Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.1.A Precalculus 2020-2021 1. ONE WHOLE IS REPRESENTED BY THE 2. RECTANGLE BELOW IN THE DIAGRAM ABOVE, WHAT PORTION OF FOR EACH RECTANGLE WHAT DOES THE THE WHOLE RECTANGLE DOES EACH SHADED AREA REPRESENT? INDIVIDUAL BOX REPRESENT? FRACTION: ______PERCENT: _______DECIMAL: ______ FRACTION: ______ PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE ! FILLED IN TO REPRESENT \" ? _________ FRACTION: ______ PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE FILLED IN TO REPRESENT 0. 3 ? _________ FRACTION: ______ PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE FILLED IN TO REPRESENT 40% ? _________ Answer: ! , 12.5%, 0.125; ! , 25%, 0.25; Answer:!!& , 10%, 0.1; 2; 3; 4 # $ ! % , 50%, 0.5 3. SOLVE AND REPRESENT THE SOLUTION ON 4. SOLVE AND REPRESENT THE SOLUTION ON THE NUMBER LINE THE NUMBER LINE ������ ������ 8 = 5 2 ≥ 8 − 2 ������ = 8 − 3 ������ ≤ 9 3 4 20 = 5 12 < 4 ������ ������ Answer: ������ = 40; ������ = −12; ������ = 4 Answer: ������ ≥ 16; ������ ≥ −12; ������ > 3
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.1.A Precalculus 2020-2021 1. ONE WHOLE IS REPRESENTED BY THE 2. RECTANGLE BELOW FOR EACH RECTANGLE WHAT DOES THE IN THE DIAGRAM ABOVE, WHAT PORTION OF SHADED AREA REPRESENT? THE WHOLE RECTANGLE DOES EACH INDIVIDUAL BOX REPRESENT? FRACTION: ______ PERCENT: _______DECIMAL: ______ FRACTION: ______PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE ! FILLED IN TO REPRESENT \" ? _________ FRACTION: ______ PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE FILLED IN TO REPRESENT 0. 3 ? _________ FRACTION: ______ PERCENT: _______DECIMAL: ______ HOW MANY BOXES WOULD NEED TO BE FILLED IN TO REPRESENT 40% ? _________ Answer: ! , 12.5%, 0.125; ! , 25%, 0.25; # $ Answer:!!& , 10%, 0.1; 2; 3; 4 ! % , 50%, 0.5 3. SOLVE AND REPRESENT THE SOLUTION ON 4. SOLVE AND REPRESENT THE SOLUTION ON THE NUMBER LINE THE NUMBER LINE ������ ������ 8 = 5 2 ≥ 8 − 2 ������ = 8 − 3 ������ ≤ 9 3 4 20 = 5 12 < 4 ������ ������ Answer: ������ = 40, ������������������ ������������������������ℎ ������������������������������; Answer: ������ ≥ 16, ������������������ ������������������������ℎ ������������������������������; ������ = −12, ������������������ ������������������������ℎ ������������������������������; ������ ≥ −12, see graph above; ������ = 4, see graph above ������ > 3, see graph above
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.1.B Precalculus 2020-2021 1. ONE WHOLE IS REPRESENTED BY THE 2. ONE WHOLE IS REPRESENTED BY THE RECTANGLE BELOW RECTANGLE BELOW WRITE TWO DIFFERENT FRACTIONS THAT HOW MANY TWELTHS ARE DEPICTED IN REPRESENT THE SHADED AREA BELOW EACH RECTANGLE BELOW? HOW MANY BOXES REPRESENT EACH VALUE? !' _________ (! ___________ 2 ________ 50% _________ 33.3% ___________ Answer: 2; 1; 12; 3; 2 AIFnYsOwUerC: O!)%M ;!B$%I N;!(E% T;!!H%) EoSr H1A!*D% E; D PORTIONS ABOVE, HOW MUCH WOULD YOU HAVE? 3. SOLVE AND REPRESENT THE SOLUTION ON 4. 85 STUDENTS OUT OF A TOTAL OF 106 TH������E NUMBER LINE STUDENTS WERE TREATED FOR AN ILLNESS 10 = 3.5 CAUSED BY A VIRUS. ESTIMATE THE PERCENTAGE OF THE STUDENTS THAT WERE 2 ������ > 4.2 TREATED FOR THE ILLNESS? EXPLAIN YOUR 3 REASONING. 20.5 ≤ 100 A. 20% ������ B. 40% C. 60% Answer: ������ = 35; ������ > 6.3; ������ ≥ 0.205 D. 80% E. 1060% Answer: D
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.1.B Precalculus 2020-2021 5. ONE WHOLE IS REPRESENTED BY THE 6. ONE WHOLE IS REPRESENTED BY THE RECTANGLE BELOW RECTANGLE BELOW WRITE TWO DIFFERENT FRACTIONS THAT HOW MANY TWELTHS ARE DEPICTED IN REPRESENT THE SHADED AREA BELOW EACH RECTANGLE BELOW? IF YOU COMBINE THE SHADED PORTIONS HOW MANY BOXES REPRESENT EACH VALUE? ABOVE, HOW MUCH WOULD YOU HAVE? '! _________ (! ___________ 2 ________ 50% _________ 33.3% ___________ Answer: 2; 1; 12; 3; 2 Answer: !)% ;!$% ;!(% ;!!%) or 1 !*% ; 7. SOLVE AND REPRESENT THE SOLUTION ON 8. 85 STUDENTS OUT OF A TOTAL OF 106 TH������E NUMBER LINE STUDENTS WERE TREATED FOR AN ILLNESS 10 = 3.5 CAUSED BY A VIRUS. ESTIMATE THE PERCENTAGE OF THE STUDENTS THAT WERE 2 ������ > 4.2 TREATED FOR THE ILLNESS? EXPLAIN YOUR 3 REASONING. A. 20% 20.5 ≤ 100 B. 40% ������ C. 60% D. 80% Answer: ������ = 35, see graph above; E. 1060% ������ > 6.3, ������������������ ������������������������ℎ ������������������������������; ������ ≥ 0.205, see graph above Answer: D
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.2.A Precalculus 2020-2021 1. ADD 2. SOLVE 1 1 2 4 − 3 + 2 ������ = 6 Answer: ! Answer: 3 ( 3. EVALUATE THE EXPRESSION 4. EVALUATE THE EXPRESSION 3 − 3 ∙ (−9) ������ 4 − ������%; ������ = 2 and ������ = 4 Answer: 30 Answer: -3 5. SIMPLIFY 6. SIMPLIFY 5(3������ + 2) − 13 −2(������ + 5) + 4(2������ + 2) Answer: 15������ − 3 Answer: 6������ − 2
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.2.A Precalculus 2020-2021 1. 1.A perform basic operations with real 2. 3.B Setup and solve (algebraic) proportions. numbers (fractions) SOLVE ADD 2 4 1 1 ������ = 6 3 2 − + Answer: ! Answer: 3 ( 3. 1.D evaluate expressions using order of 4. 1.D evaluate expressions using order of operations EVALUATE THE EXPRESSION operations 3 − 3 ∙ (−9) EVALUATE THE EXPRESSION ������ 4 − ������%; ������ = 2 and ������ = 4 Answer: 30 Answer: -3 5. 1.H Simplify algebraic expressions 6. 1.H Simplify algebraic expressions SIMPLIFY SIMPLIFY 5(3������ + 2) − 13 −2(������ + 5) + 4(2������ + 2) Answer: 15������ − 3 Answer: 6������ − 2
Name:__________________________________________Date:____________________Per:___________ 1. EVALUATE THE EXPRESSION SKILLS BUILDER 1.2.B 3 − 4 ∙ (−5) Precalculus 2020-2021 2. SIMPLIFY −(������ + 2) + 4(2������ − 5) Answer: 23 Answer: 7������ − 22 3. SUBTRACT 4. MULTIPLY 1 4 9 34K 2 − 5 − 2 ∙ J− Answer:− ' Answer: 6 !& 5. SOLVE 6. SOLVE 7 ������ 9 6 5 = 6 8 = 5������ Answer:������ = $% (������������ ������ = 8.4 ) Answer: ������ = !( (������������ ������ = 5.33) \" '
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.2.B Precalculus 2020-2021 1. 1.D evaluate expressions using order of 2. 1.H Simplify algebraic expressions operations SIMPLIFY EVALUATE THE EXPRESSION −(������ + 2) + 4(2������ − 5) 3 − 4 ∙ (−5) Answer: 23 Answer: 7������ − 22 3. 1.A perform basic operations with real 4. 1.A perform basic operations with real numbers (fractions) numbers (fractions) SUBTRACT MULTIPLY 1 4 9 34K 2 − 5 − 2 ∙ J− Answer:− ' Answer: 6 !& 5. 3.B Setup and solve (algebraic) proportions. 6. 3.B Setup and solve (algebraic) proportions. SOLVE SOLVE 7 ������ 9 6 5 = 6 8 = 5������ Answer:������ = $% (������������ ������ = 8.4 ) Answer: ������ = !( (������������ ������ = 1.07) \" !\"
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.2.C Precalculus 2020-2021 1. MULTIPLY 2. SOLVE −8 ∙ J− 52K 3������ 8 10 = 9 Answer: 20 Answer: ������ = #& (������������ ������ = 8.89 ) ) 3. EVALUATE THE EXPRESSION 4. SIMPLIFY ������ + ������ ������ −(������ + 2) + 4������ 6 + 4 ; ������ = 6 and ������ = −4 Answer: 1 Answer: 3������ − 2 5. FIND THE MISSING SIDE 6. FIND THE MISSING SIDES Answer: 4 km Answer: ������ = 9, ������ = 9
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.2.C Precalculus 2020-2021 1. 1.A perform basic operations with real 2. 3.B Setup and solve (algebraic) proportions. numbers (fractions) SOLVE MULTIPLY 3������ 8 −8 ∙ J− 25K 10 = 9 Answer: 20 Answer: ������ = #& (������������ ������ = 2.96 ) %* 3. 1.D evaluate expressions using order of 4. 1.H Simplify algebraic expressions SIMPLIFY operations −(������ + 2) + 4������ EVALUATE THE EXPRESSION ������ + ������ ������ 6 + 4 ; ������ = 6 and ������ = −4 Answer: 1 Answer: 3������ − 2 5. 3.G Apply Pythagorean triples and special right 6. 3.G Apply Pythagorean triples and special triangle relationships to solve problems. right triangle relationships to solve problems. FIND THE MISSING SIDE FIND THE MISSING SIDES Answer: 4 km Answer: ������ = 9, ������ = 9
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.2.D Precalculus 2020-2021 1. FIND THE MISSING SIDE 2. SOLVE ������ 3 11 = 6 Answer: 15 ft Answer: ������ = !! (������������ ������ = 5.5) % 3. ADD 4. SIMPLIFY 4 1 5 − 4(������ + 7) − 7 + 3 MULTIPLY Answer:−4������ − 23 −9 ∙ J− 34K 6. FIND THE MISSING SIDES Answer: − %\"!; 12 5. EVALUATE THE EXPRESSION 2������% − ������ − ������; ������ = −3 and ������ = −4 Answer: 39 Answer: ������ = 7√2, ������ = 7
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.2.D Precalculus 2020-2021 1. 3.G Apply Pythagorean triples and special right 2. 3.B Setup and solve (algebraic) proportions. triangle relationships to solve problems. SOLVE FIND THE MISSING SIDE ������ 3 11 = 6 Answer: 15 ft Answer: ������ = !! (������������ ������ = 5.5) % 3. 1.A perform basic operations with real 4. 1.H Simplify algebraic expressions SIMPLIFY numbers (fractions) 5 − 4(������ + 7) ADD 4 1 − 7 + 3 MULTIPLY −9 ∙ J− 43K Answer: − %\"!; 12 Answer:−4������ − 23 6. 3.G Apply Pythagorean triples and special 5. 1.D evaluate expressions using order of operations right triangle relationships to solve problems. EVALUATE THE EXPRESSION FIND THE MISSING SIDES 2������% − ������ − ������; ������ = −3 and ������ = −4 Answer: 39 Answer: ������ = 7√2, ������ = 7
Name:__________________________________________Date:____________________Per:___________ 1. SUBTRACT SKILLS BUILDER 1.2.E 5 1 − 7 − 4 Precalculus 2020-2021 2. EVALUATE THE EXPRESSION ������% + ������ − ������; ������ = −3 and ������ = −4 MULTIPLY 5 1 − 9 ∙ 4 Answer: Answer: 10 − %%#* ; \" 4. FIND THE MISSING SIDES − '( 3. SOLVE 9 12 5 = ������ Answer: ������ = %& (������������ ������ = 6.67) Answer: ������ = 4√2, ������ = 4 ' 6. FIND THE MISSING SIDE 5. SIMPLIFY −10(6������ + 4) − 5(������ − 5) Answer: −65������ − 15 Answer: 8 yd
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.2.E Precalculus 2020-2021 1. 1.A perform basic operations with real 2. 1.D evaluate expressions using order of numbers (fractions) operations SUBTRACT EVALUATE THE EXPRESSION 5 1 ������% + ������ − ������; ������ = −3 and ������ = −4 − 7 − 4 MULTIPLY 5 1 − 9 ∙ 4 Answer: Answer: 10 − %%*# ; \" − '( 4. 3.G Apply Pythagorean triples and special right triangle relationships to solve problems. 3. 3.B Setup and solve (algebraic) proportions. FIND THE MISSING SIDES SOLVE 9 12 5 = ������ Answer: ������ = %& (������������ ������ = 6.67) Answer: ������ = 4√2, ������ = 4 ' 6. 3.G Apply Pythagorean triples and special 5. 1.H Simplify algebraic expressions right triangle relationships to solve problems. SIMPLIFY FIND THE MISSING SIDE −10(6������ + 4) − 5(������ − 5) Answer: −65������ − 15 Answer: 8 yd
Name:__________________________________________Date:____________________Per:___________ 1. FIND n SKILLS BUILDER 1.3.A ������% 5 = 8 Precalculus 2020-2021 10 2. NAME THE QUADRANT OR AXIS WHERE EACH Answer: ������ = ±2 POINT LIES 3. FIND THE MISSING SIDES (5, −6) (0, 6) (−4,2) (4,1) Answer: quadrant IV; positive side of y-axis; quadrant II; quadrant I 4. MATCH AN EQUATION TO THE GRAPH A. y = x! + 3 B. y = x! − 3 C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: ������ = 18, ������ = 9√3 Answer: A 6. SIMPLIFY 5. FACTOR OUT THE GCF FROM THE POLYNOMIAL √18 −8������% − 48 √32 Answer: −8(������% + 6) √36 Answer:3√2 ; 4√2 ; 6
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.3.A Precalculus 2020-2021 1. 3.B Setup and solve (algebraic) proportions. 2. 1.Y Name and graph points on a plane or FIND n number line ������% NAME THE QUADRANT OR AXIS WHERE EACH 5 = 8 POINT LIES 10 (5, −6) Answer: ������ = ±2 (0, 6) 3. 3.G Apply Pythagorean triples and special (−4,2) right triangle relationships to solve problems. FIND THE MISSING SIDES (4,1) Answer: quadrant IV; positive side of y-axis; quadrant II; quadrant I 4. 3.H Relate geometric and algebraic representations of lines, parabolas, and segments MATCH AN EQUATION TO THE GRAPH A. y = x! + 3 B. y = x! − 3 C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: ������ = 18, ������ = 9√3 Answer: A 5. 1.E Factor numbers and algebraic 6. 1.P Use properties to simplify radicals, expressions: determine GCF and LCM. including rationalizing the denominator FACTOR OUT THE GCF FROM THE SIMPLIFY POLYNOMIAL √18 −8������% − 48 √32 Answer: −8(������% + 6) √36 Answer:3√2 ; 4√2 ; 6
Name:__________________________________________Date:____________________Per:___________ 1. SUBTRACT SKILLS BUILDER 1.3.B ������ 3 7 − 4 Precalculus 2020-2021 MULTIPLY 2. MATCH AN EQUATION TO THE GRAPH 5 1 A. y = x! + 3 − 2 ∙ 4������ B. y = x! − 3 C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: $+%,#%!; ,\" Answer: I #+ 4. EVALUATE THE EXPRESSION 3. FACTOR OUT THE GCF FROM THE ������% − ������ − 5; ������ = −2 POLYNOMIAL 6 − 12������ Answer:6(1 − 2������) Answer:1 5. SIMPLIFY 6. SIMPLIFY −2(6 − 6������) + 10(4������ + 10) 2√75 SOLVE −2(6 − 6������) + 10(4������ + 10) = 101 Answer: 88 + 52������ ; ! Answer: 10√3 $
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.3.B Precalculus 2020-2021 1. 1.A perform basic operations with real 2. 3.H Relate geometric and algebraic numbers (fractions) representations of lines, parabolas, and SUBTRACT segments ������ 3 MATCH AN EQUATION TO THE GRAPH 7 − 4 A. y = x! + 3 MULTIPLY B. y = x! − 3 5 1 C. y = −x! + 3 − 2 ∙ 4������ D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: $+%,#%!; ,\" Answer: I #+ 4. 1.D evaluate expressions using order of 3. 1.E Factor numbers and algebraic operations expressions: determine GCF and LCM. EVALUATE THE EXPRESSION FACTOR OUT THE GCF FROM THE ������% − ������ − 5; ������ = −2 POLYNOMIAL 6 − 12������ Answer:6(1 − 2������) Answer:1 5. 1.H Simplify algebraic expressions 6. 1.P Use properties to simplify radicals, 1.R Solve linear equations and inequalities including rationalizing the denominator SIMPLIFY SIMPLIFY −2(6 − 6������) + 10(4������ + 10) 2√75 SOLVE Answer: 10√3 −2(6 − 6������) + 10(4������ + 10) = 101 Answer: 88 + 52������ ; ! $
Name:__________________________________________Date:____________________Per:___________ 1. EVALUATE THE EXPRESSION SKILLS BUILDER 1.3.C ������% + ������ − 5; ������ = −2 Precalculus 2020-2021 2. SIMPLIFY √288 6 Answer: -3 Answer: 2√2 4. SIMPLIFY 3. FACTOR OUT THE GCF FROM THE POLYNOMIAL 7(������ − 1) − (������ − 2) 4������$ + 10������' SOLVE 7(������ − 1) − (������ − 2) = 13 Answer:2������'(2������ + 5) Answer: 6������ − 5 ; ������ = 3 5. NAME THE QUADRANT OR AXIS WHERE EACH 6. SOLVE POINT LIES ������ 7 (−7, 3) 14 = 2������ (−4, −4) (7, 6) MULTIPLY (−1, 0) 5������ 1 − 9 ∙ ������ Answer: quadrant II; quadrant III; quadrant I; negative side of x-axis. Answers: ������ = ±7; ,\" ������������ ������ ≠ 0 )
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.3.C Precalculus 2020-2021 1. 1.D evaluate expressions using order of 2. 1.P Use properties to simplify radicals, operations including rationalizing the denominator EVALUATE THE EXPRESSION SIMPLIFY ������% + ������ − 5; ������ = −2 √288 6 Answer: -3 Answer: 2√2 3. 1.E Factor numbers and algebraic expressions: 4. 1.H Simplify algebraic expressions determine GCF and LCM. 1.R Solve linear equations and inequalities FACTOR OUT THE GCF FROM THE SIMPLIFY POLYNOMIAL 7(������ − 1) − (������ − 2) 4������$ + 10������' SOLVE 7(������ − 1) − (������ − 2) = 13 Answer:2������'(2������ + 5) Answer: 6������ − 5 ; ������ = 3 5. 1.Y Name and graph points on a plane or 6. 3.B Setup and solve (algebraic) proportions. number line 1.A perform basic operations with real NAME THE QUADRANT OR AXIS WHERE EACH numbers (fractions) POINT LIES SOLVE (−7, 3) ������ 7 (−4, −4) 14 = 2������ (7, 6) (−1, 0) MULTIPLY 5������ 1 Answer: quadrant II; quadrant III; quadrant I; − 9 ∙ ������ negative side of x-axis. Answers: ������ = ±7; ,\" ������������ ������ ≠ 0 )
Name:__________________________________________Date:____________________Per:___________ 1. FIND THE MISSING SIDES SKILLS BUILDER 1.3.D Precalculus 2020-2021 2. MATCH AN EQUATION TO THE GRAPH A. y = x! + 3 B. y = x! − 3 C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answers: ������ = 12 ������������; ������ = 6, ������ = 3√2; Answer: C ������ = 6, ������ = 3 4. EVALUATE THE EXPRESSION 3. Factor out the GCF from the polynomial. −������% + ������ − 5; ������ = −2 21������ − 56������$ + 21������( Answer:7������(3 − 8������' + 3������\") Answer:-11 5. SIMPLIFY 6. SOLVE √147 ������ 4 3 6 = 3������ MULTIPLY ���4���V 12������ − 5 ∙ U− Answer: *√' Answer: ������ = ±2√2 ; '+ ! ' \"
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.3.D Precalculus 2020-2021 1. 3.G Apply Pythagorean triples and special 2. 3.H Relate geometric and algebraic right triangle relationships to solve representations of lines, parabolas, and problems. segments FIND THE MISSING SIDES MATCH AN EQUATION TO THE GRAPH A. y = x! + 3 B. y = x! − 3 C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answers: ������ = 12 ������������; ������ = 6, ������ = 3√2; Answer: C ������ = 6, ������ = 3 4. 1.D evaluate expressions using order of 3. 1.E Factor numbers and algebraic operations expressions: determine GCF and LCM. EVALUATE THE EXPRESSION Factor out the GCF from the polynomial. −������% + ������ − 5; ������ = −2 21������ − 56������$ + 21������( Answer:7������(3 − 8������' + 3������\") Answer:-11 5. 1.P Use properties to simplify radicals, 6. 3.B Setup and solve (algebraic) proportions. including rationalizing the denominator 1.A perform basic operations with real numbers SIMPLIFY (fractions) √147 SOLVE 3 ������ 4 6 = 3������ MULTIPLY 12������ ���4���V − 5 ∙ U− Answer: *√' Answer: ������ = ±2√2 ; '+ ! ' \"
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.3.E Precalculus 2020-2021 1. NAME THE QUADRANT OR AXIS WHERE 2. MATCH AN EQUATION TO THE GRAPH EACH POINT LIES A. y = x! + 3 (0, 5) B. y = x! − 3 (−5, −2) C. y = −x! + 3 (3, 2) D. y = −x! − 3 (−4, 6) E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: negative side of y-axis; quadrant III; Answer: E quadrant I; quadrant II 4. Factor out the GCF from the polynomial. 3. SIMPLIFY 48������( + 32������' + 40������% √200 4 Answer: \"√% Answer:8������%(������$ + 4������ + 5) % 6. FIND THE MISSING SIDES 5. SIMPLIFY −5(10������ − 7) − (������ − 8) SOLVE −5(10������ − 7) − (������ − 8) = 60 Answer: −51������ + 43 ; ������ = − ! Answer: ������ = 8 ; ������ = 4√3 '
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.3.E Precalculus 2020-2021 1. 1.Y Name and graph points on a plane or 2. 3.H Relate geometric and algebraic number line representations of lines, parabolas, and NAME THE QUADRANT OR AXIS WHERE segments EACH POINT LIES MATCH AN EQUATION TO THE GRAPH (0, 5) (−5, −2) A. y = x! + 3 (3, 2) B. y = x! − 3 (−4, 6) C. y = −x! + 3 D. y = −x! − 3 E. ������ = (x + 3)! F. ������ = (x − 3)! G. ������ = −(x + 3)! H. ������ = −(x − 3)! I. None of these Answer: negative side of y-axis; quadrant III; Answer: E quadrant I; quadrant II 4. 1.E Factor numbers and algebraic expressions: 3. 1.P Use properties to simplify radicals, determine GCF and LCM. including rationalizing the denominator Factor out the GCF from the polynomial. SIMPLIFY 48������( + 32������' + 40������% √200 4 Answer: \"√% Answer:8������%(������$ + 4������ + 5) % 6. 3.G Apply Pythagorean triples and special right 5. 1.H Simplify algebraic expressions triangle relationships to solve problems. 1.R Solve linear equations and inequalities FIND THE MISSING SIDES SIMPLIFY −5(10������ − 7) − (������ − 8) SOLVE −5(10������ − 7) − (������ − 8) = 60 Answer: −51������ + 43 ; ������ = − ! Answer: ������ = 8 ; ������ = 4√3 '
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.4.A Precalculus 2020-2021 1. Name the quadrant or axis where the point 2. ������(������) = ������% − 4; FIND ������(−9) (������, ������) lies if ������ > 0 and ������ < 0 Answer: Quadrant IV Answer: ������(−9) = 77 3. SIMPLIFY 4. SIMPLIFY & RATIONALIZE 54 3√8 2 √6 7 Answer: !$ Answer:2√3 \" 5. SOLVE 6. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 4 ������ − 5 % 5 = 10 GRAPH THE LINE ������ = ' ������ − 1 SLOPE:________ Y-INT:__________ Answer: ������ = 13 Answer: see above
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.4.A Precalculus 2020-2021 1. 1.Y Name and graph points on a plane or 2. 1.D evaluate expressions using order of number line operations / 2.G Represent functions in Name the quadrant or axis where the point multiple ways (������, ������) lies if ������ > 0 and ������ < 0 ������(������) = ������% − 4; FIND ������(−9) Answer: Quadrant IV Answer: ������(−9) = 77 3. 1.A perform basic operations with real 4. 1.P Use properties to simplify radicals, numbers (fractions) including rationalizing the denominator SIMPLIFY SIMPLIFY & RATIONALIZE 45 3√8 2 √6 7 Answer: !$ Answer:2√3 \" 5. 3.B Setup and solve (algebraic) proportions. 6. 3.H Relate geometric and algebraic SOLVE representations of lines, parabolas, and 4 ������ − 5 segments. 5 = 10 IDENTIFY THE SLOPE & Y-INTERCEPT THEN GRAPH THE LINE ������ = % ������ − 1 ' SLOPE:________ Y-INT:__________ Answer: ������ = 13 Answer: %'; −1; see graph above
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.4.B Precalculus 2020-2021 1. NAME THE QUADRANT OR AXIS WHERE THE 2. FIND THE EXACT VALUE POINT (������, ������) LIES IF ������ < 0 AND ������ > 0 cot ������ = _________ Answer: Quadrant II Answer: *√% 3. ������(������) = 4t + 1; FIND ������(−7) !% 4. SIMPLIFY ���5��� 2 ������ Answer: ������(−7) = −27 Answer:+!&! 5. MATCH AN EQUATION TO THE GRAPH 6. Which angle might be represented in the A. ������ = |x + 2| diagram? B. ������ = |x| + 2 C. ������ = |3x| + 2 A. \". D. ������ = |3x + 2| $ E. ������ = |5x| + 2 F. ������ = |5x + 2| B. !'. G. None of these !( C. \". !% D. !(. ) Answer: E Answer: B
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.4.B Precalculus 2020-2021 1. 1.Y Name and graph points on a plane or 2. Review of Right Triangle Trig number line FIND THE EXACT VALUE NAME THE QUADRANT OR AXIS WHERE THE cot ������ = _________ POINT (������, ������) LIES IF ������ < 0 AND ������ > 0 Answer: Quadrant II Answer: *√% 3. 1.D evaluate expressions using order of !% operations / 2.G Represent functions in 4. 1.A perform basic operations with real multiple ways numbers (fractions) ������(������) = 4t + 1; FIND ������(−7) SIMPLIFY ���5��� 2 ������ Answer: ������(−7) = −27 Answer:+!&! 5. 3.H Relate geometric and algebraic 6. Review Radians representations of lines, parabolas, and Which angle might be represented in the segments diagram? MATCH AN EQUATION TO THE GRAPH A. \". A. ������ = |x + 2| $ B. ������ = |x| + 2 C. ������ = |3x| + 2 B. !'. D. ������ = |3x + 2| !( E. ������ = |5x| + 2 F. ������ = |5x + 2| C. \". G. None of these !% D. !(. ) Answer: E Answer: B
Name:__________________________________________Date:____________________Per:___________ 1. ℎ(������) = ������% + ������ + 3; FIND ℎ(−3) SKILLS BUILDER 1.4.C Precalculus 2020-2021 2. SIMPLIFY 8 8 9 Answer: ℎ(−3) = 9 Answer: 9 3. SOLVE 4. SIMPLIFY & RATIONALIZE 4 8 2 3 = ������ − 4 5√5 Answer: ������ = 10 Answer: %√\" %\" 5. MATCH AN EQUATION TO THE GRAPH A. ������ = |x + 2| 6. IDENTIFY THE SLOPE & Y-INTERCEPT THEN B. ������ = |x| + 2 GRAPH THE LINE ������ = −������ + 5 C. ������ = |3x| + 2 D. ������ = |3x + 2| SLOPE:________ Y-INT:__________ E. ������ = |5x| + 2 F. ������ = |5x + 2| G. None of these Answer: C Answer: see above
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.4.C Precalculus 2020-2021 1. 1.D evaluate expressions using order of 2. 1.A perform basic operations with real operations / 2.G Represent functions in numbers (fractions) multiple ways SIMPLIFY ℎ(������) = ������% + ������ + 3; FIND ℎ(−3) 8 8 9 Answer: ℎ(−3) = 9 Answer: 9 3. 3.B Setup and solve (algebraic) proportions. 4. 1.P Use properties to simplify radicals, SOLVE including rationalizing the denominator 4 8 SIMPLIFY & RATIONALIZE 3 = ������ − 4 2 5√5 Answer: ������ = 10 Answer: %√\" %\" 5. 3.H Relate geometric and algebraic representations of lines, parabolas, and 6. 3.H Relate geometric and algebraic segments representations of lines, parabolas, and MATCH AN EQUATION TO THE GRAPH segments. IDENTIFY THE SLOPE & Y-INTERCEPT THEN A. ������ = |x + 2| GRAPH THE LINE ������ = −������ + 5 B. ������ = |x| + 2 C. ������ = |3x| + 2 SLOPE:________ Y-INT:__________ D. ������ = |3x + 2| E. ������ = |5x| + 2 F. ������ = |5x + 2| G. None of these Answer: C Answer: −1; 5; see graph above
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.4.D Precalculus 2020-2021 1. FIND THE MEASURE OF THE ANGLE (IN 2. FIND THE EXACT VALUE RADIANS) cos ������ = _________ Answer: \"/ Answer: √% ( % 3. ℎ(������) = ������% − ������; FIND ℎ U− $*V 4. IDENTIFY THE SLOPE & Y-INTERCEPT THEN ' GRAPH THE LINE ������ = − \" ������ + 5 SLOPE:________ Y-INT:__________ Answer: ℎ U− *$V = ** Answer: see above !( 6. Name the quadrant or axis where the point 5. SIMPLIFY (������, ������) lies if ������ < 0 and ������ < 0 67 Answer: Quadrant III 2 * Answer: !%
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.4.D Precalculus 2020-2021 1. Review of Right Triangle Trig and Degrees and 2. Review of Right Triangle Trig Radians FIND THE EXACT VALUE FIND THE MEASURE OF THE ANGLE (IN cos ������ = _________ RADIANS) Answer: \"/ Answer: √% ( % 3. 1.D evaluate expressions using order of 4. 3.H Relate geometric and algebraic operations / 2.G Represent functions in representations of lines, parabolas, and multiple ways / 1.A perform basic operations segments. with real numbers (fractions) IDENTIFY THE SLOPE & Y-INTERCEPT THEN ' ℎ(������) = ������% − ������; FIND ℎ U− *$V GRAPH THE LINE ������ = − \" ������ + 5 SLOPE:________ Y-INT:__________ Answer: ℎ U− $*V = ** Answer: − ' ; 5; see graph above !( \" 5. 1.A perform basic operations with real 6. 1.Y Name and graph points on a plane or numbers (fractions) number line SIMPLIFY Name the quadrant or axis where the point 67 (������, ������) lies if ������ < 0 and ������ < 0 2 * Answer: Quadrant III !% Answer:
Name:__________________________________________Date:____________________Per:___________ 1. SIMPLIFY & RATIONALIZE SKILLS BUILDER 1.4.E 5 Precalculus 2020-2021 4√5 2. SIMPLIFY ������2������ 8 Answer: √\" Answer: 4 $ 4. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 3. SOLVE 2 GRAPH THE LINE ������ = −2������ + 5 ������ − 2 5 SLOPE:________ Y-INT:__________ 15 = Answer: ������ = 8 5. FIND THE EXACT VALUE ser: csc ������ = _________ see above 6. MATCH AN EQUATION TO THE GRAPH Answer: √!& ' A. ������ = −|x + 5| B. ������ = −|x| + 5 C. ������ = −|3x| + 5 D. ������ = −|3x + 5| E. ������ = −|5x| + 5 F. ������ = −|5x + 5| G. None of these Answer: B
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.4.E Precalculus 2020-2021 1. 1.P Use properties to simplify radicals, 2. 1.A perform basic operations with real including rationalizing the denominator numbers (fractions) SIMPLIFY & RATIONALIZE S I������2M������ PLIFY 5 8 4√5 Answer: 4 Answer: √\" 4. 3.H Relate geometric and algebraic $ representations of lines, parabolas, and segments. 3. 3.B Setup and solve (algebraic) proportions. IDENTIFY THE SLOPE & Y-INTERCEPT THEN SOLVE GRAPH THE LINE ������ = −2������ + 5 ������ − 2 2 15 = 5 SLOPE:________ Y-INT:__________ Answer: ������ = 8 Answer: -2; 5; see graph above 5. Review of Right Triangle Trig 6. 3.H Relate geometric and algebraic FIND THE EXACT VALUE representations of lines, parabolas, and csc ������ = _________ segments MATCH AN EQUATION TO THE GRAPH Answer: √!& ' A. ������ = −|x + 5| B. ������ = −|x| + 5 C. ������ = −|3x| + 5 D. ������ = −|3x + 5| E. ������ = −|5x| + 5 F. ������ = −|5x + 5| G. None of these Answer: B
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.5.A Precalculus 2020-2021 1. IF )(1,$) = ������ + 10, FIND 4������ = ______ 2. SIMPLIFY. RATIONALIZE AS NEEDED. % 5√5 √4 √6 ∙ √6 Answer: ������ = 8 ∴ 4������ = 32 Answer: \"√\" ' 3. DETERMINE IF (−1, −4) IS A SOLUTION TO 7������ + 4������ = −23 4. WRITE THE POLYNOMIAL IN FACTORED FORM ������(������) = ������% − 2������ − 24 Answer: Yes, it is a solution Answer: ������(������) = (������ + 4)(������ − 6) 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 6. FIND THE SLOPE-INTERCEPT EQUATION FOR THE GRAPH THE LINE y = 1 % SLOPE:________ Y-INT:__________ LINE THROUGH (−3, 5) WITH SLOPE = − ' (Hint: You may wish to start with point-slope form and convert it into slope intercept form) Point-Slope Form: Slope-intercept Form: ������ − ������! = ������(������ − ������!) ������ = ������������ + ������ Answer: 0; 1; see graph above Answer: ������ = − % ������ + 3 '
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.5.A Precalculus 2020-2021 1. IF )(1,$) = ������ + 10, FIND 4������ = ______ 2. SIMPLIFY. RATIONALIZE AS NEEDED. % 5√5 √4 √6 ∙ √6 Answer: ������ = 8 ∴ 4������ = 32 Answer: \"√\" ' 3. DETERMINE IF (−1, −4) IS A SOLUTION TO 7������ + 4������ = −23 4. WRITE THE POLYNOMIAL IN FACTORED FORM ������(������) = ������% − 2������ − 24 Answer: Yes, it is a solution Answer: ������(������) = (������ + 4)(������ − 6) 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 6. FIND THE SLOPE-INTERCEPT EQUATION FOR THE GRAPH THE LINE y = 1 % SLOPE:________ Y-INT:__________ LINE THROUGH (−3, 5) WITH SLOPE = − ' (Hint: You may wish to start with point-slope form and convert it into slope intercept form) Point-Slope Form: Slope-intercept Form: ������ − ������! = ������(������ − ������!) ������ = ������������ + ������ Answer: 0; 1; see graph above Answer: ������ = − % ������ + 3 '
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.5.B Precalculus 2020-2021 1. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 2. FIND THE AREA OF THE TRIANGLE. INCLUDE GRAPH THE LINE y = −4 ! SLOPE:________ Y-INT:__________ UNITS IN YOUR ANSWER. (Hint: ������ = % ������ℎ) Answer: 0; -4; see graph above Answer: ������������������������ = 40 ������������% 3. IF −5������ = +3%%%, FIND 3������ = ______ 4. WRITE THE POLYNOMIAL IN FACTORED FORM ������(������) = ������% − 17������ + 72 Answer: ������ = −2 ∴ 3������ = −6 Answer: ������(������) = (������ − 9)(������ − 8) 5. SIMPLIFY. RATIONALIZE AS NEEDED. 6. FIND THE SLOPE-INTERCEPT EQUATION FOR THE ) 5 ∙ 2√2 LINE THROUGH (−2, −4) WITH SLOPE = % √20 5 (Hint: You may wish to start with point-slope form and convert it into slope intercept form) Point-Slope Form: Slope-intercept Form: ������ − ������! = ������(������ − ������!) ������ = ������������ + ������ Answer: √!& Answer: ������ = ) ������ + 5 \" %
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.5.B Precalculus 2020-2021 1. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 2. FIND THE AREA OF THE TRIANGLE. INCLUDE GRAPH THE LINE y = −4 ! SLOPE:________ Y-INT:__________ UNITS IN YOUR ANSWER. (Hint: ������ = % ������ℎ) Answer: 0; -4; see graph above Answer: ������������������������ = 40 ������������% 3. IF −5������ = +3%%%, FIND 3������ = ______ 4. WRITE THE POLYNOMIAL IN FACTORED FORM ������(������) = ������% − 17������ + 72 Answer: ������ = −2 ∴ 3������ = −6 Answer: ������(������) = (������ − 9)(������ − 8) 5. SIMPLIFY. RATIONALIZE AS NEEDED. 6. FIND THE SLOPE-INTERCEPT EQUATION FOR THE ) 5 ∙ 2√2 LINE THROUGH (−2, −4) WITH SLOPE = % √20 5 (Hint: You may wish to start with point-slope form and convert it into slope intercept form) Point-Slope Form: Slope-intercept Form: ������ − ������! = ������(������ − ������!) ������ = ������������ + ������ Answer: √!& Answer: ������ = ) ������ + 5 \" %
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.5.C Precalculus 2020-2021 1. DETERMINE IF (6, −7) IS A SOLUTION TO 2. SIMPLIFY. RATIONALIZE AS NEEDED. 7������ + 4������ = −23 5√3 ∙ √4 3√20 Answer: No, it is not a solution Answer: √'!\" 3. FIND THE AREA OF THE TRIANGLE. INCLUDE 4. IF −5 = ������ + \"#, FIND 8������ = ______ UNITS IN YOUR ANSWER. Answer: ������������������������ = 5.6 ������������% Answer: ������ = − $\" ∴ 8������ = −45 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN # GRAPH THE LINE x = −1 6. FIND AN EQUATION FOR THE LINE THROUGH SLOPE:________ Y-INT:__________ (1, −5) AND (2, 2) (Hint: First find ������ by using formula for slope ) Point-Slope Form: Formula for Slope: ������ − ������! = ������(������ − ������!) ������ = ������% − ������! ������% − ������! Answer: undefined; none; see graph above Answer: ������ + 5 = 7(������ − 1) or ������ − 2 = 7(������ − 2) ������������ ������ = 7������ − 12
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.5.C Precalculus 2020-2021 1. DETERMINE IF (6, −7) IS A SOLUTION TO 2. SIMPLIFY. RATIONALIZE AS NEEDED. 7������ + 4������ = −23 5√3 ∙ √4 3√20 Answer: No, it is not a solution Answer: √'!\" 3. FIND THE AREA OF THE TRIANGLE. INCLUDE 4. IF −5 = ������ + #\", FIND 8������ = ______ UNITS IN YOUR ANSWER. Answer: ������������������������ = 5.6 ������������% Answer: ������ = − $\" ∴ 8������ = −45 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN # GRAPH THE LINE x = −1 6. FIND AN EQUATION FOR THE LINE THROUGH SLOPE:________ Y-INT:__________ (1, −5) AND (2, 2) (Hint: First find ������ by using formula for slope ) Point-Slope Form: Formula for Slope: ������ − ������! = ������(������ − ������!) ������ = ������% − ������! ������% − ������! Answer: undefined; none; see graph above Answer: ������ + 5 = 7(������ − 1) or ������ − 2 = 7(������ − 2) ������������ ������ = 7������ − 12
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.5.D Precalculus 2020-2021 1. SIMPLIFY. RATIONALIZE AS NEEDED. 2. MATCH EACH ITEM IN COLUMN 1 WITH A CORRESPONDING ANSWER IN COLUMN 2. 2 ∙ √5 COLUMN 1 COLUMN 2 4√2 1. Vertical Line A. ������ = 3������ 2. Horizontal Line B. ������ = 2 3. Slanted Line C. ������ = 4 Answer: √!& Answer: 1.C; 2.B; 3.A $ 3. WRITE THE POLYNOMIAL IN FACTORED 4. IF ,$13$# = ������ + 1, FIND 3������ = ______ FORM ������(������) = ������% + 8������ − 9 ) Answer:������(������) = (������ − 1)(������ + 9) Answer: ������ = 3 ∴ 3������ = 9 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 6. FIND AN EQUATION FOR THE LINE THROUGH GRAPH THE LINE y = 5������ (−2, −1) AND (0, −1) SLOPE:________ Y-INT:__________ (Hint: First find ������ by using formula for slope ) Point-Slope Form: Formula for Slope: ������ − ������! = ������(������ − ������!) ������ = ������% − ������! ������% − ������! Answer: 5; 0; see graph above Answer: ������ = −1; horizontal line
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.5.D Precalculus 2020-2021 1. SIMPLIFY. RATIONALIZE AS NEEDED. 2. MATCH EACH ITEM IN COLUMN 1 WITH A CORRESPONDING ANSWER IN COLUMN 2. 2 ∙ √5 COLUMN 1 COLUMN 2 4√2 1. Vertical Line A. ������ = 3������ 2. Horizontal Line B. ������ = 2 3. Slanted Line C. ������ = 4 Answer: √!& Answer: 1.C; 2.B; 3.A $ 3. WRITE THE POLYNOMIAL IN FACTORED 4. IF ,$13$# = ������ + 1, FIND 3������ = ______ FORM ������(������) = ������% + 8������ − 9 ) Answer:������(������) = (������ − 1)(������ + 9) Answer: ������ = 3 ∴ 3������ = 9 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN 6. FIND AN EQUATION FOR THE LINE THROUGH GRAPH THE LINE y = 5������ (−2, −1) AND (0, −1) SLOPE:________ Y-INT:__________ (Hint: First find ������ by using formula for slope ) Point-Slope Form: Formula for Slope: ������ − ������! = ������(������ − ������!) ������ = ������% − ������! ������% − ������! Answer: 5; 0; see graph above Answer: ������ = −1; horizontal line
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.6.A Precalculus 2020-2021 1. WRITE THE POLYNOMIAL IN FACTORED FORM 2. MULTIPLY ℎ(������) = ������% − 3������ − 28 (������ + 2)(������ − 5) Answer: ℎ(������) = (������ + 4)(������ − 7) Answer:������% − 3������ − 10 3. FIND THE AREA & CIRCUMFERENCE OF THE 4. POINT P HAS COORDINATES (3, 4). WRITE CIRCLE. LEAVE ANSWERS EXACT AND INCLUDE AN EQUATION FOR THE LINE PASSING UNITS. (Hint: ������ = 2������������ & ������ = ������������%) THROUGH THE ORIGIN AND POINT P. (Hint: Find Slope First) Answer: ������������������������ = 121������ ������������% ; Answer: ������ = $ ������ ������������������������������������������������������������������������������ = 22������ ft ' 5. IF 4+,5 = ������ , THEN ������ = ________ 6. SIMPLIFY 4,! 9������������ 81������������ Answer: ������ = ������ Answer: )+6
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.6.A Precalculus 2020-2021 1. WRITE THE POLYNOMIAL IN FACTORED FORM 2. MULTIPLY ℎ(������) = ������% − 3������ − 28 (������ + 2)(������ − 5) Answer: ℎ(������) = (������ + 4)(������ − 7) Answer:������% − 3������ − 10 3. FIND THE AREA & CIRCUMFERENCE OF THE 4. POINT P HAS COORDINATES (3, 4). WRITE CIRCLE. LEAVE ANSWERS EXACT AND INCLUDE AN EQUATION FOR THE LINE PASSING UNITS. (Hint: ������ = 2������������ & ������ = ������������%) THROUGH THE ORIGIN AND POINT P. (Hint: Find Slope First) Answer: ������������������������ = 121������ ������������% ; Answer: ������ = $ ������ ������������������������������������������������������������������������������ = 22������ ft ' 5. IF 4+,5 = ������ , THEN ������ = ________ 6. SIMPLIFY 4,! 9������������ 81������������ Answer: ������ = ������ Answer: )+6
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.6.B Precalculus 2020-2021 1. WRITE THE POLYNOMIALS IN FACTORED 2. SQUARE THE BINOMIAL FORM (������ + 9)% ������(������) = ������% − 12������ + 36 ℎ(������) = ������% − 49 Answer:������(������) = (������ − 6)%; Answer:������% + 18������ + 81 ℎ(������) = (������ + 7)(������ − 7) 4. SIMPLIFY 3. IF 4,+ = −2 , THEN ������ = ________ 4������%������% ∙ 5������������'������ + Answer: ������ = −������ Answer: 20������'������\"������ 5. FIND THE AREA OF THE TRIANGLE. INCLUDE 6. POINT P HAS COORDINATES (8,12). WRITE UNITS IN YOUR ANSWER. (hint: 1������������ = 3������������) AN EQUATION FOR THE LINE PASSING THROUGH THE ORIGIN AND POINT P. Answer: ������������������������ = 24 ������������% Answer: ������ = ' ������ %
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.6.B Precalculus 2020-2021 1. WRITE THE POLYNOMIALS IN FACTORED 2. SQUARE THE BINOMIAL FORM (������ + 9)% ������(������) = ������% − 12������ + 36 ℎ(������) = ������% − 49 Answer:������(������) = (������ − 6)%; Answer:������% + 18������ + 81 ℎ(������) = (������ + 7)(������ − 7) 4. SIMPLIFY 3. IF 4,+ = −2 , THEN ������ = ________ 4������%������% ∙ 5������������'������ + Answer: ������ = −������ Answer: 20������'������\"������ 5. FIND THE AREA OF THE TRIANGLE. INCLUDE 6. POINT P HAS COORDINATES (8,12). WRITE UNITS IN YOUR ANSWER. (hint: 1������������ = 3������������) AN EQUATION FOR THE LINE PASSING THROUGH THE ORIGIN AND POINT P. Answer: ������������������������ = 24 ������������% Answer: ������ = ' ������ %
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.6.C Precalculus 2020-2021 1. IF (3������ + 2)(4������ − 3) = 12������% + ������������ − 6 , 2. DEGREES CELCIUS AND DEGRESS FIND ������ FAHRENHEIT ARE BOTH MEASURES OF TEMPERATURE. \" IF ������ = ) (������ − 32) , THEN ������ = ________ Answer: ������ = −1 Answer: ) ������ + 32 3. FIND THE AREA & CIRCUMFERENCE OF THE \" CIRCLE. LEAVE ANSWERS EXACT AND INCLUDE 4. WRITE THE POLYNOMIALS IN FACTORED UNITS. FORM ������(������) = ������% + 9 ℎ(������) = ������% − 1 Answer: ������������������������ = 49������ ������������% ; Answer: ������(������) does not factor; ������������������������������������������������������������������������������ = 14������ ft ℎ(������) = (������ + 1)(������ − 1) 6. POINT P HAS COORDINATES (-4,10). WRITE 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN AN EQUATION FOR THE LINE PASSING GRAPH THE LINE ������ = 4 THROUGH THE ORIGIN AND POINT P. SLOPE:________ Y-INT:__________ Answer: undefined; none; see graph above Answer: ������ = − \" ������ %
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.6.C Precalculus 2020-2021 1. IF (3������ + 2)(4������ − 3) = 12������% + ������������ − 6 , 2. DEGREES CELCIUS AND DEGRESS FIND ������ FAHRENHEIT ARE BOTH MEASURES OF TEMPERATURE. \" IF ������ = ) (������ − 32) , THEN ������ = ________ Answer: ������ = −1 Answer: ) ������ + 32 3. FIND THE AREA & CIRCUMFERENCE OF THE \" CIRCLE. LEAVE ANSWERS EXACT AND INCLUDE 4. WRITE THE POLYNOMIALS IN FACTORED UNITS. FORM ������(������) = ������% + 9 ℎ(������) = ������% − 1 Answer: ������������������������ = 49������ ������������% ; Answer: ������(������) does not factor; ������������������������������������������������������������������������������ = 14������ ft ℎ(������) = (������ + 1)(������ − 1) 6. POINT P HAS COORDINATES (-4,10). WRITE 5. IDENTIFY THE SLOPE & Y-INTERCEPT THEN AN EQUATION FOR THE LINE PASSING GRAPH THE LINE ������ = 4 THROUGH THE ORIGIN AND POINT P. SLOPE:________ Y-INT:__________ Answer: undefined; none; see graph above Answer: ������ = − \" ������ %
Name:__________________________________________Date:____________________Per:___________ SKILLS BUILDER 1.6.D Precalculus 2020-2021 1. WRITE THE POLYNOMIALS IN FACTORED 2. DETERMINE IF (2, 6) IS A SOLUTION TO FORM 7������ + 4������ = −23 ������(������) = ������% + 4������ + 1 ℎ(������) = ������% + 16 Answer: both ������(������) and h(������) cannot be Answer: No, it is not a solution factored 4. IF −2 = ������ + $), FIND 9������ = ______ 3. SQAURE THE BINOMIAL (3������ − 7)% Answer: 9������% − 42������ + 49 Answer: ������ = − %% ∴ 9������ = −22 ) 5. KINETIC ENERGY CAN BE CALCULATED IF MASS 6. FIND THE AREA OF THE TRIANGLE. INCLUDE AND VELOCITY ARE KNOWN. UNITS IN YOUR ANSWER. (hint: 1������ = ! 100������������ IF ������ = % ������������%, FIND ������ = ____________ Answer: ������ = ±i%87 Answer: 13.5 ������%
Name:__________________________________________Date:____________________Per:___________ KEY: SKILLS BUILDER 1.6.D Precalculus 2020-2021 1. WRITE THE POLYNOMIALS IN FACTORED 2. DETERMINE IF (2, 6) IS A SOLUTION TO FORM 7������ + 4������ = −23 ������(������) = ������% + 4������ + 1 ℎ(������) = ������% + 16 Answer: both ������(������) and h(������) cannot be Answer: No, it is not a solution factored 4. IF −2 = ������ + $), FIND 9������ = ______ 3. SQAURE THE BINOMIAL (3������ − 7)% Answer: 9������% − 42������ + 49 Answer: ������ = − %% ∴ 9������ = −22 ) 5. KINETIC ENERGY CAN BE CALCULATED IF MASS 6. FIND THE AREA OF THE TRIANGLE. INCLUDE AND VELOCITY ARE KNOWN. UNITS IN YOUR ANSWER. (hint: 1������ = ! 100������������ IF ������ = % ������������%, FIND ������ = ____________ Answer: ������ = ±i%87 Answer: 13.5 ������%
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