Name:_______________
Algebra Review
THESE ARE THE ALGEBRA SKILLS YOU WILL NEED FOR HONORS GEOMETRY! ENJOY
To receive credit, you must clearly show all work. The formula is simple, NO WORK = NO CREDIT
1. Solve by elimination. (aka Addition)
2. Solve by substitution or elimination
3x – 5y = 3
2x +y +6x +8 =90
9x – 20y = 6
23y +90 +4x +4 = 180
3. Solve any method:
4. Any method
x  3y 1
x  2y  9
a b 5
 
6 4 2
2a b
  2
3 2
5. Solve by any method.
2x + 3y = 31
y = x +7
6. Simplify, leave as a fraction. No calc.
1F
1I 1 F
3 IO4
L

M
P
2H
3K 2 H
4K
N
Q 3
7. Simplify:
10  1 
5
   4   Leave as an improper fraction.
3 4
3
8. Solve. –5 - (15y - 1) = 2(7y - 16) – y
9. Solve by factoring. t2 +8t – 48 = 0
10. Solve x2 – 26x = - 120
11. x2 -25x = -150
Following will need factor by grouping or the quad formula.
12. 9u2 –9u = -2
13.
2 x 2  x  15  0
6 x 2  x  12  0
14.
15.
10 x 2  7 x  6  0
16. Simplify NO DECIMALS
a.
12
20
b.
c. 4 48
d. 4 36
e. 2 300
17. Heron’s formula is a formula you will use later in this class. You will need to know how to use a
formula in geometry…. This one is used to find the area of a triangle, given 3 sides.
Herons: Area = s(s  a)(s  b)(s  c)
s = (a+ b+ c)/2
a, b and c are the lengths of the sides.
Find the area of this triangle.
12
14
22 inches
18. Solve for x. Graph your solution on the number line.
a. 5  2x  3  12
b.
8  2x  4  16
19. Pythagorean theorem. Solve for the missing side. Leave answer as a simplified radical please.
a.
b.
c.
d. is this triangle right?
e.
20. Lastly, higher level apps. A focus of honors geometry! Here you will have to draw the pic, and solve
the problem. Hint, if you struggle, try using graph paper. Don’t have any? GOOGLE some.
John walks 2 miles north, then goes 5 miles east. He then goes 3 more miles north, and 7 more miles east.
If he runs directly back, how many miles will he need to run?
21. A, catcher for NY needs to throw a man running to second base out!! The baseball “diamond”, is
actually a square, with each side (distance between bases) 90 ft. The second baseman is standing on
second, waiting for the catcher to throw. How far does he need to throw? Round nearest 100ths place.
22. Lastly, 2 hours 30 minutes is same as 2.5 hours. How many hours is 3 hours 12 mins? How about 3
hours, 15 minutes and 30 seconds?
answers: 1. (2,3/5) 2. (10,2)
10. (6,20)
11. 10, 15
24, 20 3 17.
e. 171
5760
3. (3,8) 4. (5,2) 5. (2,9) 6. 13/32
12. 2/3, 1/3
13. 3, -5/2
18. -1<x<7.5 and 2≤x<6
14. -3/2, 4/3
19. A. 25 b.
7. 15/2
15. ½, -6/5
8. 1
9. -12, 4
16. 2 3 , 2 5 ,16 3
205 c. 11 d. no b.c. 97≠100
20. an even 13 miles! 21. 127.28 22. 3.2hours and 3.258333333
Lastly, if you need more practice on any of this, go to www.interactmath.com then, either choose any
algebra book if you need practice for algebra problems, or a geometry book if you need practice on
geometry problems. You should check this site out regardless, it’s great for practicing the basics!! Play
with the site. This could be very helpful throughout high school and into college.