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Function, Pythagorean Theorem, and Number of Solutions Review

Total questions: 39

Worksheet time: 2hrs 10mins

Name
Class
Date
1.

Solve the linear equation 3x + 5 = 3x + 5

a)

5

b)

1

c)

10

d)

Any real number

2.

Find the value of y in the equation 2y - 7 = 2y + 4

a)

No Solution

b)

y = 0

c)

y = -3

d)

y = 5

3.

What is the solution to the equation 4(x - 2) = 4x - 8

a)

x = 13

b)

x = 10

c)

x = -3

d)

x = 7

e)

All real numbers

4.

Determine the value of x in the equation 2(3x - 4) = 6x - 8

a)

x = 10

b)

x = -2

c)

x = 3

d)

x = Infinite Solutions

5.

In a right-angled triangle, if the length of the two shorter sides are 3 and 4, what is the length of the hypotenuse?

a)

5

b)

8

c)

7

d)

6

6.

A ladder is leaning against a wall. If the ladder is 10 feet long and the base is 6 feet away from the wall, how high up the wall does the ladder reach?

a)

12 feet

b)

8 feet

c)

4 feet

d)

2 feet

7.

Evaluate f(3) if f(x) = 2x - 5

a)

1

b)

6

c)

0

d)

10

8.

If g(x) = 3x2 - 4x + 2

find g(2)

a)

6

b)

3

c)

10

d)

14

9.

Given h(x) = 4x - 7, what is the value of h(5)

a)

11

b)

13

c)

27

d)

2

10.

If a triangle has sides of length 5, 12, and 13, is it a right-angled triangle?

a)

Yes

b)

No

c)

Cannot be determined

d)

Insufficient information

11.

Calculate the value of f(4)

if f(x) = 3x + 2

a)

14

b)

16

c)

12

d)

10

12.

Solve the equation 5x - 3 = 2x + 4

a)

x = 1

b)

x = 3/7

c)

x = 7/3

d)

x = 4

13.

The equation has how many solutions:

2x + 4 = 2x + 42x\ +\ 4\ =\ 2x\ +\ 4  

a)

One Solution

b)

None Solution

c)

Infinite Solutions

14.

The equation has how many solutions.

3x − 4=3x + 93x\ -\ 4=3x\ +\ 9  

a)

One Solution 

b)

No Solution

c)

Infinite Solutions

15.

How many solutions does the equation have? 



2x − 8 = x + 92x\ -\ 8\ =\ x\ +\ 9  

a)

One Solution 

b)

No Solution

c)

Infinite Solutions

16.

How many solutions does the equation have? 



3x + 12 = 3(x + 4)3x\ +\ 12\ =\ 3\left(x\ +\ 4\right)  

a)

One Solution 

b)

No Solution

c)

Infinite Solutions

17.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
18.
The Pythagorean Theorem ONLY works on which triangle? 
a)
obtuse
b)
scalene
c)
isosceles
d)
right
19.
Find the missing side
a)
9
b)
41
c)
6.4
d)
3
20.
What is the length of the missing side? *NOTE: side lengths of 10 and 12.
a)
15.6
b)
6.6
c)
44
d)
16
21.
What is the height of the cone? 
a)
14 cm
b)
8 cm
c)
12 cm
d)
13.9 cm
22.
Which set of sides would make a right triangle?
a)
4,5,6
b)
8,10,12
c)
5,12,13
d)
5,10,12
23.
The Pythagorean Theorem is
a2 + b3 = c4
a)
false
b)
true
24.
Side a on a right triangle is ALWAYS the longest side.
a)
true
b)
false
25.
What is the opposite of squaring a number?
a)
divide
b)
multiply 
c)
fractions
d)
square root
26.
a)
The top of the ladder is 8.9 ft from the ground
b)
The top of the ladder is 9.2 ft from the ground
c)
The top of the ladder is 16.5 ft from the ground
d)
The top o the ladder is 14.4 ft from the ground
27.

A soccer field is a rectangle 90 meters wide and 120 meters long. The coach asks players to run from one corner to the corner diagonally across. What is this distance?

a)

210 m

b)

180 m

c)

150 m

d)

79 m

28.
Find the length of the missing side. 
a)
25 cm
b)
42 cm
c)
52 cm
d)
48 cm
29.
Find the missing side
a)
√29.2
b)
√400
c)
√20
d)
√10
30.

A baseball "diamond" is actually a square with sides of 90 feet. If a runner tries to steal second base, how far must the catcher, at home plate, throw to get the runner "out"? (Distance across the diagonal)

a)

180 feet

b)

90 feet

c)

13.4 feet

d)

127.3 feet

31.

Your family wants to purchase a new laptop with a 17" widescreen. Since the 17 inches represents the diagonal measurement of the screen (upper corner to lower corner), you want to find out the actual dimensions of the laptop. When you measured the laptop at the store, the height was 10 inches, but you don't remember the width. Calculate the width of the laptop to the nearest tenth of an inch.

a)

7 inches

b)

10 inches

c)

19.7 inches

d)

13.7 inches

32.

Find the area of the missing square off of leg A if the area of one square is 369 and the area of another is 81?

a)

21.2

b)

17

c)

450

d)

288

33.

An electricity pole measures 25 feet high. There is a stabilization cable that stretches from the top of the pole to the ground. On the ground, the distance from the pole to the cable is 8 feet. How long is the stabilization cable?

a)

561\sqrt[]{561}  

b)

389\sqrt[]{389}  

c)

689\sqrt[]{689}  

d)

33\sqrt[]{33}  

34.
Durham and Chapel Hill are 14 miles apart.  Chapel Hill and Raleigh are 28 miles part. Raleigh and Durham are 25 miles part. Do these three cities form a right triangle?
a)
Yes they form a right triangle
b)
No they do not form a right triangle
35.
Evaluate f(-2) if f(x) = x2+ 3
a)
-1
b)
1
c)
7
d)
-7
36.
For the function f(x) = -3(x-1) find f(0).
a)
0
b)
-3
c)
3
d)
-1
37.
given f(x)=x2+5 find f(5)
a)
10
b)
30
c)
20
38.
Is this graph a function or not a function? 
a)
Function 
b)
Not a Function
39.
Is this mapping a function or not a function? 
a)
Function
b)
Not a Function

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