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ASU Mathematics Placement Test Sample Problems June, 2000, Study notes of Mathematics

Mathematics

M150 ROM Exercises ... Prevent contractures and shortening of musculoskeletal structures. ... Areas of passive versus active range of motion.

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ASU Mathematics Placement Test Sample Problems June, 2000
1. Evaluate (11.5)(0.06)
2. Evaluate (1.062) ÷(0.08)
3. Evaluate (2 −2)5
4. Evaluate 13 −3 [ 8 + (4 −9) ]
5. Evaluate −17 + (−11)
6. Evaluate 23 −(−8)
7. Evaluate 3−2
5
8. Evaluate µ21
2µ−8
3µ−21
16
9. Evaluate 3
8÷15
10. Evaluate 2.31 −1.009 + 1.5
11. Evaluate (−2)4
12. Evaluate 25 −£33−42¤
13. Evaluate the expression
x2−xy + 2y2
when x= 1 and y=−2
14. Evaluate the expression
¯¯x3−1¯¯
when x=−1
15. Evaluate the expression
x−3
6 + 2x
when x= 3
16. Multiply and simplify (2 −3v)2
17. Multiply and simplify
2x(x−4) −(x+ 2)(x−1)
18. Simplify
·(x+ 1)2
x3·5x
x3+ 9x¸÷x+ 1
x2+ 9
19. Add and simplify 1
2+2
x+3
x2
20. Simplify (−2xyz)3
21. Simplify (a2b)2(ab2)3
22. Rewrite 3x−3without negative exponents
23. Simplify (2xy−2)−3
24. Simplify √175
25. Simplify √12x2
26. Simplify 6x2(x−2)2
x(x−2)6
27. Multiply and simplify
x2+ 2x−3
x+ 2 ·x2+ 2x
x2−1
28. Divide and simplify
8x3+ 27
2x2+ 3x÷4x2−6x+ 9
3x3
29. Simplify µ2
t2+t−2
µ4
t2−t−6
30. Rationalize the denominator and simplify 4
√28
31. Rationalize the denominator and simplify r18
t
32. Divide and simplify 4y2
9x÷16
27xy2
33. Simplify rx
9−rx
16
34. Simplify −18x2yz
−21xy2z
35. Divide 3x2−9x
3x
pf3
pf4
pf5

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ASU Mathematics Placement Test Sample Problems June, 2000

  1. Evaluate (11.5)(0.06)
  2. Evaluate (1.062) ÷ (0.08)
  3. Evaluate (2 − 2)^5
  4. Evaluate 13 − 3 [ 8 + (4 − 9) ]
  5. Evaluate −17 + (−11)
  6. Evaluate 23 − (−8)
  7. Evaluate 3 −
  1. Evaluate
  1. Evaluate

÷ 15

  1. Evaluate 2. 31 − 1 .009 + 1. 5
  2. Evaluate (−2)^4
  3. Evaluate 25 −

[

]

  1. Evaluate the expression

x^2 − xy + 2y^2

when x = 1 and y = − 2

  1. Evaluate the expression ∣ ∣x^3 − 1

when x = − 1

  1. Evaluate the expression

x − 3 6 + 2x

when x = 3

  1. Multiply and simplify (2 − 3 v)^2
  2. Multiply and simplify

2 x(x − 4) − (x + 2)(x − 1)

  1. Simplify [ (x + 1)^2 x^3

5 x x^3 + 9x

]

÷

x + 1 x^2 + 9

  1. Add and simplify

x

x^2

  1. Simplify (− 2 xyz)^3
  2. Simplify (a^2 b)^2 (ab^2 )^3
  3. Rewrite 3 x−^3 without negative exponents
  4. Simplify (2xy−^2 )−^3
  5. Simplify
  1. Simplify

12 x^2

  1. Simplify 6 x^2 (x − 2)^2 x (x − 2)^6
  2. Multiply and simplify x^2 + 2x − 3 x + 2

x^2 + 2x x^2 − 1

  1. Divide and simplify 8 x^3 + 27 2 x^2 + 3x

÷

4 x^2 − 6 x + 9 3 x^3

  1. Simplify

t^2 + t − 2

t^2 − t − 6

  1. Rationalize the denominator and simplify
  1. Rationalize the denominator and simplify

t

  1. Divide and simplify

4 y^2 9 x

÷

27 xy^2

  1. Simplify

x 9

x 16

  1. Simplify

− 18 x^2 yz − 21 xy^2 z

  1. Divide

3 x^2 − 9 x 3 x

  1. Simplify

2 x^2 − 5 x − 3 x^2 − 9

  1. Multiply and simplify

2 u − 3

3 − u 8

  1. Simplify 4 a + 12 b − 5 a − 32 b
  2. Simplify 2 t −

[

3 t −

5 − t + 4t^2

) ]

  1. Simplify 5 xy − x(x − y)
  2. Multiply and simplify

− 3 u(2 − u − u^2 )

  1. Simplify 2 x − 3 [x − 2(x + 7) ]
  2. Simplify x 4

x 3

  1. Simplify
  1. Multiply and simplify √ 3 (4 −
  1. Simplify

9 x^4 y^3

  1. Multiply and simplify

(

x − 3)(

x + 1)

  1. Add (7 − 4 x − 3 x^2 ) + (3y + 1)
  2. Subtract and simplify

4 x x^2 − 4

x + 2

  1. Subtract (7 − 4 x − 3 x^2 ) − (3x + 1)
  2. Simplify

x − 1

x

  1. Multiply and simplify

(x + 2)(x^2 − 2 x + 4)

  1. Multiply and simplify [2 − (x − y) ]^2
  2. Rationalize the denominator and simplify √ 3 √ 2 − 1
  3. Solve (2x − 5)(x + 3) = 0
  4. Solve

x

  1. Solve the inequality 4 x − 1 ≤ 15
  2. Solve for y when

y − 2[y + 2(2y − 1)] = 40

  1. Solve the system of equations { −x + 2y = 2 3 x − y = 9
  2. Solve (2x + 1)(x − 2) = 18
  3. Solve the inequality 3 > 3 − x > 1
  4. Solve 1 x − 2

x + 3

x^2 + x − 6

  1. Solve 4 − t = 3
  2. Solve

x + 3 = x − 3

  1. Solve 3 x^2 − 12 x − 6 = 0
  2. Solve for l when P = 2w + 2 l
  3. Solve 9 x^3 − 4 x = 0
  4. Solve 4 − (x − 1) = 2x + 1
  5. Solve 2 + 0. 5 x = 5
  6. Solve the system of equations { 3 x + 4y = − 5 x − 2 y = 15
  7. Solve for x when x^2 + 2x = 24
  8. Solve 3 x − 10 = 11
  1. Using the slope, determine whether the graph of the line that is given by the equation x−y +1 = 0 rises, falls, is horizontal, or is vertical. (a) Rises (b) Falls (c) Horizontal (d) Vertical (e) None
  2. Find an equation for the line passing through the points (2, −1) and (− 6 , 1). (a) 4 x + y = 7 (b) y + 1 = 0 (c) x + 4y + 2 = 0 (d) x + 4y + 6 = 0 (e) None 105. Determine the slope of a line parallel to the line given by 3 x − y + 8 = 0. (a) 3 (b) 83 (c) − (^38) (d) − 15 (e) None of these 106. Find the y-intercept of the graph of the equation − 6 x + 8y = 3 (a) (− 12 , 0) (b) (^38) (c) (0, 38 ) (d) (− 6 , 8) (e) None of these
  3. Determine the graph of the equation 2 x − y = − 3

(a) (b) (c) (d) (e) None of these

  1. Sketch the half-plane determined by the inequality x − y > 1

(a) (b) (c) (d) (e) None of these

  1. Find an equation for the horizontal line passing through the (3, −4). (a) y + 4 = 0 (b) x − 3 = 0 (c) y − 3 = 0 (d) x + 3 = 0 (e) None of these
  2. Find an equation for the line passing through the point (4, −1) with the slope m = (^23) (a) y = 23 x − 1 (b) 2 x − 3 y = 11 (c) 2 x − 3 y = − 5 (d) 3 x − 2 y = − 5 (e) None of these
  3. Find an equation for the line passing through the point (2, −6) and perpendicular to the line y − 4 = 0

(a) 2 x − 6 y = 0 (b) x = 2 (c) y + 6 = 0 (d) y = 6 (e) None of these

  1. Evaluate 6 + 3 · 2 − 4 ÷ 4 (a) 72 (b) 2 (c) 11 (d) 17 (e) None of these
  2. Simplify (a^2 b−^2 )^3 (a^3 b) (a)

a^18 b^5

(b)

a^8 b^4 (c)

a^9 −b^7

(d)

a^9 b^5 (e) None of these

  1. Simplify

3 x 5

3 x 7 (a)

6 x 35

(b) 0

(c) −

6 x 35

(d) 6 x (e) None of these

  1. Solve the inequality 12 − 5 x ≥ 37 (a) x ≥ 5 (b) x ≤ − 5 (c) x < 5 (d) x ≤ − 495 (e) None of these
  2. Multiply (x − 2)^2 (a) x^2 − 4 x − 4 (b) x^2 + 4 (c) x^2 − 4 (d) x^2 − 4 x + 4 (e) None of these
  3. Solve 5 x^2 = − 2 x (a) x = 0 (b) x = 0, (^25) (c) x = 0, − (^25) (d) No real solutions (e) None of these
  4. Write without negative exponents 3 xy−^2

(a)

3 x y^2

(b) − 3 xy^2

(c)

3 xy^2

(d)

xy^2 (e) None of these

  1. Find the slope of the line going through (− 3 , 2) and (− 4 , 2) (a) 0 (b) undefined (c) − 47 (d) − (^74) (e) None of these 120. Simplify

(a) 19 (b) (^13) (c) − 13 (d) − 13 , (^13) (e) None of these

  1. Solve

x

x + 2

(a) − 1 ± 2

3 (b) − 1 ±

(c) − 1 ±

3 (d) ±

(e) None of these

  1. Evaluate the expression a^2 − 2 a + 5 given that a = − 3 (a) − 2 (b) 20 (c) 5 (d) 19 (e) None of these
  2. A man has 21 coins in dimes and nickles. His total is $ 1. 55. How many nickles does he have? (a) 10 (b) 21 (c) 11 (d) Cannot be solved (e) None of these
  3. Solve x^2 + 2x = 4 (a) ± 2

5 (b) − 1 ± 2

(c) No real solution (d) 1 ±

5 (e) None of these

  1. Simplify

a^1 /^2 · a−^5 /^2 a^3 /^2 (a) a^3 /^2 (b) a−^7 /^2 (c)

a^7 /^2

(d) a^9 /^2 (e) None of these