Download 2) simplify (8x

Typical Questions on the Algebra Challenge Exam
A. Polynomials
1) simplify (5x 2 – 3x + 4) – (9x 2 + 4x – 1)
2) simplify (8x 2 y – 3xy 2 + 4) + (5xy 2 – 3) + (4x 2 y – 7)
3) simplify (4x – 5)(2x + 6)
4) simplify (7x – 3) 2
5) factor 4x 2 – 9
6) factor 3x 2 – x – 2
7) solve by factoring 7x 2 – 2x – 5 = 0
8) solve by factoring 2x 2 – 11x + 12 = 0
9) graph y = x 2 – 4 by making a table of values
B. Lines
10) In the point (4, -3) on the line 2x – y = 11
11) Graph the line that goes through the point (4, 5) and has a slope of – ½
12) Find the slope of the line that contains the points (4, -8) and (-3, -2)
13) Graph the line y = 2x – 3
14) Graph the line 5x – 2y = 8
15) Graph both lines: y = 4 and x = -2
16) Find the x and y intercepts of 4x – 7y = 28
17) Write the equation of the line that contains the point (4, 6) and slope = - ½
18) A taxi cab charges $5 to come to your house plus $2.25 for every mile it takes
you. Write a linear equation to fit this information using “m” for miles and “c”
for cost. Graph your equation.
C. Miscellaneous
19) simplify 12 + 24 ÷ 8 × 3 − 4
20) simplify 40 − 2 × 8 ÷ 80 ÷ 20 ÷ 22
21) simplify 4 – 3(2 – 9) + 6
22) Simplify -4 2 – 3ab if a = 2/3 and b = 7 [hint: -4 2 implies –(4) 2 ]
23) Accurately graph x ≥ −7 / 3 on a number line
24) Without a calculator simplify ¾ + 7/12
25) Without a calculator simplify 5 18 [hint:
12 = 4 × 3 = 2 3 ]
D. Solving. If answer is not a whole number, give fractional answer, not decimal.
26) 3 – 2(x – 5) – (x – 8) = 13
27)
5
x−3= 7
4
28)
2x − 7 x + 1
(hint: begin by cross multiplying)
=
3
2
29) Solve the system of equations
2x – y = 5
x+y=4
30) 7 x + 2 = 4