A) Math Question 50

Perimeter, Area, Volume

- Other Shapes


Choice K

71a

2×4+2×4 =8+8 =16


Choice A

2x3y=6(1) (1)×3 6x9y=18 9=k


Choice F

20=1 x2+1=0 x2=1 x=±I


2012 December(71A) Math Question 53

Angles

- Circles


Choice D

71a

πr2 =π102 =100π


2012 December(71A) Math Question 54

Angles

- Circles


Choice G

AB^ =2πr×12 =2π(20)×12 =20π


2012 December(71A) Math Question 55

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice D

71a

c(10,3)


2012 December(71A) Math Question 56

Angles

- Circles


Choice J

71a

90°÷2=45°


Choice E

71a

10LL=10 (L4)10=10L40


2012 December(71A) Math Question 58

Sequences and Patterns

- General Sequences


Choice K

T64=1+2+3+...+64 =(1+64)642 =65×32 =2080


2012 December(71A) Math Question 59

Quadratic Equations

- Factoring


Choice A

x2+kx+17=0 (x17)(x1)=0 x2x17x+17=0


2012 December(71A) Math Question 60

Trigonometry

- Pythagorean Theorem & sin cos tan


Choice F

XY=12 tanθ=49=XYXZ=12XZ 4×XZ=9×12 XZ=27 Area=XZ×XY×12