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Precalculus Practice Test (F08)
P.1 to P.5, A.1 & A.2
Name:__________________
Date:___________ Per:____
Any problems without work will be marked wrong on all tests! No calculator.
1. Write the number in scientific notation:
a) The diameter of a red blood corpuscle
is about 0.000007 of a meter.
2. a) Find the value of x.
x
−2
11
b) ( 8 × 10 )( 3.5 × 10 )
( 2 ×10 )
5
b) Do sides of
7 , 3, 4 form a right triangle?
9
3 2
3. Solve: − 6 ≤
2x + 1
≤6
4
4. Simplify:
a) 2t2 · (t n+1)3· tn-3.
b) (3p2)(-2pq2)
5. Find an equation of the circle with
center (-3, 0) and radius 7 and graph.
6-7. Simplify (simple radical form & rationalize).
a) 18 + 3 8 − 50
b)
25m 3
7n 2
c)
50 x 3 y 4
d)
3
16a 4 b 3
8. Convert:
9.
Simplify:
2
a)
x+
3
1
3
x to exponential form.
3
b) a 2 b −1c 2 to radical form.
3
⎛ 34 ⎞ ⎛ 14 ⎞
⎜ a b ⎟ ⎜ ab ⎟
⎠ ⎝
⎠
a) ⎝
1
1 ⎛
− ⎞
( ab ) 2 ⎜ bc 4 ⎟
⎝
⎠
b)
4
8 x3 4 x3
⋅4 2
y3
y
10. Express in simplest form, using only positive exponents:
a)
x 2 y −3
(x y )
3
−1
11. Solve:
a) 3(x + 2) = 5(2x – 3) – 7
12. Solve:
2 − 4y 2y + 7
−
< 1− y
3
4
⎛ − 8m 6
b) ⎜⎜ −3
⎝ n
2
⎞3
⎟⎟
⎠
b) -3x – 4 < -2 (Answer in interval notation.)
13. Find an equation for the line through (4, 7) with the given relationship to y = 2x -4:
b) perpendicular
a) Parallel
14. Solve:
a) 3 + 5 x = 7
b) 9(3x – 4)2 = 16
15. Solve by completing the square:
x2 + 14x = -9
16. Solve using the quadratic formula:
2x2 + 7x – 15 = 0
17-18 Perform the operation:
17. (3x4 – 4x3 + 6x2 – 1) – (2x4 – 8x2 – 6x + 5)
18. (2x + 3)(3x2 – 2x + 4)
19-20. Factor completely:
a) 24x2 – 7x – 5
c) z3 + 64
b) 5xy – 3y + 10x – 6
d) 3x4 - 48
21. a) Find the distance between P(-6, 5) &
Q(3, 2) in simple radical form.
b) Find the distance between −
2
3
and on
3
4
the real number line.
22. a) Find the coordinates of W, for segment
WX with X(-5, 6) and midpoint M(3, -4).
b) Find the midpoint of the line segment with the
given endpoints: (-2, 3 ), (5, 0).
23. Write the equation of the line below in
general form (3pts):
24. Write a linear equation for someone’s weekly
earnings who gets paid $7 per hour and spends
$5 each week to ride the bus to work. (3 pts).
25. Derive the quadratic formula: