Algebra Placement Test Study Guide
1. Simplify: – 19 – (– 7)
Find the number of nickels and the
number of dimes.
2. Simplify: 6[17 – 7(4 – 5) – 15]
3. Add.
- 38 +
21. Simplify: 7x 8 + 8x 3 - 5x 8 + x 8 - 9x 3
5
6
22. Find the product: –9w(6 – 7w)
4. Four times the sum of a number and – 72
equals – 16. Find the number.
5.† Kev invested part of his $10,000 bonus
in a cd that paid 6% interest, and the rest
in a fund that paid 11% interest. If his
total interest was $900, how much did
Kev invest in the fund?
23. The ratio of blue jacks to green jacks is 5
† 8. If you have 180 blue jacks, find the
to
number of green jacks.
24. Find the product: (z - 7)
25. Multiply: (4x – 1)(3x + 5)
26. Ky bikes at a constant speed for 24
† returns home at the same
miles. He
constant speed but on a different 29
miles route. His return trip takes an hour
longer. Find his speed.
6. Solve: – 17.5 = 3.5 c
7. 45 % of the students at PS High attended
the assembly. If 288 students attended
the assembly, how may students are
enrolled at the school?
8. Solve:
x
3
27. Write 0.000090415 in scientific notation.
-10 = -4
28. Solve the equation: x (35x + 14) = 0
9. Use the formula F = 95 C + 32 to write –
20° C as degrees Fahrenheit.
†
10. Solve: 2 y + 5 - 3 y - 6 = 35
(
)
(
29. Solve the equation: x 2 - 4 x = 45
30. Solve:
)
number is 25. Find the number.
14. Is the ordered pair (–2, 3) a solution of
the equation 5x – y = –7?
† Find the slope of the line containing the
15.
points (7, –9) and (1, 12).
33. Solve the quadratic equation:
2
(5x + 5) = 100
2
34. Subtract (3x - 2) from (5x - 3)(2x -1)
16. Find the slope of the line given by the
equation: 15x – 25y = 50
35. Add:
†
5
x +4
+
40
2
x -16
2y
†
†
36. Subtract: y 2 +7y +6
18. Find f (-1) when f ( x ) = 3x 2 - 2x + 7
19. Write the equation of the line that passes
through the points (–2, 8) and (6, –4).
†20. Ava has†52 coins. The value of her
coins (only dimes and nickels) is $4.15.
- x3 = 3
32. The sum of two numbers is –1. Five
times the first number equals 3 times the
second number. Find the two numbers.
13. Solve 6x - 7y = 14 for y.
17. Graph: y = –2x + 4
2x
5
31. Ann decides to fence in the garden. The
†
length is 11 feet more than 3 times the
† width. She needs 70 feet of fencing.
Find the length and the width of the
garden.
† graph:
11. Solve and
-7( x - 2) - 3( 4 - 6x ) £ 12x + 5
† A number increased by two-thirds of the
12.
†
2
x 2 -x-2
†
37. Divide: x 2 +4 x +3
2
38. Solve: a
†
†
†
4
- y 2 -2y-3
2
÷ xx 2+3x-10
-x-12
- 43 = - 18
39. Simplify: 3x 2 y (-2x 3 y 4 )
40. Simplify:
2
Ï2x - 3y = 11
46. Solve: Ì 3
Ó2 y - x = 7
-8
(
)
-9
- y -16 ( x -2 )
4 x 6 x -2 y 2
†
41. Simplify:
225x16 y 7
(
† Simplify: -2 3 x 3 y
42.
†
z +1
43. Solve: 11
Ï
y = 3x
47. Solve: Ì
Ó x + 15y = -92
†
Ï 1 x + 5y = 16
48. Solve: Ì 21
Ó 4 x - 16 y = 0
†
16x 3
15
49. Simplify: 5 ⋅ 12x 4
)
2
z-3
z-12
=
44. Solve:
3 x - -5 x = 7
†
†
x 2 +6x +9
50. Simplify: x 2 -6x-7
45. Factor: 8x 2 -19x -15
2
-9
÷ 12x 2x-72x-84
†
†
†
†
ANSWERS
1) –12
6) – 5
11) x ≥ –3
16) m =
†
(2, 0)
26) 5 mph
(0, 4) 18) 12
†
2
22) 63w - 54w 23) 288
† - 5 28) x = 0,
27) 9.0415 ¥10
31) 29 ft x 6 ft
32)
-3
36) ( y +6)( y +1)( y-3)
†
37)
x-4
x +5
15x 8 y 3 y
†
42)
21)
†
†
3) 11 24
8) 18
13) y = 6 7 x - 2
2) 54
7) 640
12) 15
17)
3
5
3x 8 - x 3
x = -25
†
2y 2 -10y-24
41)
46) no solution
†
†
†
†
8
,
-5
33) 1, – 3
8
38)
†
-18x 3 y
†
47) (– 2, – 6 )
16
†
5
43) z = 21, z = 1
48) (2, 3)
†
†
†
†
4) 68
9) – 4° F
14) No
19) y = - 3 2 x + 5
5)
10)
15)
20)
24) z 2 -14z + 49
29) x = – 5,
x=9
25) 12x 2 + 17x - 5
30) 45
x 2 + x -1 †
8 9
39) 12x y
35)
5
x-4
40)
-4x4
44) x = – 3.5
45)
(8x + 5)( x - 3)
50)
12( x +3)
( x-3)
34)
49)
4
x
†
†
†
†
†
$6,000
–7
m = -72
21 nickels,
31 dimes
†