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Chasing 800 - MATH

August 4, 2017

 

January 2017 SAT AKA Practice Test 8

 

In the quest for a perfect score one can seldom afford an error. Below we provide what we actually did when solving the math problems ourselves. These solution strategies are independent of the official answer explanations that the College Board provides. Please note we are only presenting one way to attack each problem and that other ways do exist. When we work with students, we explore various approaches to each problem so the students can choose the approach that suits them best. Please feel free to share this. Be sure to like us on Facebook here. if you found this helpful. Email us at info@capitaltestprep.com to find out more about our tutoring services.

 

Section 3

 

1 Combine like terms, get numbers on one side and variables on the other. 6x-5=7+2x becomes 4x=12

Answer: D

 

2 y-intercept = 0, so eliminate C,D. Slope= 2 (calculate using coordinates of points on line) Answer: A

 

3 Isolate P by multiplying both sides by 6, then subtract O and 4m

Answer: A

 

4 Because <UTR and <STR are supplementary m<STR = 66. Because triangle STR must have angles add to 180, the third angle must measure 83. Since triangle RTU is isosceles, m<TRU is 33. When it comes to the small triangle in the bottom right, you know there is an angle measuring 83 degrees (vertical angle) and one measuring 33 degrees. The last angle, <RVS must measure 64 degrees.

Answer: C

 

5 Draw a diagram and label one side x and the other 6+w. Double each side and add the results together to get the perimeter.

Answer: B

 

6 Change the top inequality to y+1>2x. Use substitution to combine the inequalities to get y+1>5. Subtract 1 from each side.

Answer: B

 

7 Test the values in the answer choices. -1 does not work, but 5 does.

Answer: B

 

8 Factor the numerator into x(x2-9) into x(x+3)(x-3) based on difference of squares. Factor denominator into (x-3)(x+1). Cancel the (x-3) term.

Answer: D

 

9 Given the equation of the circle (x-h)2 + (y-k)2=r2, the radius is 4, making the diameter 8. Keeping y constant and going through x=6, moving 8 units horizontally puts one at (2.-5). Answer: A

 

10 Create a system of equations, using L for large tents and S for small tents. 4L + 2S =202 and L +S= 60. Substitute for L to solve for S.

Answer: C

 

11 This crosses the x-axis at -3 and 2 and bounces at 0, making (x+3) and (x-2) factors and x a double factor.

Answer: B

 

12 Divide both sides by 2 so a/b = ¼. Flip both to answer the question.

Answer: D

 

13 Production dropped so A and B can be eliminated. The decrease was 2.1 million barrels over 13 years.

Answer: C

 

14 A line and parabola can’t cross more than twice so A is eliminated. Hand graph these using the y-intercepts - parabola (0,-7) and line (0,-8) -  to assist. Note that line’s x-int (8/5,0) is inside the x-int of the parabola determined via quadratic formula.

Answer: C

 

15 Plug 0 in for x in 2x-1, so g(0)= -1. Use f(x) to get 1- -1 = 2.

Answer: D

 

16 Factor into (x-3)(x+4), so x=3 is the positive root.

Answer: 3

 

17 Stack these expressions and add them to get x2+8x+23. Add 1+8+23 to get 32. Answer: 32

 

18 Add these equations as they are stacked to eliminate x and get 4y=6. Solve for y. Answer: 3/2

 

19 When x=0, there were 8 employees so b=8.

Answer: 8

 

20 Use pizza proportionality (arc/circumference = central angle/360) to get 2/5 = x/360. Solve for x.

Answer: 144

 

Section 4

 

1 Multiply pounds by per pound price for total cost

Answer: A

 

2 Fastest decrease means steepest downward slope

Answer: C

 

3 Set up proportion 3/200=x/10,000

Answer: A

 

4 Using equation provided and noting meaning of variables, make x=19 and solve for y

Answer: C

 

5 Label angle measures. Unlabeled angle in top triangle is corresponding angle to angle y, so it is 20 degrees. Using rule of 180 for sum of angles in triangle, calculate x.

Answer: B

 

6 Eliminate C for wrong # tix sold. Eliminate A for wrong revenue. Eliminate B for flipped prices.

Answer: D

 

7 Recognize slope intercept form, y=mx+b, and set m=3.

Answer: C

 

8 Note what question wants, x+1. Rearrange equation so (x+1)2=2 and take square root of each side.

Answer: B

 

9 Using equation provided and noting desired unit, set V=473 and solve for k. (Don’t forget to divide by pi and raise to ⅓ power, using parentheses for power.)

Answer: D

 

10 Glass diameter increases so height increases more slowly as time goes on, requiring steepness to decrease.

Answer: C

 

11 Use dimensional analysis to divide total fl.oz.(128) by fl.oz. per glass (16) to get # glasses.

Answer: B

 

12 At least means greater than or equal to and target was not met so must be less than 57 policies, eliminating B and D. Total value was greater than 3,000,000, eliminating A.

Answer: C

 

13 Goal is to isolate a. Raise each side to the -2 power.

Answer: C

 

14 Must find x value that makes denominator zero. Factor to (x+5)(x-2). Positive 2 is the value that makes (x-2) equal zero.

Answer: D

 

15 Calculate volume as lwh, so 60,000. Using density equation, d=m/v, insert 60,000 for v and 2.8 for d then solve for m.

Answer: D

 

16 Of those who received a sugar pill means denominator is 150 and contracted cold means 33 is numerator. Simplify.

Answer: B

 

17 Mode, 18, is most frequently observed. Median, 19, is determined by getting rid of high and low with machete approach until 2 left and averaging. Mean, 20, is determined by multiplying across the rows and adding those values then dividing by 20.

Answer: A

 

18 Process meaning of graph, set x=-2 and find y value from line.

Answer: C

 

19 Range is less than or equal to 4, so 4 is a global maximum, eliminating C and D. x=1 is a zero, eliminating B.

Answer: A

 

20 Annual savings is the difference in cost per year, eliminating C and D. Savings should exceed installation cost, eliminating A.

Answer: B

 

21 Using the equation 3.39 is m, or slope, so rise over run, amount of plastic per year.

Answer: D

 

22 The year 2000 is 15 years after 1985, so find y value when x=15, which is 100.The year 2003 is 18 years after 1985, so y value is about 110 when x=18. An increase of 10 represents 10 percent of 100. Note reference value for taking percent.

Answer: A

 

23 There are 4 quarters in a year, so 4t=q thereby q/4=t, eliminating everything but A.

Answer: A

 

24 Nothing is known about the preferences of the other 90%, goodbye A. Nothing is known about the ages, goodbye B. Switching the method of voting wouldn’t change the vote itself, goodbye C.

Answer: D

 

25 Change in population is -16 over 10 years with linear relationship, so slope is -1.6.

Answer: A

 

26 Read information. Need one that MUST be true. Choice of playground is biased against families with older children or no children at all.

Answer: C

 

27 Any point on a line is solution to the equation, so first point gives equation p+b=r and second point gives equation 4p+b=5r. Subtract first equation from the second to eliminate b, getting 3p=4r. Rearrange to desired r/p.

Answer: B

 

28 Range is max-min, so range for each is 32, eliminating B and C. Distribution is not the same so standard deviations are different.

Answer: D

 

29 Constant rate means linear relationship, eliminating C and D. 30% of 5000 is 1500. 1500/20 gives slope of 75 pages/min.

Answer: B

 

30 The maximum of f is a y value of 3. g(3)=6

Answer: B

 

31 For HYDROGEN it’s 2 atoms/molecule so multiply by 51.

Answer: 102

 

32 Plugin 1 for x and solve for a.

Answer: 2

 

33 Second equation is obtained by multiplying the first by 3. 10 times 3 gets c.

Answer: 30

 

34 Need miles on top and hours on bottom, so 11/(26/60) because minutes/(minutes/hr) gives hours.

Answer: 25.4, 127/5

 

35 Plot (0,10) and (10,0) for the line and connect the points. Find intersection.

Answer: 2, 8

 

36 Draw in segment SW. <RSW and <WST are complementary so the sin of one is the cos of the other, making values the same (difference of zero).

Answer: 0

 

37 Read question very carefully as difference is needed and different volumes are used. After 5 minutes, it’s 152 micrograms/mL so 1520 micrograms for 10 mL. After 10 minutes, it’s 118 micrograms/mL so 944 micrograms for 8 mL. Subtract 944 from 1520.

Answer: 576

 

38 We know 5 minutes after is 152 micrograms/mL so when t=5 the exponent is 1. When 200b=152, b rounds to 0.8.

Answer: 0.8, 4/5

 

 

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