Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Early problems drill one technique at a time. Later ones build models for gardens, cars, mixtures and budgets.
Standards: A-SSE.A.1, A-SSE.A.2, A-CED.A.1, A-CED.A.2, A-CED.A.3, A-CED.A.4, A-REI.D.11, A-APR.C.5, N-CN.C.8, N-CN.C.9 · Level: Grade 11 Algebra 2
Problem 1 Interpret a model ★★★
The value of a savings account is A = 500(1.04)t, where t is years. Explain what 500 and 1.04 mean.
Problem 2 Difference of squares twice ★★★
Factor x4 − 625 completely over the real numbers.
Problem 3 Factor with a coefficient ★★★
Factor 16x4 − 81 completely over the real numbers.
Problem 4 Rearrange a volume formula ★★★
The volume of a cone is V = (1/3)πr2h. Solve for h.
Problem 5 Rearrange a trapezoid area formula ★★★
A designer knows the area A, the height h and one base b1 of a trapezoid and needs the other base. Rewrite A = (1/2)h(b1 + b2) with b2 alone on one side.
Problem 6 Expand with Pascal’s triangle ★★★
Use row 4 of Pascal’s triangle to expand (x + 2)4.
Problem 7 Expand with a negative term ★★★
Expand (2x − 1)3.
Problem 8 A single coefficient ★★★
In the expansion of (x + 2)6, which term contains x2, and what is its coefficient?
Problem 9 Factor over the complex numbers ★★★
Factor x2 + 25 over the complex numbers and verify by multiplying.
Problem 10 Zeros and factors of a quadratic ★★★
Find the zeros of x2 − 4x + 13 and write it as a product of linear factors.
Problem 11 Generate a Pythagorean triple ★★★
Verify the identity (x2 + y2)2 = (x2 − y2)2 + (2xy)2 by expanding, then use x = 4 and y = 1 to find a triple.
Problem 12 Solve f(x) = g(x) from a graph ★★★
A parabola f(x) = x2 − 6x + 7 and a line g(x) = x − 3 are sketched below. Use the sketch to estimate where the two outputs are equal, then verify by solving an equation.
Problem 13 Solve with a table ★★★
Ravi tabulated two models, f(x) = x2 + 6 and g(x) = 5x. Scan the table for the inputs that give identical outputs.
Problem 14 Garden constraint ★★★
A rectangular garden has a perimeter of 24 feet and an area of at least 20 square feet. If the width is w, write an inequality in w and find the possible widths.
Problem 15 Depreciation model ★★★
A car worth $24,000 loses 12% of its value each year. Write V(t) and find when its value reaches $15,000, to the nearest tenth of a year.
Problem 16 Mixture as a rational equation ★★★
A tank holds 20 liters of a 20% acid solution. How many liters of pure acid must be added to reach a 50% solution? The concentration after adding x liters is (4 + x)/(20 + x).
Problem 17 Ticket sales system ★★★
A school play sold 150 tickets for $1,330. Adult tickets cost $12 and child tickets cost $7. How many of each were sold?
Problem 18 Budget constraints ★★★
Jada has $60 to spend on notebooks at $4 each and pens at $1.50 each, and she needs at least 6 notebooks. Write the system of inequalities and test whether 6 notebooks and 20 pens is allowed.
Problem 19 Binomial Theorem with complex numbers ★★★
Use Pascal’s triangle to compute (1 + i)4.
Problem 20 Identities for mental arithmetic ★★★
Use x4 − y4 = (x2 + y2)(x + y)(x − y) to compute 124 − 54 without finding each fourth power.
