Math CST: Review 2009
Vision Textbook: Answers to the Overview at the end of each chapter.
Note, not all of the answers have been verified so if you arrive at a different answer and you think you did it correctly, let us know…
Chapter 1:
1. a) 1. ≈10.82 2.y = 0.33x 3. (1.5,1)
b) 1. 9.43 2. Y=-1.6x-1.5 3. (-1.5,1)
2. a)(12,16) b) (9,19 )
c) Ratio 2:2 means 2/4 (1/2) along the line. Answer: ( -4, 4.5)
d) 2:5 means 2/7 along a line: Answer: -23, 13
3. Show that the slopes of the opposite lines are the same.
a=(y2-y1)/(x2-x1) Line AD (2b-b)/(a-0) = b/a and Line BC (b-0)/(2a-a) = b/a
Line AB (b-2b)/(2a-a) = -b/a Line DC (0-b)/(a-0) = -b/a
The slopes of the opposite sides are the same therefore they are parallel
4.
x / ya) / 4 / -9
b) / 2.25 / -2.25
c) / 4.5 / -4.5
d) / -2 / -1
e) / -12 / -4
f) / -2.54 / 2.6
5. a) y≥-3x
b) y>.6x-20
c) y<-.5x-1
d) y≤11x+2
6. a) 2x + y < 80
question / Coordinates / solution1 / 0,80 / no
2 / 20,20 / yes
3 / 30,30 / no
4 / 0,0 / yes
5 / 40,0 / no
6 / 35,11 / no
7. a) parallel
b) perpendicular
???? c) These to lines intersect at 4, 6. They are not perpendicular
8. a) Mt. Everest = y, Mt. Iberville = x y=3x+300
b) y= # of medals won by China in 2004 x= # medals won by Greece in 2004
y = 3x
c) y = population of the united states in 2004 x = the population of Canada in 2004. y=9x
d) y = the weight of a 10 wheel vehicule x = weight of cargo y + x ≤ 25 250kg
9.a) a = 3 (parallel lines have the same slope) Now find b
x=2 y=1 plug them in 1=3(2) + b 1-6=b b=-5
Equation y=3x-5
b) 2x + 2y -6 = 0
Isolate y to find a: 2y = -2x + 6 (divide everything by 2)
y = -x + 3 a = -1
A perpendicular slope is the negative reciprocal of “a” (-1/-1) = 1 and b = 8.
y = x + 8
10. Area of a parallelogram (b x h) h is perpendicular to b
Length of BC is 5 (the change in y coordinates since the line is vertical)
The distance between the lines is the change in x coordiantes (perpendicular to y axis) It is 4. b x h is 5 x 4 = 20.
11.a) b)
c) d)
e) f)
12. y is the salary x is the weekly sales
a) A: y = .04x + 200 B: y = .05x
b) x = 20 000 y = 1000
????c) If Philip’s weekly sales are 20 000 he will make the same amount at both dealerships. If he sells more than this he will make more at B. If he sells less than this he will make more at dealer A.
13. x = width y =4x = length. Perimeter is x + x + y + y = 140
x + x + 4x + 4x = 140. 10x = 140 x=14m y = 56m. Area=x*y=56*14=784m2
14. x = orange juice y= banana juice
x = 5y
x + y = 930ml 6y=930 y= 155 x=775 Answer: 155 ml of banana juice
15. Find Area (area of a trapezoid is (B x b)/2: B = AD and b = BC
Price is Total Cost / Area Answer:??????
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22.
Chapter 2:
1. A - 4 B – 3 C -1 D – 2
2. 1,3,2
3 a) A b) A = 0.91 B= -0.7 C=0 D=-.76
4. A
5. Height of the birch trees
6. Group B
7.
0 / 0 0 0 0 0 0 0 0 0 0 1 1 2 4 5 6 71 / 2 3 5 6
2 / 0 5 5 6 7 8
3 / 0 4 7 7 8
4 / 0 1
8. A
9. a) 75 b) 2006m c) Hulk Hogan
10. a) 12h b) 20h c) ≈ 20.89h d) 25h
11. No. In the contingency table the values are not concentrated along the diagonal.
12. 63
13. ≈ 16
14. In the Deux-Rives Marathon
15. in 2018
16. a) 4:53, 4:55, 5:01
b) 4:34, 4:37, 4:45, and 4:51
17. a)70 b)100 c)39 d)2
18. a) 2 and 3 b) 1 and 3 c)2 d) 2 e)2
19. Yes. The linear correlation coefficient is ≈0.98.
20. a) 25 b) Yes the linear correlation coefficient (r) ≈0.96
c) 1) 95 2) 2 cousins 3) 3 cousins
d) ≈ 175
21. a)No, the curve is a good representation of the scatter plot, it is not linear.
b) Yes. The scatter plot shows a decreasing tendency.
c) 1. A family making about $18 000 sets aside 45% of their income
2. A family with an annual income of about $25 000 sets aside 95% of their income for basic needs.
d) 10 families
22. Find the linear correlation coefficient (≈-0.84) to show that there is a strong correlation indicating that his prediction is probably true.
23. a) Denmark b) Denmark c) ≈169.33 cm d) 184.79 cm
e) approximately in 1875 f)y≈0.1x-27.54 g) y≈0.11x – 30.88 h)approx. in 2198
Chapter 3:
1. a)SSS b)SAS c)ASA d)SSS
2. a) congruent: SAS b)similar: SSS c) neither (angle is not sandwiched between congruent or similar sides) d) neither e) similar: SSS f) similar: AA
3. a) False
b) True
c) True
d) False: the are similar but not necessarily congruent
4. a) similar but not congruent b)yes, all 4 sides are congruent on a square c) No ) d) No, it doesn’t mean the sides are equal e) no, similar, not congruent.
5. a) 3.6cm b) 2.88cm c) 1.2cm d) DE = 2 use Pythagoras x=.87cm
++++6. a) True (2 triangles and SAS) b) True (2 congruent triangles: ASA or SAS) c) True (SAS)
7. Measure the diagonals BD and AC; they should be congruent if it is a rectangle.
8.a) ABE, ABC, ABD, BCE, CED, ACD, AED, DBC b) AED = BEC BCD = ACD ADB = ACB
*9. A) 1) 12/17 = .71 cm. 2)1.62cm 3 and 4 ) There is missing information in the question
B) No because EFand GH are not parallel.
10. 1.22 km.
11.living room = 8*6*9 / 2= 216 m3 bedroom = 4.5*6*9 / 2 = 121.5 m3 m3 bathroom = 1.5*2*9 / 2 = 13.5 m3 shed = 1.125*1.5*9 / 2= 7.59 m3 dining room = 1.5*12.5*9 = 168.75
12. set up ratios and solve for x, x=7. AB = 5, BE = 3, CD = 4.2 cm
13. metric relations: find the altitude of the large right angle triangle. Area is base x height (alt)= 100*48.99 = 4899 cm2
14. 907 cm or 9.07m tall
*15.a) 1_many possible answers ex: ABD, BCD, ADF, and BDF are similar to ABC
2) EBC ( its congruent therefore similar) 3) No triangle is similar to BED
b) 1) EBG is congruent to ECG 2) none
16. a) SAS, SSS or ASA b) AA c) Pythagorean Theorem c) side2 = its projection * hypotenuse (AB)2 = AC x AE d)altitude2 = projection1 * projection2
17. A, C, D and F are congruent (isometric) , B and E are isometric (congruent) (SSS)
Chapter 4:
Answers:
1. a) periodic b) exponential c) 2nd degree or d) linear or first degree
2. a) 2nd degree b) exponential c) piecewise d) periodic
e) 1rst degree or linear f) step
3.
Graph 1
a) 1) domain: ]-∞ , ∞[ or R range [-3,3]
2) zero(s): {… -8,-4,0,4,8,…}
3) maximum: 3 minimum: -3
4) initial value (y – intercept): 0
b) type of function: periodic
c) is the inverse a function (vertical line test): no
Graph 2
b) 1) domain: ]-∞ , ∞[ range: [0 , ∞[
2) zero(s): 0
3) maximum: none minimum: 0
4) initial value (y – intercept): 0
b) type of function: second degree
c) is the inverse a function (vertical line test): no
Graph 3
c) 1) domain ]-∞ , ∞[ range: [0 , ∞[
2) zero(s): none
3) maximum: none minimum: none
4) initial value (y – intercept): 1
b) type of function: exponential
c) is the inverse a function (vertical line test) : yes
Graph 4
d) 1) domain: ]-∞ , ∞[ range: [-3 , ∞[
2) zero(s): 0.5 and 3.5
3) maximum: none minimum: -3
4) initial value (y – intercept): 1
b) type of function: piecewise (or absolute value)
c) is the inverse a function (vertical line test): no
4. Exponential: Each value if followed by the double of its own value.
Y = 2x
X = 0, 1, 2, 3, 4, 5, 6, 7
5. a) y ≈ -(5/8)x + 2.5
b) y = (1/16 )x2
c) y = 2(.5)x y=2(1/2)x
d) y= (1/x)
6. 1) step
2) exponential
3) piecewise
7.
Time since the camp was founded (years) / Number of children / Number of groups / Number of leaders / Number of children per leader0 / 15 / 3 / 3 / 5
1 / 15 / 3 / 3 / 5
2 / 15 / 3 / 3 / 5
3 / 20 / 4 / 4 / 5
4 / 20 / 4 / 4 / 5
5 / 20 / 4 / 4 / 5
6 / 25 / 5 / 5 / 5
7 / 25 / 5 / 5 / 5
8 / 25 / 5 / 5 / 5
9 / 30 / 6 / 6 / 5
10 / 30 / 6 / 6 / 5
******use graphs from answer book
c) 1. 45 children 2. 9 groups
d) degree 0 (polynomial)
8. a) y= -2x2 b) y = (-2)(3)x
9. a) period: 10
b) 1) f(13) = 1 2) f(24) = f(24-10) = f(14) = 1
3) f(41) = f (41-30) = f(11) = 2 *30 is a multiple of 10
10.
a) Step function. Each step increases by 1.3 every km.
b) at 9.7 km the cost will by $14.85
c) at least 6 km. or more but less than 7( [6,7[ )
11. a) $3600 b)
c) inverse variation (y = 3600/x or y = 3600 x (1/x) )
d) y = 3600/15 = $240
12. a) 1) 10 minutes 2) 50 minutes
b) 65 minutes c) 12.7 km.
13. a) graph
initial value 25, rule: y = 25 (1.92) x
Note: if the initial value is 25 and y = 48 when x = 1 then 48 = 25 (keep)1 and
“keep” = 48/25. That is how we find the rule for exponential
13.b) exponential
c) Between 7 and 8 years
3500 = 25 (1.92) x (divide both sides by 25)
140 = 1.92x (do trial and error) then about 7.6 years
14. a)
x / 0 / 0.1 / .25 / .4 / .49 / .5 / .6 / .75 / .9 / .99 / 1 / 1.1 / 1.25 / 1.4 / 1.49 / 1.5 / 1.6 / 1.75 / 2y / 0 / 0 / 0 / 0 / 0 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 1 / 2 / 2 / 2 / 2
b) the step has a length of 1 except for the first step which has a length of .5 and the counterstep (change in y) is 1. The critical points (where there is a change in y) occurs at (.5, 1.5, 2.5, …)
15. less than 10., but there is no one right answer…
16. a)
Length of the foot (cm) / Length of the luff (cm) / Area of the sail (cm2)2 / 6 / 2*6/2 = 6
4 / 12 / 24
6 / 18 / 54
8 / 24 / 96
10 / 30 / 150
b)
Graph:
c)
Equation: 1) y = 3x 2) y = 1.5x2
d) x * 1.5x = 337.5
1.5x2 = 337.5
x2 = 225
x = √225 = 15cm
17. a) second degree
b) 9 m
c) 6 seconds
Chapter 5
1. a) sin 63 = x/4.6 x=4.10cm cos 63 = y/4.6 y=2.09cm
b) cos X = 1.8/3.7 X=cos-1(1.8/3.7) X=60.89 deg. sin 61 = y/3.7 y = 3.23cm
c) tan x = 3.7/3.4 x= tan-1(3.7/3.4) =47.42 deg. y = 90-47.4 = 42.58 deg.
d) x = 68.46 deg y = 3.33cm
e) x = 4.27cm y =3.09cm
f) x = 130.62 deg. y = 2.33cm
2. Area (approximate in cm2)
a) 5.41 b) 10.81 c) 11.54 d) 3.78 e) 7.59 f) 5.11
3. Length = (approx.) 19.32 m
4. Hero’s Formula (answers are approx )
a) 8.33 cm2 b) 2498.04mm2 c) .43 km2 d) 18 596.76 cm2
5. a) 3.58 deg
b) 17.28 m3
c) 28.86m2
6. a) find the side opposite 50 degrees (radius of the circle formed on the surface) Area of the circle = 1784.77m2
b)The light creates a cone, base has a radius of r = 23.84 (use trig), height of 20m
Volume = 11 898.48 m3
7. a) 218.81 m
b) 17.97 m
c)219.54 m
8. Volume = 10 524.21 m3
9. a) 12.81 m
b) 51.34 deg.
10. Speed = 53.44 km/h
11. Distance between the entry point and the exit point is 8.78 m
12. Length of the tunnel is 271.89 m
13. a) note: Altitude is the height above see level therefore a change in altitude is a vertical distance.
Altitude of the Relay Station: 2317 m
Altitude of the Top Station: 3787 m
b) angle of elevation from the horizon (horizontal line)
1) first stage (base to relay) = 30.06 deg
2)second stage (relay to top) = 30.85 deg
c)(base to top) = 5419.87 m.
14. Area of lot 16 = 159.8m2 Cost: $199 734.67
15. Notice the 2 triangles created by BE, measures DE and BC are ½ the length of the paddle
Maximum measure of angle DEB: 62.7 deg
Length of paddle if DEB is 45 degrees: 106.07 cm. (no matter what length of the paddle, the minimal distance between the paddle and the second kayakist will be 106.7)
16. a) 26.22 m
b) 90 deg, 23.54 deg, 66.46 deg.
17. a) 9.37 m
b) 1. 600 m.
2. 0.76 deg.
18. 17.04 m
19. 159.66
20. a) 4.85 m
b) 2.23 m
21. There is missing information in the question
1