Show:
Heart of Algebra
Passport to Advanced Mathematics
Problem Solving & Data Analysis
Additional Topics in Math
No Calculator Allowed!
100
If 2a/b = 1/2, what is the value of b/a? A) 1/8 B) 1/4 C) 2 D) 4
What is D?
100
f (x) = x^3 − 9x g(x) = x^ 2 − 2x − 3 Simplify f (x)/g(x) , for x > 3 ?
What is x(x+3)/(x+1)
100
−x + y = −3.5 x + 3y = 9.5 Solve for y
What is 1.5?
100
what is the sum (7 + 3i) + (−8 + 9i) ?
What is -1+12i?
100
A photocopy machine is initially loaded with 5,000 sheets of paper. The machine starts a large job and copies at a constant rate. After 20 minutes, it has used 30% of the paper. Which of the following equations models the number of sheets of paper, p, remaining in the machine m minutes after the machine started printing? A) p = 5,000 - 20m B) p = 5,000 - 75m C) p = 5,000(0.3)^(m/20) D) p = 5,000(0.7)^(m/20)
What is B? p = 5,000 - 75m
200
3x + x + x + x − 3 − 2 = 7 + x + x In the equation above, what is the value of x ? A) -5/7 B) 1 C) 12/7 D) 3
What is D? what is 3?
200
y = x^2 + 3x − 7 y − 5x +8 = 0 How many solutions are there to the system of equations above? A) There are exactly 4 solutions. B) There are exactly 2 solutions. C) There is exactly 1 solution. D) There are no solutions.
What is B? Exactly 2 solutions
200
In a random sample of 200 cars of a particular model, 3 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect? A) 150 B) 200 C) 250 D) 300
What is A? 150
200
In a right triangle, one angle measures x°, where sin x° =3/5. What is cos(90° − x°) ?
What is 3/5?
200
On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
What is 5m+4p?
300
The formula below is often used by project managers to compute E, the estimated time to complete a job, where O is the shortest completion time, P is the longest completion time, and M is the most likely completion time. E = (O + 4M + P)/6 Solve for P in terms of E, O and M
What is P = 6E - O - 4M ?
300
g(x) = 2x − 1 h(x) = 1 − g(x) The functions g and h are defined above. What is the value of h(0)? A) -2 B) 0 C) 1 D) 2
What is D? 2
300
A granite block in the shape of a right rectangular prism has dimensions 30 centimeters by 40 centimeters by 50 centimeters. The block has a density of 2.8 grams per cubic centimeter. What is the mass of the block, in grams? (Density is mass per unit volume.) A) 336 B) 3,360 C) 16,800 D) 168,000
What is D? 168,000
300
In the xy-plane, the graph of which of the following equations is a line with a slope of 3 ? A) y = 1/3 x B) y = x − 3 C) y = 3x + 2 D) y = 6x + 3
What is C? 3x + 2
300
There are two atoms of hydrogen and one atom of oxygen in one molecule of water. How many atoms of hydrogen are there in 51 molecules of water?
What is 102? 51 * 2
400
The width of a rectangular dance floor is w feet. The length of the floor is 6 feet longer than its width. Which of the following expresses the perimeter, in feet, of the dance floor in terms of w ? A) 2w + 6 B) 4w + 12 C) w^2 + 6 D) w^2 + 6w
What is B? 4w + 12
400
The sum of −2x 2 + x + 31 and 3x 2 + 7x − 8 can be written in the form ax 2 + bx + c , where a, b, and c are constants. What is the value of a + b + c?
What is 32?
400
Ages of 20 students enrolled in a College Class Age Frequency 18 6 19 5 20 4 21 2 22 1 23 1 30 1 The table above shows the distribution of ages of the 20 students enrolled in a college class. Which of the following gives the correct order of the mean, median, and mode of the ages? A) mode < median < mean B) mode < mean < median C) median < mode < mean D) mean < mode < median
What is A? mode<median<mean
400
Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill an 8 oz. glass with 1 gallon of water? a) 16 b) 8 c) 4 d) 3
What is 16?
400
x − (1/2)a = 0 If x = 1 in the equation above, what is the value of a ?
What is 2?
500
y > 2x − 1 2x > 5 Which of the following consists of the y-coordinates of all the points that satisfy the system of inequalities above? A) y> 6 B) y > 4 C) y > 5/2 D) y > 3/2
What is B? y> 4
500
A start-up company opened with 8 employees. The company’s growth plan assumes that 2 new employees will be hired each quarter (every 3 months) for the first 5 years. If an equation is written in the form y = ax + b to represent the number of employees, y, employed by the company x quarters after the company opened, what is the value of b?
What is 8?
500
The number of adults contracting colds Cold No cold Total Vitamin C 21 129 150 Sugar pill 33 117 150 Total 54 246 300 The table shows the results of a research study that investigated the therapeutic value of vitamin C in preventing colds. A random sample of 300 adults received either a vitamin C pill or a sugar pill each day during a 2-week period, and the adults reported whether they contracted a cold during that time period. What proportion of adults who received a sugar pill reported contracting a cold? A) 11/18 B) 11/50 C) 9/50 D) 11/100
What is B? 11/50
500
The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost? A) 25,000> (4,334 - 2,712)t B) 25,000< (4,334 - 2,712)t C) 25,000 - 4,334 > 2,712t D) 25,000 > (4,332/2,712)t x feet D B
What is B? 25000<(4,334-2712)t
500
On April 18, 1775, Paul Revere set off on his midnight ride from Charlestown to Lexington. If he had ridden straight to Lexington without stopping, he would have traveled 11 miles in 26 minutes. In such a ride, what would the average speed of his horse have been, to the nearest tenth of a mile per hour?
What is 25.4?