Heart of Algebra
Passport to Advanced Mathematics
Problem Solving & Data Analysis
Additional Topics in Math
No Calculator Allowed!
Spring Trivia
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
On Thursday, 240 adults and children attended a show. The ratio of adults to children was 5 to 1. How many children attended the show?
A) 40
B) 48
C) 192
D) 200
A) 40
100
In the xy-plane, the graph of which of the following equations is a line with a slope of 1/3 ? A) y = 1/3 x B) y = x − 3 C) y = 3x + 2 D) y = 6x + 3
What is A? 1/3 x
100
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?
100
Is this true or false? Tornadoes are more prevalent in the spring.
True
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
what is the sum (7 + 3i) + (−8 + 9i) ?
What is -1+12i?
200
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
According to legend, if a groundhog does not see his shadow when he emerges from his hole on Groundhog Day, Spring will arrive (late or early)?
Early
300
A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14, 2)
D) (14, 2)
300
g(x) = ax² + 24
For the function g defined above, a is a constant and g(4) = 8. What is the value of g(-4)?
A) 8
B) 0
C) -1
D) -8
A) 8
300
On an architect's drawing of the floor plan for a house, 1 inch represents 3 feet. If a room is represented on the floor plan by a rectangle that has sides of lengths 3.5 inches and 5 inches, what is the actual floor area of the room, in square feet?
A) 17.5
B) 51.0
C) 52.5
D) 157.5
D) 157.5
300
In right triangle ABC, B is the right angle. What is the greatest possible integer measurement of one of the acute angles?
89
300
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
In the Southern Hemisphere, which month marks the start of spring?
September
400
Which of the following numbers is NOT a solution of the inequality 3x - 5 ≥ 4x - 3 ?
A) -1
B) -2
C) -3
D) -5
A) -1
400
If a2 + 14a = 51 and a > 0, what is the value of a + 7?
10
400
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
400
In a right triangle, one angle measures x°, where
sin x° =3/5. What is cos(90° − x°) ?
What is 3/5?
400
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
March is named after which Roman God?
Mars (Aries), the Roman God of war.
500
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
500
What are the solutions to the equation x2 - 3 = x?
A) (−1 ± √11) / 2
B) (−1 ± √13) / 2
C) (1 ± √11) / 2
D) (1 ± √13) / 2
D) (1 ± √13) / 2
500
County Y consists of two districts. One district has an area of 30 square miles and a population density of 370 people per square mile, and the other district has an area of 50 square miles and a population density of 290 people per square mile. What is the population density, in people per square mile, for all of County Y?
320
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
What is B? 25000<(4,334-2712)t
500
x − (1/2)a = 0
If x = 1 in the equation above, what is the value of a ?
What is 2?
500
Which ancient building in Africa was constructed facing the direction where the sun rises on the first day of spring?
Great Sphinx
