Algebra 1 Keystone Exam Review

Real Number Operations

100

Simplify 7 times the square root of 54 minus 2 times the square root of 24

What is 17 times the square root of 6

200

Simplify this expression: 

(3x³ + 18x² - 15x) / 3x

What is x² + 6x - 5

300

Evaluate the following expression when r=3 and t=2. (2 x r^t)^-2

What is 1/324

400

What is the greatest common factor of:

14x³y³z²  and  22xy²

What is 2xy²

500

What is the least common multiple the following:

6u²v²w³   and   10u³vw⁴

What is 30u³v²w⁴

Linear Equations

100

A rental car company charges a base fee of $50.47 plus 0.50 per mile driven. If x represents the number of miles driven and y represents the total cost of the bill, write an equation for this situation.

What is y = 0.50x + 50.47 ?

200

Solve for x:

9x - 5 = 6x + 9x + 10

What is x = - 5/2

300

Solve the system of equations: 

5x + y = 10

2x - 3y = 4

What is x = 2, y = 0

400

What is the solution of the equation: 

(3/4)x - 5 = 10?

What is x=20

500

Reed and Sharon work in two different clothing stores. Reed's store sells shirts $14 apiece and pants for $39 each. Sharon's store sells shirts for $12 apiece and pants for $44 each. Reid sold $145 worth of shirts and pants and Sharon's sales of shirts and pants were worth $156. Use a system of equations to find out how many shirts and pants Reed sold.

What is 2 shirts and 3 pants ?

Linear Inequalities & Equations

100

Solve the following inequality: 

24 < -2(x-3) < 36

What is -15 < x < -9

200

At an ice-cream parlor, ice-cream cones cost x dollars each and sundaes cost y dollars each. The total cost of 4 cones and 3 sundaes is more than $20. The total cost of 5 cones and 1 sundae is less than $16. Represent this by a system of inequalities.

4x + 3y > 20 

5x + y < 16

300

Graph the solution to 

-1/2 x - 4 < 0

              O-------->

-9        -8       -7

400

Solve the inequality: 

|3x + 4| < 8

What is -4 < x < 4/3

500

Graph the solution of 

|2x + 4| > 2

<-------O      |     O------->

-3     -2    -1

Functions & Geometry

100

A line with a slope of 1/3 and passes through (-4,5). What is the equation of the line?

What is y = 1/3x - 11/3

200

The first five terms of a sequence are given below: 15, 24, 33, 42, 51, .... What is the 32nd term of the sequence

What is 294 ?

300

Which of these relations is a function:

A: (1,4)(-4,6)(1,3)(-8,2)  B: (1,4)(-4,2)(6,1)(-8,2)

C: (1,0)(-4,3)(6,1)(-4,5)  D: (6,1)(-4,4)(1,1)(6,2)

What is B?

400

According to this table, what is the range of the data:

(20,26) , (21,27) , (22,28) , (23,29)

What are 26, 27, 28, 29 ?

500

What simple test can you perform to test if a graph is a function?

What is the vertical line test?