SAT Math problems

P(x) = x^2 -11x+k In the polynomial p(x) defined above, k is a constant. if2 is a zero of the function what is the value of k?

2 is a zero--> plug in (2,0) 0=4-22+k k=18

x+1 = 2/(x+1) Which of the following is a possible value of x+1?

Circle x+1 use quad formula x=-1+/-sqrt(2) so x=+/-sqrt(2)

On average, 10% of the net energy of one trophic level is transferred to the next trophic level in an ecosystem. Based on the energy pyramid, if primary producers have 5,000 joules (J) of energy, approximately how much of this energy, in calories, is transferred to the secondary consumers in this ecosystem? (1 calorie = 4.18 J)A. 11.96B. 20.90C. 119.6D. 209.0

Circle: in calories, secondary consumers, A

Delete

Delete

What should you do here?: If u +t =5 and u-t =2, what is the value of (u-t)(u^2 -t^2)

Difference of 2 squares: a^2 -b^2 = (a-b)(a+b) So.... (u-t)(u^2-t^2) = (u-t)(u-t)(u+t) =20

What should you do here?:

Distribute write above the printed text

Never 31.3% Rarely 24.3% Often 13.5% Always 30..9% The table above shows the results of a survey in which tablet users were asked how often they would watch video advertisements in order to access streaming content for free. Based on the table, which of the following is closest to the probability that a tablet user answered "Always," given that the tablet user did not answer "Never"? A) 0.31 B) 0.38 C) 0.45 D) 0.69

Remember: P(A|B)= P(A∩B)/P(B) so... P(Always)/P(Rarely, Often, Always)

What should you do here?: The graphs in the xy-plane of the following quadratic equation each have x-intercepts of −2 and 4. The graph of which equation has its vertex farthest from the x−axis?

Remember: af(x) --> vertical stretch when |a|>1 f(bx) --->horizontal stretch when |b|<1

What should you do here?: h(x) = x^3 + ax^2 +bx +c The function h is defined above where a b and c are integer constants. If the zeros of the function are -5,6,7,what is the value of c

Remember: with zeroes we can write function in factored form. Since leading coefficient is 1 we can write: f(x) = (x-z1)(x-z2)(x-z3)..... c=210

What should you do here?: For what percent of the tosses did the dime land on heads?

Write fraction: # heads by dime/ total dime tosses

Points A and B lie on a circle with radius 1, and arc AB has length pi/3. What fraction of the circumference of the circle is the length of arc AB?

circumference: 2pir = 2pi (pi/3)/(2pi)= 1/6

What is the solution set? (x-2)/(x-3)=1/x +1/(x-3)

common denominator of x(x-3), disregard denom on both sides--> solve--> check for extraneous =1

What should you do here?: Which of the following describes a circle with radius 10 that passes through the origin?

whenever it's passing thru a point: Plug in 0 for x-->which results in 0 for y?

Upward parabola with y-int>0 The vertex of the parabola in the xy-plane above is (0, c). Which of the following is true about the parabola with the equation y = - a(x - b)^2 + c ? A) The vertex is (b, c) and the graph opens upward. B) The vertex is (b, c) and the graph opens downward. C) The vertex is (-b, c) and the graph opens upward. D) The vertex is (-b, c) and the graph opens downward.

- in front ->downward B

x+1 = 2/(x+1) In the equation above, which of the following is a possible value of x+1? A) 1-sqrt2 B) sqrt2 C) 2 D) 4

B

(10, 0.5), (20, 1.5), (30, 2.5) The scatterplot above shows the federal-mandated minimum wage every 10 years between 1940 and 2010. A line of best fit is shown, and its equation is y = 0.096x − 0.488. What does the line of best fit predict about the increase in the minimum wage over the 70-year period? A) Each year between 1940 and 2010, the average increase in minimum wage was 0.096 dollars. B) Each year between 1940 and 2010, the average increase in minimum wage was 0.49 dollars. C) Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.096 dollars. D) Every 10 years between 1940 and 2010, the average increase in minimum wage was 0.488 dollars.

Change: $1 every 10 years -> $0.1 every 1 year =A

A circle in the xy-plane has a diameter with endpoints (-1,-3) and (7,3). If the point (0,b) lies on the circle and b>0, what is the value of b?

Distance formula --> D=10 --> r=5 (x-h)^2 +(y-k)^2 =r^2 (x-h)^2 +(y-k)^2 =25 find midpoint and finalize equation plug in 0 b=4

What should you do here?: The sum of three numbers is 855. One of the numbers, x, is 50 percent more than the sum of the other two numbers. What is x?

Don't take short cuts!!! a+b+c=855 a=1.5(b+c) b+c=(2/3)a a+(2/3)a=855 (5/3)a=855 a=513

What should you do here?: A rectangle was altered by increasing its length by 10 percent and decreasing its width by p percent. If these alterations decreased the area of the rectangle by 12 percent, what is the value of p?

Draw an example(pick numbers- 1 and 1) p=20

What should you do here?: In the xy-plane, if a point with coordinates (a, b) lies in the solution set of the system of inequalities below, what is the maximum possible value of b? y less than or equal to -15x + 3000 y less than or equal to 5x

Graph, but don't forget to shade cuz inequalities--> notice its at intersection--> solve b= 750

5x-y=9 -60x+12y=-108 How many solutions does the given system of equations have? A. Zero B. Exactly one C. Exactly two D. Infinitely many

How to solve 1.put both equations in slope-int form(y=mx+b) -> same equation(y=5x-9) D

Students in a science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?

How to solve: 1. Equations -> L=4R+2C, S+3R+1C -> each group =1L+1S 2. Combine equations ->each group= 7R+3C 3. Plug in(find limiting agent) -> 7R=100 --> 14 groups -> 3C=70 ---> 23 groups

When a buffet restaurant charges $12.00 per meal, the number of meals it sells per day is 400. For each $0.50 increase to the price per meal, the number of meals sold per day decreases by 10. What is the price per meal that results in the greatest sales, in dollars, from meals each day? A. $16.00 B. $20.00 C. $24.00 D. $28.00

How to solve: 1. Two equations(S=np, n=mp+b) 2. Linear equation(n=mp+b -> 400=m(12)+b-> 400 = (-10/0.5)(12)+b-> b= 640 ->n=-20p+640 ) 3. combine into quadratic(S=(-20p+640)p 4. solve for vertex(x-value at -b/2a= 16) A

What should you do here?: If x^4 - y^4 = -15 and x^2 - y^2 = -3, what is x^2 +y^2?

Just begin factoring --> x^4 - y^4 = (x^2 - y^2)(x^2 +y^2)

Mr. Kohl has a beaker containing n milliliters of solution to distribute to the students in his chemistry class. If he gives each student 3 milliliters of solution, he will have 5 milliliters left over. In order to give each student 4 milliliters of solution, he will need an additional 21 milliliters. How many students are in the class?

List variables n= #of mL of sol s= # of students Set up system of equations: n=3s+5 n+21=4s s=26

What should you do here?: The side length of square ABCD is twice the side length of square EFGH. If the area of square EFGH is 9, what is the area of square ABCD?

Make sure diagrams mach words before starting

(3/4)x-(1/2)y=12 ax-by=9 The system of equations above has no solutions. If a and b are constants, what is the value of a/b?

No solutions-> parallel lines->same slope, different y-ints a = 3/4 b=1/2

If 4x^2+bx+9, where b is a constant, has exactly one solution, what is a possible value of b ? A) 72 B) 36 C) 12 D) 6

One solution-->perfect square (2x+3)^2 = 4x^2 +12x+9 =12

Which of the following expressions is equivalent to (x^2 -2x-5)/(x-3)

Polynomial Long Division: x+1 - 2/(x-3)

What should you do here?: In the figure above, lines k,l, and m intersect at a point. If x+y=u+w, which of the following must be true?I. x=z. II. y=w. III. z=t

Remember law: opposite angles of intersecting lines equal.

A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?A)$10,800 B)$16,200 C)$21,600 D)$29,700

Remember: circle "how much is it worth" Set up eq: y=mx+b y=mx+32400 m= -32400/12 plug in x=4 y=(-32400/12)(4) +32400 y=-32400/3 +32400 y=-10800+32400 =C

When designing a stairway, an architect can use the riser-tread formula 2h + d = 25 , where h is the riser height, in inches, and d is the tread depth, in inches. For any given stairway, the riser heights are the same and the tread depths are the same for all steps in that stairway. The number of steps in a stairway is the number of its risers. For example, there are 5 steps in the stairway in the figure above. The total rise of a stairway is the sum of the riser heights as shown in the figure An architect wants to use the riser-tread formula to design a stairway with a total rise of 9 feet, a riser height between 7 and 8 inches, and an odd number of steps. With the architect's constraints, which of the following must be the tread depth, in inches, of the stairway? (1 foot = 12 inches) A) 7.2 B) 9.5 C) 10.6 D) 15

Remember: circle what we're solving for: Tread depth =C

What is the acronym for sum/difference of two cubes?

SOAP(same, opposite, always positive): a^3 + b^3 = (a + b)(a^2 - 2ab +b^2) a^3 - b^3 = (a - b)(a^2 + 2ab +b^2)

Juliet rented a car for one day from a company that charges $80 per day plus $0.15 per mile driven. If she was charged a total of $98 for the rental and mileage, for how many miles of driving was Juliet charged? (Assume there is no tax.) A) 15 B) 120 C) 533 D) 633

Set up equation: 80 +0.15m =98 m= 18/0.15 -->turn into fractions m= 18/(15/100)= 1800/15=120

M = 1,800(1.02)t The equation above models the number of members, M, of a gym t years after the gym opens. Of the following, which equation models the number of members of the gym q quarter years after the gym opens? A) M = 1,800(1.02)q/4 B) M = 1,800(1.02)4q C) M = 1,800(1.005)4q D) M = 1,800(1.082)q

The rate doesn't change, just representing it differently. =A

Diagram: right triangle with hypotenuse of 10 units In the right triangle above, sin = θ 2/5 . If AC = sqrt(n), what is the value of n ?

Use defintion of sine then pythagorean formula. n=84

2x2 - 4x = t In the equation above, t is a constant. If the equation has no real solutions, which of the following could be the value of t ? A) −3 B) −1 C) 1 D) 3

Use discriminant. b^2 -4ac<0 --> no real solutions =A

What should you do on arithmetic sequence problems?

Use formula: An = A1 + d(n-1)

Hongbo sold x cell phones in 2013. The number of cell phones he sold in 2014 was 128% greater than in 2013, and the number of cell phones he sold in 2015 was 29% greater than in 2014. Which of the following expressions represents the number of cell phones Hongbo sold in 2015? A) (0.29)1.28x B) (0.29)2.28x C) (1.29)1.28x D) (1.29)2.28x

When percents in problem, circle greater than, less than, etc. 128% greater --> 2.28*x 29% greater --> 1.29*y =D

5 Gisela would owe $15,500 in taxes each year if she were not eligible for any tax deductions. This year, Gisela is eligible for tax deductions that reduce the amount of taxes she owes by $2,325.00. If these tax deductions reduce the taxes Gisela owes this year by d%, what is the value of d ?

When percents in problem, circle reduce, increase, etc. (15500-2325)/15500=0.85 How much is it reduced -> 1 - 0.85 = 0.15 = 15 percent

What should you do here?: Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal. What is the sum of the areas of the four triangles that will be removed from the rectangle?

remember sum of interior angles of polygon formula: (n-2)*180 where n = number of sides

What should you do here?:when 9 is increased by 3x the result is greater than 36. What is the least possible interger value for x?

remember: increased by means addition here

What should you do here?:the angles shown above are acute and sin(a degrees) = cos(b degrees). If a =4k-22 and b=6k-13, what is the value of k?

remember: sin(90-x) = cosx and cos(90-x) = sinx k=12.5

What should you do here?: x-2 = sqrt(x+10)

remember: sqrt means only positive root

1/x+1/(x-1) = 0

shift one to the other side--> solve =1/2

what are the dimensions of a 30 60 90 triangle?

short leg: a, long leg: a(sqrt3), hyp: 2a

sqrt(x-3) = 3-sqrt(x) If x is the solution to the equation above, what is the value of sqrt(x-3)

square both sides, subtract x's =1

x : 1 3 5 f(x): 5. 13. 21 Some values of the linear function f are shown in the table above. Which of the following defines f ? A) f(x) = 2x +3 B) f(x) = 3x +2 C) f(x) = 4x +1 D) f(x) = 5x

use An=A1 +d(n-1), where d= the difference between consecutive y terms so... d= (13-5)/(3-1) = 8/2 = 4

Alan drives an average of 100 miles each week. His car can travel an average of 25 miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on gasoline by $5. Assuming gasoline costs $4 per gallon, which equation can Alan use to determine how many fewer average miles, m, he should drive each week? A. the fraction 25 over 4, end fraction, times m, equals, 95 B. the fraction 25 over 4, end fraction, times m, equals, 5 C. the fraction 4 over 25, end fraction, times m, equals, 95 D. the fraction 4 over 25, end fraction, times m, equals, 5

use dimensional analysis to solve =D