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 pattern begins: 2, 6, 18, __, __. Find the missing terms and the 8th term.
$-5x + 13 \geq -7$. Solve and state whether you flipped the inequality.
A number pattern starts at 7. Each term is 9 more than the one before. Find the 12th term.
A pattern starts at 4. The 4th term is 108. Each term is the same multiple of the one before. Find that multiplier and write a formula for the $n$th term.
$3x + 7 = 28$. 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.
A number pattern has its 3rd term equal to 22 and its 8th term equal to 47. The gap between consecutive terms is always the same. Find the gap, find the 1st term, and write the formula for the $n$th term.
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 $x$.
A pattern starts at 2 and decreases by 5 each step. Write the formula for the $n$th term. Find the first term that is negative, and which position it is.
What's next → Lesson 11 is a targeted practice session built around the specific spots where the data shows you got stuck: geometric sequences with fractional and decimal ratios, identifying sequence types from scratch, equations and inequalities with fractional coefficients, and finding the common difference from non-first terms. Lesson 12 after that is the rich-tasks session.