Mathematics in 4th Year of ESO
Mathematics in 4th year of ESO, Options A and B: sequences, inequalities and intervals, functions and rate of change, compound probability, trigonometry and analytic geometry. Each topic includes exercise models ready for printable worksheets.
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What does a 4th-year ESO student learn in mathematics?
In fourth year of ESO, both options share sequences and their general term, linear intervals and inequalities, factorization of polynomials, rate of change, and comparison of linear, quadratic, inverse proportionality and exponential functions. In statistics, contingency tables, variance and the regression line appear, and in probability, compound experiments with tree diagrams and counting techniques. Matemáticas A adds compound interest and the slope of a line in everyday situations; Matemáticas B adds the trigonometric ratios of an acute angle, the analytic geometry of the line, powers with fractional exponents, geometric progressions and simple non-linear equations.
About the curriculum: in fourth year the minimum teaching requirements of ESO (Royal Decree 217/2022, of 29 March, BOE no. 76, of 30 March 2022) set up the subject in two options, Matemáticas A and Matemáticas B, each with its own basic content; this page brings together what is common to both and points out what is specific to each option. Each autonomous community completes this national minimum with its own curriculum. The basic content, quoted literally, is in the section below.
Task templates to print
Every task type, grouped by skill. Clicking one opens the worksheet generator with it already selected.
Other task types
- Calculation program (grade 4–6)
- A table that takes away (grade 2–4)
- Fill in the table using the multiplying rule (grade 2–4)
- Choose what comes out of the machine (grade 2–4)
- Correct the mistake in the table (grade 3–4)
- Function table: find the rule (grade 2–4)
- Which number went into the machine (grade 2–4)
- Complete the proportion (grade 5–6)
- Scale up from one group to another (grade 5–6)
- Find the range (grade 5–6)
- Compare bars in a bar chart (grade 4–6)
- Inverse proportion (grade 7–8)
- Scientific notation (grade 7–8)
- Missing exponent — rules of exponents (grade 7–8)
- Simplify a square root (grade 8)
- Sum of two dice (grade 8)
- Two draws with replacement (grade 8)
- Evaluate an expression (grade 7–8)
- System of two equations (grade 8)
- Which number was it? (grade 5–6)
- How many were there at the start? (grade 5–6)
- Rearrange the formula for x (grade 7–8)
- What does the sample tell us about the whole school? (grade 7–8)
- Predict with a line of fit (grade 8)
- Trip graph: how long was the stop? (grade 7–8)
- Trip graph: how far in total? (grade 7–8)
- Trip graph: speed in the first part (grade 7–8)
- Two-way table: the missing cell (grade 8)
- Two-way table: what fraction of the group? (grade 8)
- Largest integer in a set (grade 7–8)
- Smallest integer in a set (grade 7–8)
- Arithmetic sequence — nth term (grade 11–12)
- Arithmetic sequence — sum of terms (grade 11–12)
- Permutations — standing in a queue
- Arrangements — awarding prizes
- Even numbers containing a digit once (grade 11–12)
- Odd numbers containing a digit once (grade 11–12)
- Variance of a data set (grade 11–12)
- Drawing balls without replacement (grade 11–12)
- Factoring out a monomial
- Factoring by grouping
- Sum and difference of cubes
- Linear inequality
- Quadratic equation
- Linear function through two points
- Parallel line through a point
- The function f(x) = a/x
- Average rate of change
- Value of a quadratic function
- Compare function values: graph and formula
- Which function has the greater maximum?
- Function value from a graph
- Zeros from a graph
- A function defined piecewise
- Domain from a graph
- Range from a graph
- Where the function decreases (from a graph)
- Where the function increases (from a graph)
- Where the function is positive — from a graph
- Does the endpoint belong to the interval? (grade 9)
- Write the interval shown on the number line (grade 9)
- Exponential growth overtakes linear growth
- Bounds of a rounded value
- Population density: a quantity for comparison
- Area from sides measured to the nearest unit
- Cost as a linear function and its graph
- The nth term of a linear sequence
- The nth term of a quadratic sequence
- Direct proportion: y = kxⁿ
- Inverse proportion: y = k/xⁿ
- Round to significant figures (grade 8–9)