GSE Algebra 1 UNIT 1 – Quantities & Expressions Test Study Guide UNIT 1 – Relationships with Quantities & Expressions Name: ____________________________ Date: _______ Period: _______ Rational Radicals: All Perfect Squares are RATIONAL If is it NOT a Perfect Square, it is IRRATIONAL 1.) List the first 20 perfect squares … like so: 2 = 1… √1 =1 2 = 4… √4 =2 2.) Are these perfect squares? Yes I want you to try these out… to do so, expand the variable to show me how many were multiplied together. **The exponent tells you this.** Then every PAIR can come OUT the radical. If any ONE is left— it is NOT a perfect square. TRY! √ 6 √ 7 Count how many pairs can come out. That is your exponent OUTSIDE the radical. If the amount of the variable is EVEN, none will be left under the radical. If the amount of variable is ODD, only ONE will be left under the radical. Irrational Radicals: All radicals that are not perfect squares are IRRATIONAL Simplify them by factoring, and finding perfect squares that can be factored out of the radical 4.) √56 = 5.) √150 = 6.) √54 = 7.) √147 =
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GSE Algebra 1 UNIT 1 – Quantities & Expressions Test Study Guide
UNIT 1 – Relationships with Quantities & Expressions
Count how many pairs can come out. That is your exponent OUTSIDE the radical. If the amount of the variable is EVEN, none
will be left under the radical. If the amount of variable is ODD, only ONE will be left under the radical.
Irrational Radicals:
All radicals that are not
perfect squares are
IRRATIONAL
Simplify them by factoring, and
finding perfect squares that can be
factored out of the radical
4.) √56 =
5.) √150 =
6.) √54 =
7.) √147 =
GSE Algebra 1 UNIT 1 – Quantities & Expressions Test Study Guide
Combining Radical
Expressions
Adding –or– Subtracting
Can only be done with Square
Roots that have the SAME
RADICAND
PAY ATTENTION TO YOUR SIGNS
14.) √5 − 3√5
15.) 7√6 − 2√24
16.) −8√7 + 3√7
17.) 2√300 + √75
Multiplying Radicals:
Multiply EVERYTHING
18.) −7√3(√6 + √3) 20.) (√2 + 2)(3√10 + √5)
Units (METRIC SYSTEM):
Refer to the chart above.
21.) How many liters is in 4.7 kilo meters?
22.) If a car is traveling 45.7 kilometers per hour, what is the
rate in decimeters per hour?
23.) How many centimeters is in 12 decameters?
24.) 1 kilogram = 2.2 pounds How many kilograms is equivalent
to 80 pounds?
GSE Algebra 1 UNIT 1 – Quantities & Expressions Test Study Guide
Units 1 Step:
Solve by either multiplying or
dividing once. (big -> small =
multiply; small -> big = divide)
25.) 4 yd = _________ in
26.) If a car is driving 60 mph, what is the speed in miles per min?
27.) How many ft are in 60in?
28.) Employees at your job start off making $13/hr. How much do they make per minute?
Units 2+ Steps: Recognize when the problem is
asking for you to do something with
the conversion you’ve completed.
Recognize when you have to convert
BOTH units.
29.) You decide to repaint the 4 walls in your bedroom. Each wall will be a different color. If the
paint you chose costs
$3.50/quart, how much will it cost you in all to buy a gallon of each color?
30.) If a car is going 72 mph…
A) What is the speed in feet per minute?
B) What is the speed in feet per second?
ADDING & SUBTRACTING POLYNOMIALS: Combine like terms (same variable and exponents) Remember to distribute your negative when you subtract. For “Perimeter”, you add up all the sides of the shape to get the full length all the way around. So “Perimeter” is addition of each polynomial.
1. (4 + 2n3 ) + (5n3 + 2)
2. (−10k2 + 7k + 6k4 ) + (−14 − 4k4 − 14k)
3. (4r3 + 3r4 ) − (r4 − 5r3) 4. Perimeter
MULTIPLYING POLYNOMIALS: You can use Distribution, Vertical Method, F.O.I.L., or create an Area Model for your multiplication problems.
