Math unit38 vectors
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This document contains 6 presentations on vectors: 1) Identifying equivalent and opposite vectors in a diagram 2) Calculating components of vectors 3) Writing vector expressions in terms of other vectors 4) Illustrating vector addition and subtraction on a grid 5) Expressing vectors in terms of other vectors using properties of midpoints 6) Expressing vectors in terms of other vectors and proving collinearity using properties of parallelograms
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Math unit38 vectors
This document contains 6 presentations on vectors:
1) Identifying equivalent and opposite vectors in a diagram
2) Calculating components of vectors
3) Writing vector expressions in terms of other vectors
4) Illustrating vector addition and subtraction on a grid
5) Expressing vectors in terms of other vectors using properties of midpoints
6) Expressing vectors in terms of other vectors and proving collinearity using properties of parallelograms
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2) Solving systems of equations, calculating proportions, and simplifying polynomials.
3) Graphing lines and finding intersections of lines and circles.
4) Calculating angles, similarities of triangles, and loci of points.
5) Conducting statistical analysis on survey data including calculating range, mean, and percentages.
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This document contains 6 presentations on vectors:
1) Identifying equivalent and opposite vectors in a diagram
2) Calculating components of vectors
3) Writing vector expressions in terms of other vectors
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5) Expressing vectors in terms of other vectors using properties of midpoints
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This document contains a mathematics exam with 7 sections covering topics such as:
1) Choosing correct answers and justifications for systems of equations and inequalities.
2) Solving systems of equations, calculating proportions, and simplifying polynomials.
3) Graphing lines and finding intersections of lines and circles.
4) Calculating angles, similarities of triangles, and loci of points.
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This document outlines the key concepts and examples for matrices including: addition and subtraction of matrices with the same dimensions; scalar multiplication by multiplying each element of the matrix by the scalar; matrix multiplication where the number of columns of the first matrix equals the number of rows of the second matrix; determinants of 2x2 matrices; inverse matrices for non-singular 2x2 matrices; solving systems of equations using matrices; and geometric transformations using matrices including rotation, reflection, translation and examples of applying transformations.
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AB Tech Page 1 of 15 McCormick
Name: _____________________________ Date:___________
MULTIPLE CHOICE. Circle or underline the one alternative that best completes the statement or
answers the question. USE A PENCIL!
1) Which of the following is a correct form of Boolean addition?
A) 0 ∙ 0 = 0 B) 0 + 1 = 1 C) 0 ∙ 1 = 0 D) 0 + 1 = 0
2) Which of the following is a correct form of Boolean multiplication?
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3) In Boolean algebra, the expression "_ " means the complement of A.
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Figure 4-2
4) The symbol shown in Figure 4-2 is a(n) , and the output will be for the input shown.
A) buffer; 1 B) inverter; �̅� C) inverter; 1 D) buffer; not A
ELN-133 Chapter 4 Homework Spring 2015
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AB Tech Page 2 of 15 McCormick
Refer to the figure below to answer the following question(s).
Figure 4-3
5) The symbol shown in Figure 4-3 is a(n) gate.
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6) The Boolean expression for the symbol in Figure 4-3 is .
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Refer to the figure below to answer the following question(s).
Figure 4-4
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8) The Boolean expression for the symbol in Figure 4-4 is .
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AB Tech Page 3 of 15 McCormick
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Figure 4-5
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- 2. Unit 38 38.1 Equal Vectors
- 3. In the following diagram, state Which pairs of vectors are equivalent and which pairs of vectors are opposite directions Equivalent vectors: a and b b and i f and g Vectors in opposite directions c and b e and j? ??? ?
- 5. Does ? ? ? ? ? Given that , , calculate ? ? ? ? ? ? No
- 6. Unit 38 38.3 Vector Expressions
- 7. Write down each of the following in terms of d and/or e. (a) (b) (c) ? ?? ?? Mark clearly on the diagram (a) the point P such that (b) the point Q such that Q P ?
- 8. Unit 38 38.4 Addition and Subtraction of Vectors
- 9. Given that On the grid below, illustrate the following vectors (i) b – c (ii) c + a (iii) a + b (iv) a + c – b b - c - c b (i) (ii) c + a c a (iii) a + b b a (iv) a + c - b a + c - b
- 10. Unit 38 38.5 Vector Geometry 1
- 11. Express, in terms of u and v, (a) (b) (c) , where M is the midpoint of AC, ? ? ?
- 12. Express, in terms of u and v, (d) (e) , where N is the midpoint of BD, (f) ? ? ? ? ?
- 13. What can you deduce about points M and N? They are coincident. Hence and
- 14. Unit 38 38.6 Vector Geometry 2
- 15. ) Express in terms of x and y, (i) (ii) (iii) olution In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (i) (ii) (iii) ? ? ? ?
- 16. ? In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (b) Show that Solution ?
- 17. In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that (c) Given that E is the midpoint of DC, prove that A, P and E are collinear. Solution so Hence A, P and E are collinear? ? ?? ? from part (b) from part (a)