Sarah swims in a rectangular-shaped swimming pool 18 feet wide

Sarah swims in a rectangular-shaped swimming pool
18 feet wide and 24 feet long. About how many feet
long is a diagonal of the surface of the water in the
pool?
24
F. 21
G. 30
H. 42
J. 441
K. 900
18
ACT Practice
Plane Geometry
xx
a2 + b2 = c2 {Pythagorean Theorem}
182 + 242 = x2 {substituted given values into Pythagorean Theorem}
324 + 576 = x2 {evaluated exponents}
900 = x2 {added 324 and 576}
x = 30 {took square root of each side}
© Mr. Sims
Let a, b, c, and d be positive real numbers such that
a10 < b10 < c10 < d10. Which of the numbers a, b, c, or d
is the greatest?
A.
B.
C.
D.
E.
ACT Practice
Intermediate Algebra
All the numbers are shown as being less than d10
a
therefore d is the greatest number
b
c
d
Cannot be determined from the given information
© Mr. Sims
What value of x makes the equation 7x – 3(2x – 4) = 10
true?
F. -12
G. -2
H.
J.
2
−
13
7x – 3(2x – 4) = 10
7x – 6x + 12 = 10
x + 12 = 10
-12
ACT Practice
Elementary Algebra
{used distributive property}
{combined like terms}
-12
x = -2
{subtracted 12 from each side}
22
13
K. 22
© Mr. Sims
Which of the following (x,y) pairs is the solution for
the system of equations x + 2y = 5 and -2x + y = 10 ?
A.
B.
C.
D.
E.
(-3,4)
(-1,3)
(1,2)
(5,0)
35
3
, −
x + 2y = 5
-2x + y = 10
10
3
ACT Practice
Elementary Algebra
2x + 4y = 10 {multiplied top equation by 2}
-2x + y = 10 {bottom equation stays the same}
5y = 20 {added the two equations together}
y = 4 {divided each side by 5}
x + 2y = 5
x + 2(4) = 5
x+8=5
{top equation}
{substituted 4, in for y, into top equation}
{multiplied 2 by 4}
-8 -8
x = -3
{subtracted 8 from each side}
© Mr. Sims
ACT Practice
Elementary Algebra
For nonzero numbers x and y, which of the following
−x
expressions is NOT equivalent to
?
y
F.
G.
−x
−y
The entire fraction is negative
- the negative sign could be on the top, middle, or bottom
- therefore it is the same as G and H
x
−y
𝑥
𝑦
H. −
J.
−πx
πy
K. −
simplify by cancelling the π’s on top and bottom, then it equals −
1
y
x
divide by multiplying by reciprocal, −1 ⋅
x
y
, then it equals −
x
y
x
y
© Mr. Sims
ACT Practice
Elementary Algebra
5
1
5
Percent that is shaded
17
=
{shaded area divided by total area}
25
= 0.68
= 68%
{divided}
1
Area of entire object
= 5 x 5 {length x width}
= 25 in2 {multiplied}
Area of unshaded squares
= 8 x 1 {eight 1 in2 squares}
= 8 in2 {multiplied}
Area of shaded squares
= 25 – 8 {total minus unshaded}
= 17 in2 {subtracted}
{changed to percent moving decimal right two places}
© Mr. Sims
ACT Practice
Intermediate Algebra
substitute 3 in and determine which one yields nearly 898
100 ⋅ 33−1
= 100 ⋅ 32
= 100 ⋅ 9
= 900
© Mr. Sims
ACT Practice
Coordinate Geometry
Happy makes as much or more at 2 hours and after
Smiley charges $10 for scheduling a party
Happy does not charge for scheduling
© Mr. Sims