This worksheet is different. The problems are deliberately scrambled — no topic labels, no hints about which method to use. Your job is to read each problem, decide what kind it is, then solve it. This is harder than a topic-focused worksheet and that difficulty is the whole point: it forces you to recognise patterns rather than just follow the same steps 10 times in a row. Research shows this kind of practice leads to much stronger long-term memory.
Before you solve each problem, write one word at the top of your working to describe what type it is: equation, inequality, arith. sequence, or geom. sequence. Getting the diagnosis right is part of the skill.
18 Problems — No Topic Labels
Mia earns $w$ dollars per hour at the stables. Last Saturday she worked 7 hours, then spent $11 on a new brush. She had $38 left over. Find $w$.
A sequence begins: 3, 11, 19, __, __. Find the missing terms and the 20th term.
$x - 9 \geq 14$. Solve and describe the solution in words.
The farrier charges a $12 € call-out fee plus an hourly rate. Mia's bill was 57 €. She knows the farrier stayed for 3 hours. What is the hourly rate?
Mia needs at least $\$75$ to enter a show. She has $\$23$ saved and earns $\$13$ per week. Write and solve the inequality for the minimum number of weeks she must save. What is the earliest week she can enter?
$\dfrac{3}{5}x + 8 = 23$. Solve for $x$.
A geometric sequence: 2, 6, 18, __, __. Find the missing terms and $a_8$.
$-5x + 13 \geq -7$. Solve and state whether you flipped the inequality.
An arithmetic sequence has $a_1 = 7$ and $d = 9$. Find $a_{12}$.
A geometric sequence has $a_1 = 4$ and $a_4 = 108$. Find $r$ and write the formula for $a_n$.
$3x + 7 = 28$. Solve for $x$.
A supplement comes in a 64 mg dose. It halves in the body every day. On which day does less than 3 mg remain?
Copper started at 120 kg of hay. He eats 8 kg per day. After $x$ days, 32 kg remains. Find $x$.
$2x - 11 > 5$. Solve and graph on a number line.
The 3rd term of an arithmetic sequence is 22. The 8th term is 47. Find $d$, find $a_1$, and write the formula for $a_n$.
Copper ate $\dfrac{2}{3}$ of a bale of hay plus 5 kg of grain supplement. His total daily feed was 17 kg. How heavy is a full bale?
$\dfrac{x}{7} = 13$. Solve for $x$.
An arithmetic sequence has $a_1 = 2$ and $d = -5$. Write the formula for $a_n$. Find the first term that is negative, and which position ($n$) it is.
What's next → Lesson 11 is different from every worksheet so far. Instead of 18 short problems, there are just three. Each one takes longer, has no single obvious method, and may surprise you with its answer. These are called rich tasks — the kind of problem that shows you something new about how mathematics works.