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MATH 1175 COURSE REVIEW #1

1. Simplify:

2. Solve for x:

3. Solve for x:

4. Combine in each example below:

5. Rationalize the denominators in each example below:

6. Solve graphically:

7. Solve using the quadratic formula: 2x2−2x−1=0

8. Find x, ∠A, and ∠B

9.
a) Why are ΔACD and ΔBCD congruent?
b) Find x
c) Find the area of ΔABC

10. Simplify:

12. Solve for x: 

13. Simplify:

14.
a) Divide by long division:

b) Combine:

15. Solve using the quadratic formula: x2+2x−1=0

16. Find x, AB, BC, and AC
   
17. a) State the relationship of ΔABC to ΔADE
b) Find x, AB, AD, BC, and DE
   
18. Find x, y and the area of the rectangle. Leave
answers to the nearest tenth.
sin 53° = .7986
cos 53° = .6018
tan 53° = 1.3270
   
19.
a) Find the area of the square ABCD.
b) Find the area and the circumference of the
circle.
c) Find the area of the shaded part.
   
20.
a) Why are ΔABD and ΔCDB congruent?
b) Which sides of the congruent triangles are
equal?
c) Find x and y.
   
21.
a) Find x
b) Find sin A, cos A, and tan A.
   
22.
a) Find x and y (to the nearest tenth)
b) Find the area of ΔABC

sin 50° = .7660
cos 50° = .6428
tan 50° = 1.1918
   
23.
a) What is the relationship which exists
between Δ ABC and Δ EFG?
b) Find x.
   
24.
a) Find x (leave the answer in radical form)
b) Find the area of the parallelogram ABCD.
(Leave the answer in radical form)
   
25.
a) Find x and y
b) Find AB and BC
   
26.
a) Explain why ΔDEC is similar to ΔABC.
b) Find x
   
27. Find the area of the parallelogram ABCD to
the nearest tenth, if BE ⊥ AD, ED = 8, BC = 12,
∠A = 55°
sin 55° = .8192
cos 55° = .5735
tan 55° = 1.4281

ANSWERS:

16. x = 2; AB = 17; BC = 8;
AC = 15

19.
a) 400 sq. units
b) Area of circle = 314 sq.
units
Circumference = 62.8 units
c) 86 sq. units

22.
a) x = 23; y = 19.3
b) 222

25.
a) x = 5; y = 1
b) AB = 16; BC = 8


 

 

 


 

8. x = 7; x = – 10 (reject)
∠A = 42; ∠B = 98

17.
a) (triangles
are similar)
b) x = 6; AB = 18; AD = 12;
BC = 12; DE = 8

20.
a) ΔADB = ΔCBD;
DB = DB; ∠ABD = ∠CDB
ASA
b) AB = DC; AD = BC
c) x = 3; y = 4

23.
a) (similar)
b) x = 3

26.
a) ∠CAB = ∠CDE;
∠CBA = ∠CED
corresponding angles are =
(angles on the same side of
2 || lines and on the same
side of the transversal). If 2
angles in a
in a second Δ, the Δ's are
similar.
b) x = 4

 3. x = 8; x= 3 (reject)

6. (4, 3)

9.
a) AD = BD; ∠ADC = ∠BDC
CD = CD; SAS
b)
c) 24 sq. units

12. x = 9

18. x = 8; y = 6; Area = 48 sq.
units