SAT/ACT Math Problem Recognition Hansen
No Calculator What is the sum of all values that satisfy (4m² - 16) = 0? A. 0 B. 2 C. 3 D. 6
A. 0
No Calculator Find the values of x and y. 3x+y=0 9x-5y=-6 A. 1,3 B. 3,1 C. -1,3 D. -1, -3
A. 1,3
No Calculator ax+by=20 3x+6y= 60 In the system of equations above, a and b are constants. If the system has infinately many solutions, what is the value of b/a? A. 2 B. 9 C. 5 D. 3
A. 2
No Calculator nA=360 The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is 60°, what is the number of sides that it has? A. 6 B. 7 C. 8 D. 5
A. 6 By using the given formula and plugging in 60 for the A value, you can divide by 60 on both sides, so that you find that the polygon has 6 sides.
No Calculator (√3k²+15) - x = 0 x=4 and k>0 A. √1/3 B. 2√1/3 C. 3 D. 1
A. √1/3
No Calculator A radioactive substance decays at an annual rate of 25%. Initial amount is 300 grams. Which function models the remaining amount of substance in grams, t years later A. f(t) = 300(.75)^t B. f(t) = 300 (.25)^t C. f(t) = .75(300)^t D. f(t) .25(300)∧t
A.) f(t) = 300(.75)^t
No Calculator x + y = 0 2x + 5y = 15 Which of the following ordered pairs (x,y) satisfies the system of equations above? A. (-2 , 2) B. (-5 , 5) C. (6 , -6) D. (7 , -7)
B) (-5 , 5) No need to solve! Substitute values.
No Calculator R= F/(N+F) A website uses the formula above to calculate a seller's rating, R, based on the number of favorable reviews, F, and unfavorable reviews, N. which of the following expresses the number of favorable reviews in terms of the other variables? A) F= RN/(R−1) B) F= RN/(1−R) C) F= N/(1-R) D) F= N/(R−1)
B) F= RN/(1−R)
No Calculator The graph of a line in the xy-plane has slope 2 and contains the point (1,8). The graph of a second line passes through the points (1,2) and (2,1). If the two lines intersect at the point (a,b), what is the value of (a-b)? A. -6 B. -5 C. 6 D. 5
B. -5 Graph both equations, and by doing so, you should find that the two lines intersect at the point (-1,4). Since the points of the intersection are defined as (a,b), plug in the points from the intersection to a-b, to find that -1-4=-5.
The graph of a line in the xy-plane has slope 3 and contains the point (0, 3). The graph of a second line passes through the points (2,-1) and (5, -2). If the two lines intersect at the point (a, b), what is the value of a×b? A. -1 B. 0 C. 1 D. None of the above
B. 0
No Calculator nA=360 The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 30°, what is the greatest number of sides it can have? A. 13 B. 12 C.11 D. 10
B. 12
No Calculator If 3x + 3=30, what is the value of 3x - 23? A. 10 B. 4 C. -3 D. 6
B. 4
No Calculator The measure A, in degrees of an exterior angle of a regular polygon is related to the # of sides, n. A>60° nA = 360 A. 4 B. 6 C.10 D. 8
B. 6
No Calculator A plumbing company charge $50 for the service. Plus an additional $10 to each individual on the job per hour. Using the expression 50+((10h)w)=x, and knowing that h is the amount of hours working. What does w stand for? A. The cost of service B. The number of workers on the job. C. Total cost of the job D. Tip
B. Number of workers on the job
No Calculator Which of the following equations has a graph in the xy-plane for which y is always the same value as x? A. y=-|x| B. y=x C. y=x² D. y=(x²+3x+7)²
B. y=x Looking at it from a logical standpoint, if you're looking for a graph where y is always equal to x, then you should just look for the graph with an equal sign between the y and the x.
No Calculator If 8x+3=5 what is the value of 20x-4? A. 3 B. 1 C. 4 D. -1
B.1
No Calculator (√2k²+17) −× =0 If k>0 and x=7 in the equation above, what is the value of k? A) 2 B) 3 C) 4 D) 5
C) 4
No Calculator √(3k² - 3) - x = 0 If k > 0 and x = 12 in the equation above, what is the value of k? A. -2 B. 5 C. 7 D. 8
C) 7
No Calculator Applebee's estimates the price of a job there in dollars, using the expression 70+10nh. N= # of employees, h = # of hours. Which of the following is the best interpretation of the #10 in the expression? A. minimum of 10 workers B. price increases $10 C. $10 an hour for each employee D. each person works 10 hr. a day
C. $10 an hour for each employee
No Calculator nA=360 The measure A,in degrees , of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 28°, that is the greatest number of sides it can have? A. 10 B. 11 C. 12 D. 13
C. 12
No Calculator (√(2x²+20)-j=0 when j=6 if j=6 and x>0, what is the value of x? A. 6 B. 4 C. 2 D. 3
C. 2
No Calculator Which of the following complex numbers is equivalent to (3-5i)/(8+2i)? (Note: i = √-1) A. 3/8 - 5i/2 B. 3/8 +5i/2 C. 7/34 - 23i/34 D. 7/34 +23i/34
C. 7/34 - 23i/34 Solve by multiplying by the conjugate (the same denominator but with an opposite sign) (8-2i)
No Calculator A flooring company estimates the price of a job in dollars using the expression 50+14nh, where n is the number of floorers who will be working and h is the total number of hours the job will take using n floorers. Which of the following is the best interpretation of the number 14 in this expression? A. The price of every job increases by $14 an hour. B. There will be 14 floorers working. C. The company charges $14 per hour for each floorer. D. Each floorer works 14 hours a day.
C. The company charges $14 per hour for each floorer.
No Calculator Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to -1? A. γ= |×| − 2 B. γ= ײ − 2 C. γ= (× − 2)² D. γ= ׳− 2
C. γ= (×−2)²
http://imgur.com/390n3JR <-- GO TO THIS LINK No Calculator In the xy-plane above, line l is parallel to line k. What is the value of p? A. 9 B. 12 C. 15 D. 18
D) 18
No Calculator x + y = 2 6x - 4y = 20 Which of the following ordered pairs (x,y) satisfies the system of equations above? A. (-0.8 , 2.8) B. (-3.8 , -0.8) C. (3.8 , 0.8) D. (2.8 , -0.8)
D. multiply each side of x + y = 2 by 4 add 4x + 4y = 4 to 6x-4y=20 simplify and you get x= 2.8 substitute x in x+y=2 2.8+y=2 simplify y= -0.8
No Calculator x+y=2 2x+3y=8 Which of the following ordered pairs (x,y) satisfies the system of equations above? A. (1, 2) B. (2,- 3) C. (4, -4) D. (-2, 4)
D. (-2, 4)
No Calculator If 2x + 8 = 12, what is the value of 7x - 2? A. 6 B. 8 C. 10 D. 12
D. 12 Solve for x and then plug into 7x - 2
No Calculator If xa³/xb³=x⁷, x>0,and a+b=3 , what is the value of a-b? A. 0 B. 1 C. 2 D. 3
D. 3
No Calculator 4a⁴b²+16a³b+40ab Which of the following is equivalent to the expression above? A. a⁴+4a³+10 B. 4ab+16+40 C. 60a⁷b⁴ D. 4ab(a¹b+4a²+10)
D. 4ab(a¹b+4a²+10)
No Calculator What is the sum of all values m that satisfy 2m² - 16m + 8 = 0? A. -8 B. -4√3 C. 4√3 D. 8
D. 8 Solve by quadratic formula x= (-b=±√b²+4ac)/2a OR Solve by completing the square 1/2b²
No Calculator If x^(a²)/x^(b² ) =x¹⁶,x>1, and a+b=10, what is the value of a-b? A. 4/5 B. 7 C. 8 D. 8/5
D. 8/5 Solve by noticing the common base and then factoring the difference of squares. With those factors, use substitution to isolate a-b and solve.
No Calculator Which of the following equations has a graph in the xy-plane for which y is always greater than or equal to 2? A. y = lxl + 1 B. y = x³ - 5 C. y = x² + 1 D. y = x²+2
D. y = x² + 2 Step 1: Underline key words in the question-always, greater than Step 2: Plug in 0 to identify which problems can equal positive2 Step 3: Eliminate answers that are less than positive 2
No Calculator 3x(4x + 2) + 3(5x + 3) = ax²+ bx+ c a, b, c = constants what is the value of b? A. 5 B. 9 C. 16 D. 21
D.) 21
No Calculator The sales manager of a company awarded a total of $3000 in bonuses to the most productive salespeople. The bonuses were awarded in amounts of $250 or $750. If at least one $250 bonus and at least $750 bonus were awarded, what is one possible number of $250 bonuses awarded?
Step 1. Since one $250 and one $750 bonus were awarded, setup the equation 250x + 750x = 3000 Step 2. Solve. 1000x = 3000 x = 3
No Calculator nA= 360 The measure A, in degrees, of an exterior angle of a regular polygon is related to the number of sides, n, of the polygon by the formula above. If the measure of an exterior angle of a regular polygon is greater than 85⁰, what is the greatest number of sides it can have? A. 2 B. 3 C. 4 D. 5
substitute in 85 in place of A. divide each side by 85 round to the nearest one. c) 4