Download Advanced Geometry Placement Exam Topic List 1. Two

Advanced Geometry
Placement Exam Topic List
1.
Two-column proof (including median or altitude)
2.
Conditional statement, converse, inverse, and contrapositive
3.
Proving triangles congruent (including overlapping triangles)
4.
Addition, subtraction, multiplication, and division properties of segments
and angles
5.
Complementary and supplementary angles and their theorems
6.
Indirect proof
7.
Parallel lines and slope
8.
Properties of special quadrilaterals
9.
Properties relating to planes, parallel planes, and skew lines
10.
Regular polygons and the measures of their associated interior and
exterior angles
11.
Ratio, proportion, geometric mean
12.
Similar triangles
13.
Pythagorean Theorem and distance formula
14.
Radicals and quadratic equations
15.
Trig ratios and special right triangles (30-60-90/ 45-45-90)
16.
Pythagorean Theorem in space
17.
Area of polygons and circles
18.
Circles (radius, diameter, arcs, chords, angle-arc theorems, etc.)
19.
Surface area and volume of prisms and cylinders
20.
Triangle Inequality Theorem / Exterior-Angle Inequality Theorem
FCPS
Dec. 2007
FCPS Algebra I Placement Exam Review
1.
Simplify: 9 − 4(8 − 3) + 10 + 2
2.
Solve for k: 5(k − 6) + 3 = 8
3.
Solve for n: 3(n − 3) + 23 = 2(n − 5)
4.
Solve for y: 3( y − 2) − 16 = 8 y
5.
The length of a rectangle is 7 cm more than the width. The perimeter is 78 cm. Find
the dimensions of the rectangle.
6.
Solve using an equation: Jim is three times as old as Jill. If the sum of their ages is
20, how old is each?
7.
Graph the line, 5 x − 2 y = 6 on a coordinate plane.
8.
Find the slope of the line containing the points (-2,4) and (-7,1).
9.
Find the equation for this line
10.
Find the equation of the line through (−6,10) with a slope of
2
.
3
11. Solve the system using any method: x + 3 y = 15
2x − y = 2
12. Solve: x + y = 2
x − 2 y = −10
13. One number is 8 more than twice the second number. The sum of the number is 123.
Find the numbers.
14. Solve and graph on a number line: 4 − 5 x < 22 − 2 x
15. Solve and graph on a number line. -3< 3x – 3 ≤ 12.
16.
32 x 5 y 7 z
Simplify:
20 x 8 y 2
17. Perform the indicated operation and simplify: (3 x 2 − 5 x − 7) − (8 − 9 x 2 + 2 x)
18. Perform the indicated operation and simplify: (2 x − 8)(7 x − 3)
19. Factor completely: 49 x 2 − 25
20. Factor completely: 7 x 2 − 36 x + 5
21. Factor completely: x 3 − x 2 − 20 x
22. Solve for x: x 2 − 3 x − 10 = 0
23. Solve for r: 6r 2 + r = 12
Note to Parents, Teachers, and Students:
Topics of Ratio/Proportion and Rational Numbers (focus: radicals) will not be included on the
placement exam administered in March; but are topics that should be mastered with the
completion of Algebra 1. The following represent a sampling of these types of items:
24. Simplify: 12 75
25.
Simplify:
5
3
26. Simplify: 3 45 − 20
27.
28.
Solve the proportion for x:
8
5
=
x−3 x
 x − 4  x −3
Solve for the proportion for x: 

=
 x +5  x +9
29. The perimeter of a rectangle is 68 feet. Find the dimensions of the rectangle if the
ratio of the length to the width is 9:8.
Algebra I
Placement Exam Topic List
NOTE: The March placement exam will cover Chapters 1, 2, 3, 4, 5, 8, 9, & 10 in the
Algebra: Structure and Method (red) Algebra textbook
(McDouglal Littell/Houghton Mifflin vendor - Mary Dolciani author)
1.
Simplify numerical expressions with and without grouping
symbols.
2.
Solve linear equations.
3.
Graph a line.
4.
Find the slope of a line, given two points.
5.
Find the equation of a line.
6.
Solve a system of equations.
7.
Solve inequalities.
8.
Simplify expressions involving exponents.
9.
Operations with polynomials.
10. Factoring
11. Solve quadratic equations with factoring.
FCPS
Dec. 2007
Advanced Algebra II
Placement Exam Topic List
1.
Solve inequalities, including compound inequalities, and graph the solution set.
2.
Solve and graph absolute value equations and inequalities.
3.
Domain and range of relations and functions.
4.
Graph linear equations and quadratic inequalities.
5.
Find inverse functions and composition of functions.
6.
Write equations of lines using slope and y-intercept, two points, parallel and
perpendicular lines.
7.
Solve systems of equations by graphing, substitution, or addition method.
8.
Solve systems of inequalities.
9.
Perform addition and multiplication using matrices.
10.
Solve systems of equations using determinants and inverse matrices.
11.
Solve rational equations.
12.
Perform the four basic operations with irrational numbers and with complex
numbers.
13.
Solve quadratic equations using factoring, completing the square, and the
quadratic formula.
14.
Find rational solutions of polynomial equations using synthetic
substitution/synthetic division.
15.
Solve inverse and joint variation problems.
16.
Evaluate logarithms.
17.
Know measures of central tendencies.
18.
Calculate probabilities.
FCPS
Dec. 2007