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Integrated Math I Spring Final Study Guide
For Questions 1 and 2, graph each system on the graph provided and determine how many solutions exist
for each system of equations.
1. 𝐲 = −𝐱 + 𝟑
𝒙 + 𝒚 = −𝟏
2. 𝟐𝐱 + 𝟐𝐲 = 𝟔
𝐲 = −𝐱 + 𝟑
A. no solution
C. infinitely many solutions
B. one solution D. cannot be determined
A. no solution
C. infinitely many solutions
B. one solution D. cannot be determined
3. When solving the system of equations, which expression could be substituted for x in the second equation?
ì x + 5y =12
í
î2x - 3y = -1
A
3y -1
2
B 12 - 5y
4. Solve the system x – 9y = 6 and x + 3y = 14 for x.
C 12 + 5y
D 3y – 1
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5. Solve the following system of equations by graphing.
Date:
2
3
𝑦 = − 𝑥+1
𝑦 =𝑥−4
A. (-1, 3)
B. (3, -1)
C. (2, -2)
D. (1, -3)
6. Solve the following system of equations (6 points):
𝟖𝒙 − 𝟕𝒚 = 𝟓
𝟑𝒙 − 𝟓𝒚 = 𝟗
7. Determine the best method to solve the system of equations. Then solve the system.
𝒙 = 𝟒𝒚 − 𝟑
𝟔𝒙 + 𝒚 = 𝟑𝟐
BEST METHOD:
SOLUTION:
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8. Solve the system of linear equations by substitution method:
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𝒙 = −𝟑𝒚 + 𝟔
{
𝟒𝒙 + 𝟏𝟐𝒚 = 𝟐𝟒
A. (3, 1)
B. (3, -1)
C. No solution
D. Infinitely Many Solutions
9. Solve the system of inequalities by graphing (Graph both lines and use two colors for shading):
𝟏
−2x + 2y ≤ 6
𝒚 > −𝟐𝒙 −𝟐
10. The substitution method should be used to solve which system of equations?
A. 2x + 4y = 16
B. 4x + 3y = 24
3x + 6y = 75
4x+12y = 48
C. 5x – 3y = 15
8x+9y=72
D. x = 5y +3
2x+ 4y = 62
11. Mrs. Tovar is giving a quiz that has 15 more two-point questions (x) than four-point questions (y). The quiz is
worth 75 points. Which system represents this information correctly?
A. y = x +15
B. y = x + 15
4x+2y=75
2x+4y=75
C. x = y + 15
4x+2y=75
D. x = y + 15
2x+ 4y=75
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12. Solve the system of inequalities by graphing. Name a point that IS a solution.
1
y < x +1
3
y £ -2x
13. How many lines can be drawn for points W, X, Y and Z ?
A. 0
B. 2
C. 4
D. 6
For Exercise 14, in the figure, ⃗⃗⃗⃗⃗
𝑆𝑈 and ⃗⃗⃗⃗⃗
𝑆𝑅 are opposite rays.
14. If m<VSR = 8x +18, find the value of x so that ⃡⃗⃗⃗
𝑈𝑆 ⊥ ⃡⃗⃗⃗
𝑉𝑆.
15. Name polygon EFGHI by its sides. Then classify it as convex or concave and regular or not regular.
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16. Name 3 collinear points? (Use the figure below)
17. Name the intersection of the plane that contains points A, F, E and B and plane W.
A. point A
B. triangle ABC
C. ⃡⃗⃗⃗⃗
𝐸𝐹
D. ⃡⃗⃗⃗⃗
𝐴𝐵
18. Find the length of segment AB.
3
cm
10
B. 2
3
cm
4
D. 2
A. 2
C. 1
1
cm
2
9
cm
10
19. Given B is between M and N and ̅̅̅̅̅
𝑀𝐵 = 16𝑥, ̅̅̅̅
𝐵𝑁 = 12𝑥, 𝑎𝑛𝑑 ̅̅̅̅̅
𝑀𝑁 = 18𝑥 + 50, 𝑓𝑖𝑛𝑑 ̅̅̅̅̅
𝑀𝐵.
*Draw a picture
20. Find the length of 𝑃𝑄.
̅̅̅̅ 𝑖𝑠 2𝑥 + 4, ̅̅̅̅
21. Find the value of x if R is between Q and S, 𝑄𝑅
𝑅𝑆 𝑖𝑠 7𝑥, 𝑎𝑛𝑑 ̅̅̅̅
𝑄𝑆 𝑖𝑠 76.
*HINT: Draw a picture and label it
22. Find the distance between M(6, 8) and N(9, −3).
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A. √28
Date:
B. √130
C. 6
Period:
D. √34
23. Find the coordinates of the midpoint of 𝐴𝑆 if A ( −8 , −3) and S (14, −10).
24. Write an equation in slope-intercept form for the line that has a slope of 7 and contains (–2, 6).
25. Name the angle pair: ∠2 and ∠10
A. alternate exterior
C. consecutive interior
B. alternate interior
D. corresponding
26. Given p║ q, and m<10= 6x – 14, and m<16 = 4x + 20, find the value of x.
27. Given m∠6 + m∠11 = 180, which postulate or theorem justifies that s ║ t?
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A. Converse of Corresponding Angles Postulate
B. Consecutive Interior Angles Converse
C. Alternate Exterior Angles Converse
D. Alternate Interior Angles Converse
28. If s ║ t by the Alternate Interior Angles Theorem, which angle pair must be congruent?
A. ∠6 and ∠2
C. ∠6 and ∠4
B. ∠6 and ∠12
D. ∠6 and ∠16
29. If m<3 = 2𝑥 + 16 and m<8 = 10𝑥 − 4 find the value of x so that p ║ q.
A. 14
B. 4
C. 20
D. 2.5
30. Determine the slope of the line that contains the given points: C (−3, 7), D(2 , −8)
A. –3
1
B. − 3
C.
1
3
31. What is the distance from A to B shown in the figure?
D. 3
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3
32. If line q has a slope of − 4, what is the slope of any line perpendicular to q?
B. –4
A. 3
4
C. − 3
Period:
D.
4
3
33. Find the slope-intercept form of the equation of the line that passes through (5, −4) and is parallel to
9𝑥 + 3𝑦 = −12.
A. y = −3x − 7
B. y = −3x + 11
C. y = 3x − 19
D. y = 3x + 11
3
34. Write an equation of the line in slope-intercept form that is perpendicular to the graph of 𝑦 = 4 𝑥 − 8 that passes
through (−6, 3).
4
3
A. y = − x + 5
4
3
B. y = − x − 5
3
4
C. y = x + 4
⃡⃗⃗⃗⃗⃗ are parallel, perpendicular, or neither.
35. Determine whether ⃡⃗⃗⃗
𝑪𝑺 and 𝑲𝑷
C (5, –3), S (8, 6), K (1 , 1), P (10, –2)
4
3
D. y = − x + 11
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For problems 36 and 37 use the figure on the right:
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36. Find the values of x given m ║ n, m<5 = 4x + 46, m<13 = 8𝑥 − 14, and m<8 = 3y + 2.
37. Find the values of y given m ║ n, m<5 = 4x + 46, m<13 = 8𝑥 − 14, and m<8 = 3y + 2.
38. Write the equation 𝑦 + 20 = −4(𝑥 − 8) in slope-intercept form:
A. y = −4x + 12
B. y = −4x + 32
39. What are the missing coordinates of the triangle?
A. (𝑎, 0)
C. (𝑐, 0)
B. (0, 𝑎)
D. (𝑏, 0)
C. y = 4x + 12
D. y = −4x − 12
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40. Find the value of x.
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41. Find the value of y.
42. ABCD is a parallelogram with diagonals intersecting at E. If AE = 6x +14 and EC = 98, find the value of x.
*Hint: Draw a picture
A. 13
B. 12
C. 18.6
43. Find the values of x and y so that the quadrilateral is a parallelogram.
D. 14
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44. A quadrilateral has interior angles with measures (2x – 10)°, (3x + 70)°, (4x + 25)°, and (x + 35)°. Find the
value of x. (Hint: The sum of the measures of the interior angles of a quadrilateral is 360)
A. 18
B. 22
45. For isosceles trapezoid MNOP, find m∠MOP.
C. 24
D. 15
46. The length of one base of a trapezoid is 32 meters and the length of the median is 48 meters. Find the length of the
other base (Draw a picture).
47. For kite WXYZ, find m∠Y.
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48. The diagonals of square ABCD intersect at E. If AE = 2x – 9 and BD = 8x – 54, find AC.
A. 9
B. 72
C. 36
D. 18
49. Given rectangle ABCD, find the value of x.
50. Matthew carved an equilateral triangle that is 2 centimeters on each side on a pumpkin. Then she carved another
equilateral triangle that is 7 centimeters on each side. What scale factor did Stella use to increase the size of the triangle?
Scale Factor: ________
new
original