Name: ______________________ Class: _________________ Date: _________
Q3 Algebra Introductions Benchmark Review
Short Answer
Evaluate the expression.
1. −3 2 − 4(3 + 4 − 5 ⋅ 3)
2. −2.1 + 3.4 − 5.7 + 4.1 − 1.9
3. 2 1 + 3 1 − 1 1
3
2
4
3
2
4. 3 3 − 4 2 ⋅ 2
1 −2 −2
5. 1 3 ⋅ 2 2 ÷ 21
4
3
5
6. 2.3 + 3 − 1 3 − 1.6
4
5
Solve the equation or formula for the variable specified.
7. xy − 10z = 8 for y
8. −2df + 2h = 2g for d
Use the Equal Values Method to find the Point of Intersection.
9. y = x + 1
y = 2x
10. x = 3y − 9
x = −3y + 3
11. x = 2y − 1
x = 3+y
12. y = −4x − 1
y = −3 − 3x
Use Double Distribution on the problems below. Simplify completely.
13. (4r − 9 ) 2
14. (r − 7 ) (r + 4 )
1
ID: A
Name: ______________________
ID: A
15. (−4t − 3v) (−6t − 2v)
16. (−7k + 5)(−4k 2 + 2k − 7)
17. (7m 2 − 5m + 5)(−5m 2 − 2m − 9)
18. (b + 5 ) 2
Solve the equation. Then check your solution.
19.
x
7
=
90
9
20. -2 1 p= -3
7
21. -8p= -3 1
4
22.
a
−7 = 5
−7
23.
8
3
= z+
13
4
24.
7
8
a=
9
10
Solve the equation. Then check your solution.
25. −7m + 20 = −17m − 10
26. 4 k − 5 = −7 + 2 k
5
5
27. 1 (15 + 7d) = − d
2
4
28. − 1 x − 2 = 4 − 1 x
5
3
5
3
29. 3 + 1 (5k + 2) = 14
2
Find the slope of the line that passes through the pair of points.
30. (2, –3), (–5, 1)
31. (1, 2), (5, 4)
Write an equation of the line with the given slope and y-intercept in Slope-Intercept Form
32. slope: 27 , y-intercept: –3
2
Name: ______________________
ID: A
33. slope: 0.8, y-intercept: 10
Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle.
34. Write an equation for the total cost C of renting a bicycle and riding for m miles.
Write a linear equation in slope-intercept form to model the situation.
35. The temperature is 38° and is expected to rise at a rate of 3° per hour.
Write an equation of the line that passes through each point with the given slope.
36. (0, 6), m = −3
37. (−1, 5), m = 2
Write an equation of the line that passes through the pair of points.
38. (−5, −2)(3, −1)
39. (3, −1), (1, −7)
Write each equation in standard form.
40. y – 3 = 35 (x – 9)
41. y + 4 = (x + 8)
Write the equation in slope-intercept form.
42. y – 5 = 34 (x – 5)
43. y + 4 = −2 (x − 5 )
Find the sum or difference.
44. (6a − 2b 2 − a) + (b − 3 + 9a 2 )
45. (8a − 3a 2 ) + (3 + 7a)
46. (2a − 4a 2 ) − (−8a − 4)
47. (10p − 3q 2 − q) − (q 2 − 5p + 6p 2 )
Find the product.
48. −5r 3 (4r 2 − 2r − 5)
3
Name: ______________________
ID: A
49. −2s 2 t 4 (−6s 3 t 5 − 6st 4 − 4t)
Solve the equation.
50. 3p(3p − 8) − 8 = 9p(p − 3) + 4
51. 4x (−x − 3 ) = 2(−2x 2 − 2) − 2
52. 2y(y + 3) − 7y = y(y + 3) + y(y − 6) + 8
53. 3 (4x + 4 ) = 2 (5x + 9 ) − 12
Graph the system of equations. Then determine whether the system has no solution, one solution, or
infinitely many solutions. If the system has one solution, name it.
54. y = x + 3
y = −2x − 3
55. −5x + y = 1
−4x − 5 =
y
4
4
ID: A
Q3 Algebra Introductions Benchmark Review
Answer Section
SHORT ANSWER
1. 23
2. -2.2
3. 55
4.
5.
6.
7.
8.
12
1
10
9
-0.15
8 + 10z
y=
x
2g − 2h
d=
−2f
9.
10.
11.
12.
(1, 2)
(–3, 2)
substitution; (7, 4)
substitution; (2, − 9)
13.
14.
15.
16.
17.
18.
19.
16r − 72r + 81
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
2
2
r − 3r − 28
2
24t + 26tv + 6v
3
2
2
28k − 34k + 59k − 35
4
3
2
−35m + 11m − 78m + 35m − 45
2
b + 10b + 25
70
2
1
5
13
32
–84
7
−
52
1
1
35
–3
−5
–2
11
4
1
ID: A
30. − 47
31.
1
2
32. y = 27 x – 3
33.
34.
35.
36.
37.
38.
y = 0.8x + 10
C = 5 + 0.2m
T = 38 + 3h
y = −3x + 6
y = 2x + 7
1
11
y = x−
8
8
y = 3x − 10
3x – 5y = 12
x – y = –4
39.
40.
41.
42. y = 34 x + 54
43. y = −2x + 6
44.
45.
46.
47.
2
2
9a − 2b + 5a + b − 3
2
−3a + 15a + 3
2
−4a + 10a + 4
2
2
−6p − 4q + 15p − q
48. −20r 5 + 10r 4 + 25r 3
49. 12s 5 t 9 + 12s 3 t 8 + 8s 2 t 5
50. 4
51. 1
2
52. 4
53. −3
54. one solution; (–2, 1)
2
ID: A
55. one solution; (–1, –4)
3