1. Quarterly # 3
Algebra 1A Review:
Multiple Choice,
Select All That Apply,
Open-Ended

2. infinitely many solutions1.
infinitely many solutions
one solution
no solution
cannot be determined

3. infinitely many solutions1.
Graph the first line.
Graph the second line.
The equations are of the same line.
infinitely many solutions
Answer:

4. infinitely many solutions2.
infinitely many solutions
one solution
no solution
cannot be determined

5. 2. The graphs intersect at one point. Answer: Graph the first line.
Graph the second line.
The graphs intersect
at one point.
one solution
Answer:

6. infinitely many solutions3.
infinitely many solutions
one solution
no solution
cannot be determined

7. 3. The graphs do not intersect. Answer: Graph the first line.
Graph the second line.
The graphs do not
intersect.
no solution
Answer:

8. 4.
(2, 2)
(2, 2)
(4, 2)
(2, 4)

9. 4. The graphs intersect at the point (2, 4). Answer:
Graph the first line.
Graph the second line.
The graphs
intersect
at the point (2, 4).
(2, 4)
Answer:

10. 5. 1 1 7 7

11. 5. Substitute 5 into the equation: 2x + y = 3 2(5) + y = 3 10 + y = 3
 10
y = 7 7
Answer:

12. 6.
(2, 5)
(2, 5)
(5, 2)
(4, 7)

13. 6. 1 x + y = 3 x  y = 7 If you add the equations, y cancels out.
x = 2
x + y = 3
Use either
equation
to find y:
(2, 5)
Answer:
2 + y = 3
– –2
y = 5

14. 7. 2 2 5 5

15. 7. 6x + 5y = 27 +5y cancels with 5y  5y
5( )
+5y cancels
with 5y
6x + 5y = 27
 5y
In order to get 5y, multiply the bottom
row by 5. 5
Answer:

16. 8.
(2, 4)
(2, 4)
(4, 2)
(4, 2)

17. 8. Answer: Cancel x by making 20x and 20x. 4 ( ) 5 ( )
4 ( )
5 ( )
Get either variable to cancel.
20x + 28y = 136
20x  15y = 110
Substitute into any equation to find x:
13y = 26
4x + 3y = 22
y = 2
4x + 3(2) = 22
4x + 6 = 22
6 6
4x = 16
(4, 2)
Answer:
x = 4

18. 9.
(1, 6)
(3, 2)
(2, 3)
(4, 1)

19. 9. Answer: See which point is NOT shaded in the graph.
Plot each point:
(1, 6),
(3, 2),
(2, 3),
(4, 1)
The point (1, 6)
is outside of the shaded region.
(1, 6)
Answer:

20. 10.
(3, 1)
(0, 0)
(1, 0)
(2, 4)

21. 10. Answer: See which point is shaded in the graph. Plot each point:
(3, 1),
(0, 0),
(1, 0),
(2, 4)
The point (2, 4)
is inside of the shaded region.
(2, 4)
Answer:

22. 11.
y ≥  x + 4 1 3
y ≤  x + 4 1 3
y ≥ 3x + 4
y ≤ 3x + 4

23. 11. Answer: The shading is above the line: use ≥.
The y-intercept is 4.
The inequality is in the
form y ≥ mx + 4.
Find the slope, m.
Use (0, 4) and (1, 1).
Answer:
y ≥ 3x + 4
m =
1 – 4
1 – 0 =
– 3 1
= – 3

24. 12. 7x 8 7x 6 8x 8 8x 6

25. 12.
(7x )(x )
= 7x  x
When multiplying powers, add the exponents and keep the base.
= 7x
4+2
= 7x 6 7x 6
Answer:

26. 13. y 20 4y 5 y 9 4y 9

27. 13. Answer: (y ) When raising powers, multiply the exponents
5 4
When raising powers, multiply the exponents
and keep the base.
= y
54
= y 20 y 20
Answer:

28. 14. a 8 a 3 a 12 a 4

29. 14. Answer: a When dividing powers, subtract the exponents6 2
When dividing powers, subtract the exponents
and keep the base.
= a
6 – 2
There are 4 more factors of “a” in the numerator.
= a 4 a 4
Answer:

30. 15. 3x 4 y 5
14 x 4 y 5 3x 6 y 5
14x 4 y 5

31. 15. = = Answer: Divide the coefficients. 21x y 21 ÷ 7 = 3 7x y
5 3
7x y
1 8
Divide the coefficients.
21 ÷ 7 = 3
Place the x as x
in the numerator. 
3x x y y 8 = 3x
5+1 y
8 – 3 =
Mult.  add exponents.
Div.  subtract exponents 3x 6 y 5
Answer:

32. 16. 4x + 5x y + 3xy + 6y 5x y  4x + 3xy + 6y 6y + 3xy + 5x y  4x
5x y  4x + 3xy + 6y
6y + 3xy + 5x y  4x
6y + 5x y + 3xy  4x

33. 16. Answer: Descending Order: greatest power of x to
least power of x.
5x y y  4x x y
4x + 5x y + 3xy + 6y
Answer:
Separate the terms and determine their signs.

34. 17.
7m – 3 2 2
7m + 11
7m – 18m – 3 2 2
6m – 18m – 3

35. 17. Answer: 6m – 9m + 4 Line up the like terms. Add the coefficients.2
Line up the like terms.
Add the coefficients.
+ 1m – 9m – 7 2
7m – 18m – 3 2
Answer:

36. 18. 3 4 73 a = the cost of an adult c = the cost of a child
a = the cost of an adult
c = the cost of a child
3a + 4c = adults & 4 children
3a + 7c = adults & 7 children
Highlight the important information in order to answer the question.
The group number is not important for writing the system.

37. 18. 3a + 4c = 73 3a + 7c = 94 3a + 4c = 73 3a  7c = 94 3a + 4c = 73
1( )
3a + 4(7) = 73
3a + 28 = 73
3c = 21
28 28
 3
Adult ticket = $15
Child’s ticket = $7
3a = 45
c = 7
a = 15
Take the opposite of one row (multiply by 1) for “a” to cancel.
Solve for c.
Substitute into any of the equation to find “a”.
Explain what the solution means.

38. 19.   7x x When dividing powers, subtract the exponents.2 x 10
When dividing powers,
subtract the exponents.
The “7” is a coefficient
and cannot change location.
= 7x
210
= 7x 8
A negative exponent in the numerator = a positive exponent in the denominator. 7 x 8 =

39. 20.  4y3 + 8x3  6xy y3 – 4x3 + 12xy Line up the like terms.  18xy
Combine the like terms.
 4y3 + 8x3  6xy

40. 20.  4y3 + 8x3  6xy Find the degree of each polynomial.
1+1 = 2
The highest degree of the polynomials = 3

41. 20.
 4y3 + 8x3  6xy
The polynomial
has 3 terms:
 4y3, 8x3, 6xy

42. 20. 8x3 – 6xy – 4y3 terms and look at the exponents of x.
Separate the
terms and look at the exponents of x.
 4y3 + 8x3  6xy
 4y3 + 8x3  6x1y1
The exponents of x
are decreasing
(getting lower).
8x3
– 6xy
– 4y3

43. Keep studying for your Quarterly Exam.
The End
Keep studying for your Quarterly Exam.

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