By Enrique Ortiz EdD, Janet B. Andreasen PhD
Your entire consultant to the next ranking at the CSET: arithmetic. FeaturesВ information approximately certification requirements,В an evaluate of the try out -В with a scoring scale,В description of the try constitution and structure andВ proven test-taking suggestions В methods for answering the 3 different types of questions:
- enhanced multiple-choice
studies and perform
- Focused reports of all components verified: algebra, quantity conception, geometry, likelihood, calculus, and historical past of arithmetic
- Practice difficulties for chosen tricky components and domain names
2 Full-Length perform exams areВ structured just like the real examination and are whole with solutions and motives The thesaurus of phrases has description of Key formulation and houses Test-Prep necessities from the specialists at CliffsNotes
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Additional info for CliffsTestPrep CSET: Mathematics
10. Find –1A. 11. Find BC. 12. Find AD. 13. Find CB. R2 3 V W, find det(A). 14. If A = SS 1 5W T X V R S -1 4 - 2 W 15. If A = SS 3 2 5 WW, find det(A). S 1 3 -2W Z T X ]] x - y + z = 3 16. Determine whether the system of equations given by [ 2x - 2y + 2z = 5 has a solution. ]] x + 2y - 3z = 1 \ 47 Part I: Content Areas, Domains, and Practice Items Solutions 1. 2. 3. 4. 5. 6. 7. 8. 9. 48 R V R V 1 4 W R V R V S3 S 2 -1 3 W S -1 3 W S -1 - 2 - 5 1 W S2 S- 4 0 1 W 1 -3W W, B = S W, C = S 3 A= S 2 4 - 2 WW, and D = SS 0 4 WW.
A c a k # b = c a a # b k = a # a c b k " " " " " " " 3. a # a b + c k = a a # b k + a a # c k " " " " " " 4. a a + b k # c = a a # c k + a b # c k " " " " " " 5. a $ a b # c k = a a # b k $ c " " " " " " " " " 6. a # a b # c k = a a $ c k b - a a $ b k c Example: " " " " " " Prove property number 2: a c a k # b = c a a # b k = a # a c b k . Solution: " " " Suppose a = x a , y a , z a , b = x b , y b , z b , and c = x c , y c , z c . i j k " " " Then c a = cx a , cy a , cz a , so a c a k # b = cx a cy a cz a .
Prove: a # a b + c k = a a # b k + a a # c k . " " " " " Suppose a = x a , y a , z a , b = x b , y b , z b , and c = x c , y c , z c . Then b + c = x b + x c , y b + y c , z b + z c . Therefore, " " " a#ab+ck= i j k xa ya za xb + xc = yb + yc zb + zc ya za yb + yc zb + zc i- xa za xb + xc zb + zc j+ xa ya xb + xc yb + yc k = a y a _ z b + z c i - z a _ y b + y c ik i - a x a _ z b + z c i - z a _ x b + x c ik j + a x a _ y b + y c i - y a _ x b + x c ik k = a_ y a z b + y a z c i - z a y b - z a y c k i - a_ x a z b + x a z c i - z a x b - z a x c k j + a_ x a y b + x a y c i - y a x b - y a x c k k = a_ y a z b - z a y b i + _ y a z c - z a y c ik i - a_ x a z b - z a x b i + _ x a z c - z a x c ik j + a_ x a y b - y a x b i + _ x a y c - y a x c ik k = a_ y a z b - z a y b i i - _ x a z b - z a x b i j + _ x a y b - y a x b i k k + a_ y a z c - z a y c i i - _ x a z c - z a x c i j + _ x a y c - y a x c i k k " " " " =a a # b k + a a # c k .
CliffsTestPrep CSET: Mathematics by Enrique Ortiz EdD, Janet B. Andreasen PhD