Advanced Mathematics Unit 1: Parent Answer Guide
PARENT PDF: Open the printable Advanced Mathematics Unit 1 Parent Answer Guide (PDF). The full answer text remains copyable below. Keep the key private until students finish their work.
Companion to Advanced Mathematics Student Unit 1. These are suggested worked answers to twelve advanced lessons. The course is open to learners of any age who demonstrate the prerequisites. Keep this answer guide apart from student work and verify each solution independently.
Lesson 1: Linear equations
Answers and teaching explanation: 4(2x+1)=36 gives x=4. 5x-7=2x+11 gives x=6. Any operation on an equation must preserve equality on both sides.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 2: Inequalities
Answers and teaching explanation: 3x-5 is at most 13 gives x at most 6. -2x+7>15 gives x<-4 after reversing the inequality for division by a negative. Budget: 7+3n at most 25 gives n at most 6 whole items.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 3: Rates and proportions
Answers and teaching explanation: 3/4 cup for two servings scales to 21/8 or 2 5/8 cups for seven. 6cm at 1:25,000 means 150,000cm=1.5km. Cost per 100mL: 250mL at $1.50 costs $0.60; 400mL at $2.20 costs $0.55.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 4: Functions
Answers and teaching explanation: For y=-3x+4 and x=-2,0,2,4, outputs are 10,4,-2,-8. The pairs (1,2),(1,3),(2,4) are not a function because one input has two outputs. Taxi y=5+2x has $5 base and $2 per x-unit.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 5: Slope and systems
Answers and teaching explanation: Slope from (-2,4) to (2,-4) is -2. Equations y=2x+1 and y=-x+7 intersect at (2,5). Distinct parallel lines have no solution.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 6: Exponents
Answers and teaching explanation: 2^3 times 2^4=2^7=128. (3^2)^3=3^6=729. 0.00056=5.6 times 10^-4. (6 times 10^4)(2 times 10^-2)=1.2 times 10^3.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 7: Geometry
Answers and teaching explanation: Missing angle is 180-43-68=69 degrees. A right triangle with legs 5 and 12 has hypotenuse 13. The usual Pythagorean relation assumes a right angle.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 8: Area and scale
Answers and teaching explanation: Cylinder radius 2 and height 10 has volume 40pi cubic units. Area scale factor for sides 4 to 10 is (10/4)^2=6.25. A 4 by 5 by 6 box has volume 120 cubic cm and surface area 148 square cm.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Lesson 9: Statistics
Answers and teaching explanation: For 1,2,3,4,20 mean is 6 and median 3. The outlier raises the mean. A median can better describe a skewed income distribution. Representative sampling requires broader selection than friends.
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Lesson 10: Probability
Answers and teaching explanation: A die and coin have 12 ordered combinations. P(red then blue without replacement)=(4/10)(6/9)=4/15. Five siblings form an extremely small, dependent and unrepresentative sample for town-level inference.
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Lesson 11: Personal finance
Answers and teaching explanation: 8 percent tax on $65 is $5.20; total $70.20. Simple interest $500 at 4 percent for two years is $40, total $540. Cash price $90 is $10 below $100 installments, ignoring other terms; inspect possible fees.
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Lesson 12: Cumulative assessment
Answers and teaching explanation: 3(x+5)=2x+22 gives x=7. Graph x>=-2 with a filled endpoint at -2 and shading to the right. y=3x-4 and y=x+2 meet at (3,5). Data 4,5,5,7,19: mean 8, median 5, range 15.
Review whether the learner shows calculations, respects units, explains reasoning and solves a new related problem without seeing the key.
Mastery and Teaching Decisions
Mark each skill independent, guided or reteach. After instruction, reassess with new problems rather than the same memorized questions. This supplemental guide is not a formal grade equivalency or a complete annual standards certificate.