Algebra 1 Honors
Midterm Review Packet
Name:______________________________________ Block:______
1. After finishing this study guide and checking your answers on Black Board, how else will
you study for the midterm?
Evaluate:
wu
when w = -10 and u = 5
u
2. 3p – q when p = 7 and q = -3
3.
4. x 3 when x = -2.
5. (2xy) for x = 5 and y = -3.
6. (3q)  1 for q = -2
7. (x + 3) (10 – x) for x = 4.
3
8. Evaluate each expression.
2
3
a. (4 – 2) + (6 – 1) – (10 – 6)
2
(4  2)3  (2) 2  8  2
b.
(2)3
(4  3) 2  (7  7)
c.
(3)3
9. Evaluate each expression when x = 2, w = -6 and a = 8.
a. (a + 2)(w2 – 3x)
b. (–w)2 – (5a – 10x)
c. (x)3 + (6w – 2a + xw)
10. Translate the following into verbal or mathematical expressions.
a. (2x + 5)2 ________________________________________________________________
b. The difference of seven times a number y and 10 times a number x, divided by the product of 2
and a number p.
c.
(3x  4)
____________________________________________________________
(5 x  2)
11. Solve each equation.
a. -x + 316 = – 214
b. – 7x + 17 = 164
c. -
2
x  144
3
d.
c
 8  42
4
2
1
n8  n2
3
3
e. 5t – (2t + 3) = 21
f. 81(t + 2) = 27(t – 2)
g.
h. 3(m + 1.5) = 1.5(2m + 3)
i. 2.1x + 45.2 = 3.2 – 8.4x
j. 3x – 2(x + 3) = x
k.
n.
4 x 1
 x
5
5
x  8  12
l.
4d  5
7
7
o. 3x  5  4
m.
y4 4

y 1 3
p. 2 x  6  12  10
12. Solve each word problem using an equation.
a. Eighty-two increased by some number is -34. Find the number.
b. One and two thirds of a number equals one and a half. What is the number?
c. Four times a number decreased by twice the number is 100. What is the number?
d. Find four consecutive integers whose sum is 130.
e. Find two consecutive integers such that twice the lesser integer increased by the greater
integer is 49.
f. The sum of two number is 25. The smaller is three less than the larger.
g. Mary’s test grades are as follows: 82, 96, 74, and 88. The last test of the marking period is
coming up and Mary really wants an 86 test average to keep her grade at a B. What would she have
to get on the fifth test in order to achieve this?
1
h. Lilly’s hair is 8 inches long and grows 1 inches a month. Danny’s hair is 4 inches long and
3
grows 2 inches a month. When will Lilly and Danny have the same length hair? (equation and
solution)
i. School guidelines require that there must be at least 2 chaperones for every 25 students going
on a school trip. How many chaperones must there be for 80 students?
13. Solve each equation for the variable specified.
a.) 5x = y; solve for y.
b.) ay – b = c; solve for y.
d. )
x y
 c ; solve for x.
b
e.)
2 y  a a  3b
; solve for y.

3
4
14. Give an example 2 ordered pairs that satisfies the equation: 2x – 5y = 16
15. State the formula for slope.
16. State the Slope-Intercept Form of an equation.
17. State the Point-Slope Form of an equation.
18. State the Standard Form of an equation and list the conditions.
19. Horizontal lines have ________________ slope.
20. Vertical lines have __________________ slope.
21. The equation of a horizontal equation looks like ______________. Give an example:
22. The equation of a vertical line looks like ________________. Give an example:
23. Parallel lines have ___________________ slope and different ______________.
Give an example of two parallel line equations:
24. Perpendicular lines have ______________________ slope.
Give an example of two perpendicular line equations.
25. Find the slope between the following points.
a. (4, -2) and (10, -7)
b. (-34, 16) and (-34, - 5)
c. (-11, 25) and (12, 25)
26. Graph each point and name the quadrant in which each point is located.
Point
Quadrant
a)
(6, 8)
_______
b)
(–3, – 7)
_______
c)
(–2, 5)
_______
d)
(9, –4)
_______
27.
Graph each linear equation using x and y Intercepts.
a) y = 4x – 8
b) y = –
1
x+3
2
28. Graph a line using the given information.
a) point: (4, –6); slope:
1
3
b) point: (– 7, 2); slope: 0
c) point: (5, 9); slope: undefined
29.
a) y =
Identify the slope and y – intercept for each equation AND graph the line.
4
x–5
3
b) 4x – 6 = 12
c) x = 8
slope: ______
slope: ______
slope: ______
y – intercept: ______
y – intercept: ______
y – intercept: ______
30. a) Write the equation of the line given the following information. b) Graph the line.
a) The slope m = – 4, and the y-intercept b = 2. b) Goes through the point (1, 2) and has slope
6
5
c) Goes through the points (8, –6) and (5, 2).
d) Has an x-intercept of –4 and a yintercept of –5.
31. Parallel and Perpendicular Lines
a) Write the equation of the line parallel to 4x – 7y = 9 and passes through (1, – 3).
1
3
b) Write the equation of the line perpendicular to y =  x – 6 and passes through (–10, 8).
c) Write the equation of the line perpendicular to 4x – 7y = 9 and passes through (1, – 3).
1
3
d) Write the equation of the line parallel to y =  x – 6 and passes through (–10, 8).
32. Is the following relation a function? Explain your answer. Also, state the domain and range.
 2,3 , 2,5  ,  4,7  ,  4,9  , 11,5 
33. Find the zeros of each function.
A.
B.
x
y
-3
0
-2
3
-1
4
0
5
1
0
_____________
C. USE CALCULATOR:
Round to the nearest 100th.
f (x )  x 2  3x  6
_____________
_____________
34. Is the pattern arithmetic or geometric? Find the common ratio or difference and determine
the next three terms in the pattern.
-2, -22, -42, -62,...
35. If f(x) = -2x – 2 then find f(-4)
36. f(x) represents a linear function. If f(2)=4 and f(6)=10 find the slope of the line.
37. f(x) represents a linear function . If f(2) = 4 and f(6)=10 then write the equation in pointslope form, slope-intercept form, and standard form.
38. If f(x) = -6x and g(x) = 2x2 -5 then find
a. f(g(x) )
b. g(f(x))
c. f(g(-2))
d.
g(f(-2))
39. To rent a boat costs $120. The cost is split among several friends. Let x be the number of
friends and y be the cost per person. Does this situation represent direct or inverse variation?
Explain your reasoning and identify the equation that models this situation.
40. You download several movies for $14.99 each. Let x be the number of movies you download
and let y represent how much money you must pay. Does this situation represent direct or inverse
variation? Explain your reasoning and identify the equation that models this situation.
41. Do any of the lines in the graph to the right represent a
function with direct variation? Explain your reasoning.
42.
43.
Is it a function?____________
State the domain:__________________
State the range:__________________
Set Builder for Domain:____________
Set Builder for Range:_____________
Is the relation a function?___________
Interval Notation for
Domain:_________________
Interval Notation for
Range:__________________
Solve each inequality.
44. −11 < −𝑥 + 4 ≤ −8
47. |𝑥 − 5| > −8
45. |2𝑥 − 4| > 10
48. |4𝑥 + 12| ≤ 0
46. 𝑥 > 5 𝑜𝑟 𝑥 > 12
49. Write the inequality pictured
50. Doreen is making a rectangular garden in her yard, and she has 55 feet of fencing. She
has to make the width 8 feet across. Write and solve an inequality to determine the
possible lengths of the garden that could be enclosed by the fencing.