MCA/ACT Math Additional Practice
Algebraic Thinking
Simplify:
1. -5x(2x + 7y) + 7xy – 4x(y + 3)
2. (3x + 2)(2x2 – 7x – 4)
Factor completely:
3. 10x2 – 160
4. 2x7 + 10x5 - 28x3
Simplify:
n2 2n 24
5. 2
n 11n 28
6.
7.
3x 4
x 2 16
x2
2
x 4
8x 16
x 3
2x 8
x2 9
Name:_____________________
8. Which equation is equivalent to 4(2 – 5x) = 6 – 3(1 – 3x)?
A.
B.
C.
D.
8x = 5
8x = 17
29x = 5
29x = 17
Solve:
9. 2x + 7 = 7x – 23
10. 3(x – 6) < 5x + 6
11. 3x 7
5
12. -8 < -2x + 4 < 6
13. Which of the following absolute-value inequalities best represents the graph shown on the
number line below?
A.
x 2
3
B.
x 2
3
C.
x 3
2
D.
x 3
2
14. In 1980, the average price of a home in Brainerd County was $95,000. By 1987, the average
price of a home was $123,000. Which of the following is a linear model for the price of a home,
P, in Brainerd County in terms of the year, t? Let t = 0 correspond to 1980.
A. P = 123,000 – 4000t
B. P = 4000t + 95,000
C. P = 123,000 – 28,000t
D. P = 28,000t + 95,000
15. A car manufacturer is testing a new car on a test track. The graph below represents the
relationship between the number of miles the car has been driven on the test track and the
amount of gas in the car’s gas tank.
A. Write an equation that relates the number of gallons of gas in the gas tank (y) to the
number of miles the car has been driven (x).
B. The car’s gas tank holds 12.0 gallons. Based on the test results, how far could the car
drive on the test track if it started with a full tank of gas?
16. Write the equation in slope-intercept form. Then identify the slope and y-intercept:
18x – 42y = 24
17. Which equation best represents the line graphed below.
A.
B.
C.
D.
7x + 4y = 35
4x – 7y = 35
4x + 7y = -35
7x – 4y = -35
18. Simplify:
( 6a 3 b 5 )(2a 2 b 3 )
18a 4 b 8 c 3
19. A new computer can perform 6.0 x 108 computations in 1 second. How many computations can
the computer perform in 60 seconds?
A. 1.0 x 107
B. 1.0 x 109
C. 3.6 x 109
D. 3.6 x 1010
Solve
20. x2 – 5x = -4
21. 3x2 + 4x – 4 = 0
22. Identify the solutions for the graph:
23. An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The
equation for the object's height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 58.8,
where s is in meters. When does the object strike the ground?
24. The number of seats in each row of an outdoor theater can be found using the following
recursive function:
a1
37
an
an 1
3
Find the number of seats in the 10th row.
25. A cup of coffee contains approximately 96 mg of caffeine. When you drink the coffee, the
caffeine is absorbed into the bloodstream and is eventually metabolized by the body. Every 5
hours the amount of caffeine present in the body is reduced by one-half. How many hours does
it take for the amount of caffeine to be reduced to 12 mg?
26. What is the solution to the following system?
y
x
27. Determine the solution to the system of inequalities:
A.
B.
y
y
3x
y
x
C.
x
D.
y
y
x
x
28. Decide whether Line 1 and Line 2 are parallel, perpendicular, or neither.
Line 1 passes through (–3, –7) and (–7, –5)
Line 2 passes through (–5, –2) and (–7, –6)
29. Which of the following lines is parallel to 3x + 6y = 11?
a. y = 3x + 11
b. y = ½ x + 2
c. y = -2x + 3
d. y = - ½ x + 5
e. y = 2x + 4
x 3
y
7