Algebra II / Integrated III TMTA Test 2018
1. Given functions 𝑓(𝑥) = 9𝑥 − 3 and 𝑔(𝑥) = 3𝑥 + 4, find f g .
a) 12𝑥 2 + 1
b) 27𝑥 2 − 12
c) 27𝑥 2 − 5𝑥 − 12
d) 12𝑥 2 + 27𝑥 + 1
e) 27𝑥 2 + 27𝑥 − 12
2. Solve the system of equations.
52 + 3𝑧 = 4(𝑥 − 4𝑦)
3(𝑥 − 3𝑦 − 𝑧) = 27
−3(2𝑥 + 𝑦) + 2𝑧 = −7
a) (4, 9, 4)
b) (4, -3, 4)
c) (4, -12, 4)
d) (4, -9, 12)
e) (-4, -9, -12)
3. In how many ways can 7 women and 4 men be seated in a row of 11 seats at a movie theater
assuming that all the women must sit together, and all the men must sit together?
a) 2048
b) 52,100
c) 120,960
d) 241,920
e) 39,916,800
4. Determine the maximum possible number of turning points for the graph of the function.
𝑓(𝑥) = (5𝑥 − 3)2 (𝑥 2 + 6)(𝑥 + 8)
a) 2
b) 3
c) 4
d) 5
e) 6
1
, Algebra II / Integrated III TMTA Test 2018
5. The volume V of a given mass of gas varies directly as the temperature T and inversely as the
pressure P. A measuring device is calibrated to give V = 144 in3 when T = 240° and P = 25
lb/in2. What is the volume on this device when the temperature is 500° and the pressure is 10
lb/in2 ?
a) V = 50 in 3
b) V = 700 in 3
c) V = 730 in 3
d) V = 750 in 3
e) V = 770 in 3
6. A herd of deer is introduced to a wildlife refuge. The number of deer, 𝑁(𝑡), after t years is
described by the polynomial function 𝑁(𝑡) = −𝑡 4 + 18𝑡 + 120. As t increases, what will
eventually happen to the deer population?
a) The deer population in the refuge will die out.
b) The deer population in the refuge will stay the same.
c) The deer population in the refuge will grow out of control.
d) The deer population in the refuge will be displaced by oil wells.
e) The deer population in the refuge will reach a constant amount greater than 0.
7. Suppose that an open box is to be made from a square sheet of cardboard by cutting out 4-inch
squares from each corner. If the box is to have a volume of 16 cubic inches, find the original
dimensions of the sheet of cardboard.
a) 10 in. by 10 in.
b) 20 in. by 20 in.
c) 12√2 in. by 12 √2 in.
d) 12√3 in. by 12 √3 in.
e) 22√2 in. by 22√2 in.
8. The concentration, in parts per million, of a particular drug in a patient’s blood x hours after the
drug administered is given by the function 𝑓(𝑥) = −𝑥 4 + 13𝑥 3 − 54𝑥 2 + 84𝑥. How many
hours after the drug is administered will it be eliminated from the bloodstream?
a) 6 hours
b) 7 hours
c) 8 hours
d) 12 hours
e) 19 hours
2
1. Given functions 𝑓(𝑥) = 9𝑥 − 3 and 𝑔(𝑥) = 3𝑥 + 4, find f g .
a) 12𝑥 2 + 1
b) 27𝑥 2 − 12
c) 27𝑥 2 − 5𝑥 − 12
d) 12𝑥 2 + 27𝑥 + 1
e) 27𝑥 2 + 27𝑥 − 12
2. Solve the system of equations.
52 + 3𝑧 = 4(𝑥 − 4𝑦)
3(𝑥 − 3𝑦 − 𝑧) = 27
−3(2𝑥 + 𝑦) + 2𝑧 = −7
a) (4, 9, 4)
b) (4, -3, 4)
c) (4, -12, 4)
d) (4, -9, 12)
e) (-4, -9, -12)
3. In how many ways can 7 women and 4 men be seated in a row of 11 seats at a movie theater
assuming that all the women must sit together, and all the men must sit together?
a) 2048
b) 52,100
c) 120,960
d) 241,920
e) 39,916,800
4. Determine the maximum possible number of turning points for the graph of the function.
𝑓(𝑥) = (5𝑥 − 3)2 (𝑥 2 + 6)(𝑥 + 8)
a) 2
b) 3
c) 4
d) 5
e) 6
1
, Algebra II / Integrated III TMTA Test 2018
5. The volume V of a given mass of gas varies directly as the temperature T and inversely as the
pressure P. A measuring device is calibrated to give V = 144 in3 when T = 240° and P = 25
lb/in2. What is the volume on this device when the temperature is 500° and the pressure is 10
lb/in2 ?
a) V = 50 in 3
b) V = 700 in 3
c) V = 730 in 3
d) V = 750 in 3
e) V = 770 in 3
6. A herd of deer is introduced to a wildlife refuge. The number of deer, 𝑁(𝑡), after t years is
described by the polynomial function 𝑁(𝑡) = −𝑡 4 + 18𝑡 + 120. As t increases, what will
eventually happen to the deer population?
a) The deer population in the refuge will die out.
b) The deer population in the refuge will stay the same.
c) The deer population in the refuge will grow out of control.
d) The deer population in the refuge will be displaced by oil wells.
e) The deer population in the refuge will reach a constant amount greater than 0.
7. Suppose that an open box is to be made from a square sheet of cardboard by cutting out 4-inch
squares from each corner. If the box is to have a volume of 16 cubic inches, find the original
dimensions of the sheet of cardboard.
a) 10 in. by 10 in.
b) 20 in. by 20 in.
c) 12√2 in. by 12 √2 in.
d) 12√3 in. by 12 √3 in.
e) 22√2 in. by 22√2 in.
8. The concentration, in parts per million, of a particular drug in a patient’s blood x hours after the
drug administered is given by the function 𝑓(𝑥) = −𝑥 4 + 13𝑥 3 − 54𝑥 2 + 84𝑥. How many
hours after the drug is administered will it be eliminated from the bloodstream?
a) 6 hours
b) 7 hours
c) 8 hours
d) 12 hours
e) 19 hours
2
