year 10 maths problem solving

Year 10 maths

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• 1 Identify rational and irrational numbers
• 2 Compare and order rational numbers
• 3 Square roots
• 4 Cube roots

B. Consumer maths

• 1 Simple interest
• 2 Compound interest: word problems
• 3 Continuously compounded interest
• 4 Percent of a number: GST, discount and more
• 5 Find the percent: discount and mark-up
• 6 Multi-step problems with percents

C. Coordinate plane

• 1 Coordinate plane review
• 2 Midpoints
• 3 Distance between two points

D. Solve equations

• 1 Does x satisfy the equation?
• 2 Model and solve equations using algebra tiles
• 3 Write and solve equations that represent diagrams
• 4 Solve one-step linear equations
• 5 Solve two-step linear equations
• 6 Solve advanced linear equations
• 7 Solve equations with variables on both sides
• 8 Solve equations: complete the solution
• 9 Find the number of solutions
• 10 Create equations with no solutions or infinitely many solutions
• 11 Solve linear equations: word problems
• 12 Solve linear equations: mixed review

E. Single-variable inequalities

• 1 Graph inequalities
• 2 Write inequalities from graphs
• 3 Write and graph inequalities: word problems
• 4 Identify solutions to inequalities
• 5 Solve one-step linear inequalities: addition and subtraction
• 6 Solve one-step linear inequalities: multiplication and division
• 7 Solve one-step linear inequalities
• 8 Graph solutions to one-step linear inequalities
• 9 Solve two-step linear inequalities
• 10 Graph solutions to two-step linear inequalities
• 11 Solve advanced linear inequalities
• 12 Graph solutions to advanced linear inequalities

F. Relations and functions

• 1 Relations: convert between tables, graphs, mappings and lists of points
• 2 Domain and range of relations
• 3 Identify independent and dependent variables
• 4 Identify functions
• 5 Find values using function graphs
• 6 Evaluate a function
• 7 Complete a function table from a graph
• 8 Complete a function table from an equation
• 9 Interpret the graph of a function: word problems

G. Linear functions

• 1 Identify linear functions
• 2 Find the gradient of a graph
• 3 Find the gradient from two points
• 4 Find a missing coordinate using gradient
• 5 Find the gradient and y-intercept of a linear equation
• 6 Graph an equation in y=mx+c form
• 7 Write an equation in y=mx+c form from a graph
• 8 Write an equation in y=mx+c form
• 9 Linear equations: solve for y
• 10 Write an equation in y=mx+c form from a table
• 11 Write an equation in y=mx+c form from a word problem
• 12 Write linear functions to solve word problems
• 13 Complete a table and graph a linear function
• 14 Compare linear functions: graphs, tables and equations
• 15 Write equations in standard form
• 16 Standard form: find x- and y-intercepts
• 17 Standard form: graph an equation
• 18 Equations of horizontal and vertical lines
• 19 Graph a horizontal or vertical line
• 20 Point-gradient form: graph an equation
• 21 Point-gradient form: write an equation
• 22 Point-gradient form: write an equation from a graph
• 23 Gradients of parallel and perpendicular lines
• 24 Write an equation for a parallel or perpendicular line
• 25 Find the distance between a point and a line
• 26 Find the distance between two parallel lines
• 27 Transformations of linear functions

H. Simultaneous equations

• 1 Is (x, y) a solution to the simultaneous equations?
• 2 Solve simultaneous equations by graphing
• 3 Solve simultaneous equations by graphing: word problems
• 4 Find the number of solutions to simultaneous equations by graphing
• 5 Find the number of solutions to simultaneous equations
• 6 Solve simultaneous equations using substitution
• 7 Solve simultaneous equations using substitution: word problems
• 8 Solve simultaneous equations using elimination
• 9 Solve simultaneous equations using elimination: word problems
• 10 Solve simultaneous equations using any method
• 11 Solve simultaneous equations using any method: word problems

I. Inequalities and linear programming

• 1 Does (x, y) satisfy the inequality?
• 2 Linear inequalities: solve for y
• 3 Graph a linear inequality in the coordinate plane
• 4 Linear inequalities: word problems
• 5 Is (x, y) a solution to the simultaneous inequalities?
• 6 Solve simultaneous inequalities by graphing
• 7 Find the vertices of a solution set
• 8 Linear programming

J. Matrices

• 1 Matrix vocabulary
• 2 Matrix operation rules
• 3 Add and subtract matrices
• 4 Multiply a matrix by a scalar
• 5 Linear combinations of matrices
• 6 Multiply two matrices
• 7 Identify transformation matrices
• 8 Transformation matrices: write the vertex matrix
• 9 Transformation matrices: graph the image

K. Exponents

• 1 Powers with integer bases
• 2 Powers with decimal and fractional bases
• 3 Negative exponents
• 4 Multiplication with exponents
• 5 Division with exponents
• 6 Multiplication and division with exponents
• 7 Power rule
• 8 Evaluate expressions using properties of exponents
• 9 Identify equivalent expressions involving exponents

L. Logarithms

• 1 Convert between exponential and logarithmic form: rational bases
• 2 Evaluate logarithms
• 3 Change of base formula
• 4 Identify properties of logarithms
• 5 Product property of logarithms
• 6 Quotient property of logarithms
• 7 Power property of logarithms
• 8 Properties of logarithms: mixed review
• 9 Evaluate logarithms: mixed review

M. Exponential and logarithmic functions

• 1 Domain and range of exponential functions
• 2 Domain and range of logarithmic functions
• 3 Evaluate an exponential function
• 4 Match exponential functions and graphs I
• 5 Match exponential functions and graphs II
• 6 Solve exponential equations by rewriting the base
• 7 Solve exponential equations using common logarithms
• 8 Solve logarithmic equations I
• 9 Solve logarithmic equations II
• 10 Exponential growth and decay: word problems

N. Monomials

• 1 Identify monomials
• 2 Multiply monomials
• 3 Divide monomials
• 4 Multiply and divide monomials
• 5 Powers of monomials

O. Polynomials

• 1 Polynomial vocabulary
• 2 Model polynomials with algebra tiles
• 3 Add and subtract polynomials using algebra tiles
• 4 Add and subtract polynomials
• 5 Add polynomials to find perimeter
• 6 Multiply a polynomial by a monomial
• 7 Multiply two polynomials using algebra tiles
• 8 Multiply two binomials
• 9 Multiply two binomials: special cases
• 10 Multiply polynomials
• 11 Divide polynomials
• 12 Divide polynomials using synthetic division
• 13 Find the roots of factorised polynomials
• 14 Write a polynomial from its roots
• 15 Conjugate roots
• 16 Match polynomials and graphs
• 17 Domain and range of polynomials

P. Factorising

• 1 HCF of monomials
• 2 Factorise out a monomial
• 3 Factorise quadratics with leading coefficient 1
• 4 Factorise quadratics with other leading coefficients
• 5 Factorise quadratics: special cases
• 6 Factorise quadratics using algebra tiles
• 7 Factorise by grouping
• 8 Factorise polynomials

Q. Quadratic equations

• 1 Characteristics of quadratic functions
• 2 Complete a function table: quadratic functions
• 3 Transformations of quadratic functions
• 4 Find a quadratic function
• 5 Graph a quadratic function
• 6 Match quadratic functions and graphs
• 7 Solve a quadratic equation using square roots
• 8 Solve a quadratic equation using the zero product property
• 9 Solve a quadratic equation with leading coefficient 1 by factorising
• 10 Solve a quadratic equation with other leading coefficients by factorising
• 11 Complete the square
• 12 Solve a quadratic equation with leading coefficient 1 by completing the square
• 13 Solve a quadratic equation with other leading coefficients by completing the square
• 14 Solve a quadratic equation using the quadratic formula
• 15 Using the discriminant
• 16 Solve simultaneous quadratic and linear equations by graphing

R. Functions: linear, quadratic, exponential

• 1 Identify linear, quadratic and exponential functions from graphs
• 2 Identify linear, quadratic and exponential functions from tables
• 3 Write linear, quadratic and exponential functions
• 4 Linear functions over unit intervals
• 5 Exponential functions over unit intervals
• 6 Describe linear and exponential growth and decay

S. Parabolas

• 1 Identify the direction a parabola opens
• 2 Find the vertex of a parabola
• 3 Find the focus or directrix of a parabola
• 4 Find the axis of symmetry of a parabola
• 5 Write the equation of a parabola from its vertex and another point
• 6 Write the equation of a parabola from its vertex, focus and directrix
• 7 Convert equations of parabolas from general to vertex form
• 8 Find properties of a parabola from equations in general form
• 9 Graph parabolas

T. Hyperbolas

• 1 Find the centre of a hyperbola
• 2 Find the vertices of a hyperbola
• 3 Find the length of the transverse or conjugate axes of a hyperbola
• 4 Find the equations for the asymptotes of a hyperbola
• 5 Find the foci of a hyperbola
• 6 Write equations of hyperbolas in standard form from graphs
• 7 Write equations of hyperbolas in standard form using properties
• 8 Convert equations of hyperbolas from general to standard form
• 9 Find properties of hyperbolas from equations in general form

U. Rational exponents

• 1 Evaluate rational exponents
• 2 Multiplication with rational exponents
• 3 Division with rational exponents
• 4 Power rule with rational exponents
• 5 Simplify expressions involving rational exponents I
• 6 Simplify expressions involving rational exponents II

V. Radical expressions

• 1 Roots of integers
• 2 Roots of rational numbers
• 3 Find roots using a calculator
• 4 Simplify radical expressions
• 5 Simplify radical expressions involving fractions
• 6 Multiply radical expressions
• 7 Add and subtract radical expressions
• 8 Simplify radical expressions using the distributive property
• 9 Simplify radical expressions using conjugates
• 10 Simplify radical expressions: mixed review

W. Two-dimensional figures

• 1 Classify triangles
• 2 Polygon vocabulary
• 3 Triangle Angle-Sum Theorem
• 4 Perimeter
• 5 Area of triangles and quadrilaterals
• 6 Area and perimeter in the coordinate plane I
• 7 Area and perimeter in the coordinate plane II
• 8 Area and circumference of circles
• 9 Area of compound figures
• 10 Area between two shapes
• 11 Area and perimeter of similar figures
• 1 Identify hypotheses and conclusions
• 2 Counterexamples
• 3 Conditionals
• 4 Proofs involving angles
• 5 Proofs involving parallel lines I
• 6 Proofs involving parallel lines II

Y. Introduction to congruent figures

• 1 Congruent intervals
• 2 Congruence statements and corresponding parts
• 3 Solve problems involving corresponding parts
• 4 Identify congruent figures

Z. Congruent triangles

• 1 SSS and SAS Theorems
• 2 ASA and AAS Theorems
• 3 SSS, SAS, ASA and AAS Theorems
• 4 SSS Theorem in the coordinate plane
• 5 Congruency in isosceles and equilateral triangles
• 6 Hypotenuse-Leg Theorem
• 7 Proving triangles congruent by SSS and SAS
• 8 Proving triangles congruent by ASA and AAS
• 9 Proving triangles congruent by SSS, SAS, ASA and AAS
• 10 Proofs involving corresponding parts of congruent triangles
• 11 Proofs involving isosceles triangles

AA. Similarity

• 1 Identify similar figures
• 2 Ratios in similar figures
• 3 Similarity statements
• 4 Side lengths and angle measures in similar figures
• 5 Similar triangles and indirect measurement
• 6 Perimeters of similar figures
• 7 Similarity rules for triangles
• 8 Similar triangles and similarity transformations
• 9 Similarity of circles
• 10 Areas of similar figures
• 11 Proofs involving triangles I
• 12 Proofs involving triangles II

BB. Right triangles

• 1 Pythagoras' Theorem
• 2 Converse of Pythagoras' theorem
• 3 Pythagoras' Inequality Theorems
• 4 Special right triangles

CC. Angle measures

• 1 Quadrants
• 2 Graphs of angles
• 3 Coterminal angles
• 4 Reference angles

DD. Trigonometry

• 1 Trigonometric ratios: sin, cos and tan
• 2 Trigonometric ratios: csc, sec and cot
• 3 Trigonometric ratios in similar right triangles
• 4 Find trigonometric ratios using the unit circle
• 5 Trigonometric functions of complementary angles
• 6 Sin, cos and tan of special angles
• 7 Csc, sec and cot of special angles
• 8 Find trigonometric functions using a calculator
• 9 Symmetry and periodicity of trigonometric functions
• 10 Inverses of sin, cos and tan
• 11 Inverses of csc, sec and cot
• 12 Solve trigonometric equations I
• 13 Solve trigonometric equations II
• 14 Trigonometric ratios: find a side length
• 15 Trigonometric ratios: find an angle measure
• 16 Solve a right triangle
• 17 Law of Sines
• 18 Law of Cosines
• 19 Solve a triangle
• 20 Area of a triangle: sine formula
• 21 Area of a triangle: Law of Sines

EE. Surface area and volume

• 1 Introduction to surface area and volume
• 2 Surface area of prisms and cylinders
• 3 Surface area of pyramids and cones
• 4 Volume of prisms and cylinders
• 5 Volume of pyramids and cones
• 6 Surface area and volume of spheres
• 7 Volume of compound figures
• 8 Introduction to similar solids
• 9 Surface area and volume of similar solids
• 10 Surface area and volume review

FF. Circles

• 1 Parts of a circle
• 2 Central angles
• 3 Arc measure and arc length
• 4 Convert between radians and degrees
• 5 Radians and arc length
• 6 Area of sectors
• 7 Circle measurements: mixed review
• 8 Arcs and chords
• 9 Tangent lines
• 10 Perimeter of polygons with an inscribed circle
• 11 Inscribed angles
• 12 Angles in inscribed right triangles
• 13 Angles in inscribed quadrilaterals

GG. Circles in the coordinate plane

• 1 Find the centre of a circle
• 2 Find the radius or diameter of a circle
• 3 Write equations of circles in standard form from graphs
• 4 Write equations of circles in standard form using properties
• 5 Convert equations of circles from general to standard form
• 6 Find properties of circles from equations in general form
• 7 Graph circles

HH. Problem solving

• 1 Consecutive integer problems
• 2 Rate of travel: word problems
• 3 Weighted averages: word problems

II. Probability

• 1 Theoretical probability
• 2 Experimental probability
• 3 Find probabilities using two-way frequency tables
• 4 Find conditional probabilities using two-way frequency tables
• 5 Compound events: find the number of outcomes
• 6 Identify independent and dependent events
• 7 Probability of independent and dependent events
• 8 Geometric probability

JJ. Statistics

• 1 Mean, median, mode and range
• 2 Calculate quartiles and interquartile range
• 3 Identify representative, random and biased samples
• 4 Mean absolute deviation
• 5 Variance and standard deviation

KK. Data and graphs

• 1 Interpret histograms
• 2 Create histograms
• 3 Interpret dot plots
• 4 Create dot plots
• 5 Create frequency charts
• 6 Interpret stem-and-leaf plots
• 7 Box plots
• 8 Create scatter plots
• 9 Identify trends with scatter plots
• 10 Make predictions with scatter plots
• 11 Outliers in scatter plots
• 12 Scatter plots: line of best fit

Past examination material

MS means the mark scheme (i.e. the answers).

November examination

End of year examination, topic 11: probability, topic 12: simultaneous equations, topic 13: similar shapes, topic 14: statistics 2, topic 15: quadratics 1, topic 16: sequences and functions, topic 17: area and volume, topic 18: vectors and transformations, topic 19: proportion equations, topic test preparation.

Each topic has specific worksheets to help you prepare for topic tests.

Pre-TT: you should all complete this worksheet of past paper questions that covers all the material in the topic.

Post-TT: if you do not do well in the topic test, you should complete this worksheet to get more practice.

N.B. There is nothing stopping you completing both the Pre-TT and Post-TT worksheets before the topic test in order to give yourself the best chance of doing well.

Individual areas: These links take you to exercises on Corbett maths and are a good way to practise individual difficulties. Answers can be found by clicking on the link at the bottom of each worksheet.

Click on the play button at the top of each worksheet to find a video of the topic.

Individual areas

Topic 13: similar shapes, topic 18: vectors/transformations.

These interleaved practice worksheets will help you revise throughout the year. Regular revision during the academic year makes the End of Year Exam easier.

Please e-mail [email protected] if any of the links don't work or if you can think of a way to improve the website. We cannot guarantee an immediate response as we spend most of the day munching through 16 kg of bamboo each and our paws are a bit big for typing. Our reply might end up in your spam folder - whatever one of those is.

Year 10 Maths lessons and resources

Table of contents, year 10 overview.

Just like in Year 9, there are three Maths streams available for Year 10 students, depending on their level of achievement the previous year. These are: Standard (Stage 5.1), Intermediate (Stage 5.2) or Advanced (Stage 5.3). Depending on their mastery of the topics in Year 10 Maths, students will go on to either General, Advanced or Extension Maths in Year 11.

After Year 10, Maths is no longer compulsory, meaning for students who study at a Standard level and achieve only basic competency in Year 10, this could be their final year of Maths study.

For some students, Year 10 may also be their final year of schooling, as they are legally able to leave school at the end of this year – as long as they continue into some form of further education, training or employment.

For most, Year 10 is an important year to gain skills and understanding of mathematical concepts before moving into senior secondary school and studying towards their Senior Certificate.

What’s included in Year 10 Maths?

The Year 10 Maths curriculum includes the proficiency strands understanding, fluency, problem solving and reasoning, which are taught through three content strands: number and algebra, measurement and geometry, and statistics and probability.

Provided students achieve a good standard of learning in Year 9 Maths and have some understanding and recall of the concepts taught at that level, they should find the curriculum continues on at a steadily inclining pace in Year 10. Any gaps in knowledge should be filled to ensure they don’t fall behind.

What can students expect in Year 10 Maths?

At this year level, the proficiency strands will include the following content:

• Understanding of the four operations to algebraic fractions, being able to find unknowns in formulas after substitution, knowing how to make the connection between equations of relations and their graphs, forming comparisons between simple and compound interest in financial contexts and determining probabilities when working with two- and three-step experiments.
• Fluency involves factorising and expanding algebraic expressions, being able to use a range of strategies to solve equations, and the use of calculations when investigating the shape of data sets.
• Problem-solving at this level means calculating the surface area and volume of a diverse range of prisms in order to solve practical problems, discovering unknown lengths and angles through applications of trigonometry, using both algebraic and graphical techniques to find the solutions to simultaneous equations, and finding inequalities and investigating independence of events.
• Reasoning in Year 10 includes formulating geometric proofs with congruence and similarity, being able to interpret and evaluate media statements, and interpretation and comparison of data sets.

In terms of content strands and what they include, here’s what to expect in Year 10:

Year 10 Number and Algebra includes:

• Money and financial mathematics
• Patterns and algebra
• Linear and non-linear relationships

Year 10 Measurement and Geometry includes:

• Using units of measurement
• Geometric reasoning
• Pythagoras and trigonometry

Year 10 Statistics and Probability includes:

• Data representation and interpretation

Important skills to nail in Year 10

Many Year 10 Maths students struggle with quadratic equations, especially when it comes to finding the x intercepts in the equation. This often comes from a lack of understanding of Year 9 factorisation techniques. If there are gaps in this learning, or even if students could just do with a refresher, it may help to back-pedal slightly and ensure they can do the basics before moving into the world of quadratic equations.

Three dimensional trigonometry will be a new concept for most students and is often difficult to visualise. However, putting the time in to ensure a full understanding of this will stand them in good stead for moving into more difficult trigonometry problems in Years 11 and 12. Rather than rote learning, it is important to have a good understanding of the meaning of trigonometric ratios and how they are derived. This knowledge will make it easier to solve problems in exam situations.

Similarly, having a solid grounding in the conceptual knowledge behind logarithms is essential for manipulating equations into logarithmic form.

With a lot of concepts to absorb in Year 10 Maths, it is important that students ask for help when they don’t understand, rather than allowing gaps to grow in their knowledge. Each step leads onto the next, so any gaps will only grow bigger without clarification.

How to study effectively for Year 10 Maths

Effective study at this level is not a matter of rote learning but the application of logic, based on knowledge of the concepts involved. Good study habits will be regular and consistent, with time given to learning theory as well as putting this theory to work by solving practice equations.

Keeping track of errors and re-visiting those equations that students find difficult will allow them to gain a better understanding of the gaps in their knowledge and to bridge those gaps.

Practice tests are essential for checking how this knowledge applies when placed under time pressure. Many of these can be found online.

What assessments to expect in Year 10

The majority of schools will hold in-school exams in Year 10 to help prepare students for the senior secondary years. For those leaving at the end of this year, a Year 10 Certificate will be provided if work is achieved at a satisfactory level and there is a good record of attendance at school.

Year 10 achievement standards are based on a portfolio of work achieved over the course of the year, rather than final exams. Achieving well at this level should be seen as setting students in good stead for the Year 11 and 12 Senior Secondary school years and the Secondary Certificate exams and assessments.

See how EP can set students up for success in Year 10 Maths

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Year 10 Algebra Worksheets

Maths Worksheets / Year 10 Maths Worksheets / Year 10 Algebra Worksheets

Our year 10 algebra worksheets are here to help students master all types of algebra problems. From solving equations, to linear functions to substitution our year 10 algebra worksheets are enjoyable and easy to follow. We have algebra worksheets to suit all abilities and levels and all worksheets are supplied with answers to measure how well your pupil or child is doing. We have a wide range of KS4 maths resources to improve students’ confidence in answering all types of algebra questions. Algebra is an important topic for all year 10 maths students so make it fun by using Cazoom Maths worksheets! 

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Free Printable Math Worksheets for 10th Year

Math just got more exciting for Year 10 students! Discover a vast collection of free printable math worksheets by Quizizz, designed to help teachers enhance their students' learning experience and master essential skills.

Explore worksheets by Math topics

• Fundamentals and Building Blocks
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Math worksheets for Year 10 are essential tools for teachers looking to help their students master the challenging concepts in high school mathematics. These worksheets cover a wide range of topics, including algebra, geometry, trigonometry, and probability, ensuring that students have ample practice in each area. Teachers can use these resources to supplement their lesson plans, provide extra practice for struggling students, or even as a basis for group activities in the classroom. By incorporating Year 10 math worksheets into their curriculum, teachers can ensure that their students are well-prepared for the rigors of high school mathematics and beyond.

Quizizz is an excellent platform for teachers seeking to enhance their Year 10 math curriculum with engaging and interactive content. In addition to offering a vast collection of Math worksheets for Year 10, Quizizz also provides teachers with access to a wide variety of quizzes, games, and other educational resources. These materials can be easily integrated into the classroom, allowing teachers to create a dynamic and engaging learning environment for their students. Furthermore, Quizizz offers real-time feedback and analytics, enabling teachers to track student progress and identify areas where additional support may be needed. With Quizizz, teachers have a powerful tool at their disposal to help their Year 10 students excel in mathematics.

Category: Practice Questions

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The Beginner’s Guide to Year 10 Maths

Guide Chapters

1. Quadratic Equations

2. probability, 3. trigonometric ratios, 4. further trigonometry, 5. non-linear equations (curve sketching).

• 6: Functions

7. Logarithms

All about the beginner’s guide to year 10 maths.

The Beginner’s Guide to Year 10 Maths is your trusted Guide for acing Year 10 Maths. Year 10 is an important year for Maths students. Students in Year Maths consolidate their learning and begin acquiring the advanced knowledge and skills they will need for 2 Unit maths and beyond.

The concepts and skills learned in Year 10 prepare students for the complex and rigorous ideas they will encounter in Years 11 and 12. Students who fall behind in Year 10 have a difficult time catching back up.

We wrote the Beginner’s Guide to Year 10 Maths to help students get the right foundations before they start Year 11 and Stage 6.

Each of these articles in the Beginner’s Guide addresses the NSW Syllabus Outcomes. A complete list of these Outcomes can be found here on the NESA website .

What’s in this Guide?

6. functions, how will this guide help me.

In this guide, each article will explain the theory to you and show you how to apply it.

Throughout each article, we’ve provided some worked examples so that you can see how to apply the theory. We’ve also provided a number of questions for each subject. These will let you test your knowledge.

Finally, we’ve provided you with worked solutions so that you can check your skills and understand your mistakes.

Developing a strong understanding of the theory is the first step in our Matrix Method for Maths TM .

What are the common issues faced by Year 10 students?

Some common problems that students face are:

• Difficulty solving quadratic equations (Monic and Non-Monic) because they don’t understand the Year 9 factorisation techniques.

For example: Find the \(x\) – intercepts of the parabola \(y=x^2+6x+5\).

Unless students know how to factorise, there is no way of finding the \(x\) – intercepts of this equation. They must make sure the equation is in the form \(0=(x+5)(x+1)\) before finding the \(x\) – intercepts.

• Difficulty applying basic trigonometric concepts to harder applications, such as 3D Trigonometry. This has always been a topic that students struggle with as it is an entirely new concept with many types of functions introduced at the same time.
• Students also struggle with visualising trigonometric problems.
• Difficulty representing bearing problems as diagrams because of the language used in the question.
• Students also struggle to understand the relevance and importance of related angles.
• Students who struggle with solving simple quadratic equations (Polynomial Degree 2) will usually find it difficult to cope with Polynomials with higher degrees.
• Understanding the concept of logarithms being related to indices. This is particularly true of students who struggle with the fundamentals.

For example: Solve the equation \(3^x=12\)

Students must be able to manipulate this equation into logarithmic form in order to find the value of \(x\).

The answer would be \(x=log_312\)

Why do students struggle with Maths in Year 10?

Many students struggle in Year 10 Maths because they take the wrong approach to learning. Mathematics requires the application of logic, not rote learning.

Here are some of the common reasons we’ve found that students struggle:

• Students fail to read questions carefully – When presented with complex questions they are left confused with what steps to take.
• Students should not rote learn trigonometry – Instead, they need to understand what each trigonometric ratios means and how they are derived.
• Students do not clarify their problems when doubts arise – This only piles up to more problems that are left unresolved. When students have difficulty, they should ask questions early so they don’t fall behind.
• Students don’t see the real life applications of the concepts taught . When students don’t see the relationship between Maths and real life, they begin to think that Maths is unimportant. This means that they will become unmotivated to learn Maths.

What should I do to improve my marks in Maths?

Students should set up a consistent study rhythm where they have time set aside each week for:

• Learning theory
• Practising methods
• Testing themselves
• Logging their mistakes

It is important that you keep track of your mistakes. Keeping a journal of mistakes will allow students to reflect on their errors and develop strategies to avoid making mistakes in the future.

Take your Maths to the next level

Matrix+  gives you clear and structured online lesson videos, quality resources, and forums to ask your Matrix teachers questions and for feedback, wherever you are.  Learn more.

Get ahead with Matrix+ Online

Expert teachers, detailed feedback and one-to-one help. Learn at your own pace, wherever you are.

Review consistently to build your understanding

Now it is time to familiarise yourself with the content of this Guide. This is a resource that you should come back to consistently when you encounter the subjects at school during the year.

First up, we’ll look at quadratic equations in Part of this Guide.

Part 1: Year 10 Quadratic Equations & Non-Linear Simultaneous Equations | Free Worksheet

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More essential guides

High School Survival Guides

The Essential Guide To English Techniques

The Beginner’s Guide to ATAR & Scaling

Year 10 Student Resources

Year 10 Booklet

Booklet Answers

Year 10 Video Tutorials

Video tutorials for the content covering year 10 maths.

Year 10 Half Term Test Revision

Topic checklists, revision worksheets, mathswatch playlists, and youtube revision videos.

Year 10 End of Year Exam Revision

Topic checklist, revision worksheets, mathswatch playlist, and youtube revision revision videos. 

Year 10 Maths

Year 10 maths mainly focuses on quadratic equations, trigonometry, advanced trigonometry, functions, statistics, etc. Year 10 maths is very important for students as they are going to consolidate what they have learned in the previous two years and improve their knowledge by learning advanced concepts. Students need to get themselves exposed to context-based problems to understand the application of the concepts.

Year 10 Maths - Curriculum

Here is the complete list of year 10 maths topics. It is very important to have them in hand as it helps them throughout the year.

Number System:

• Prime factorization
• HCF and LCM
• Rational and irrational numbers
• Converting repeating decimals into fractions
• Square roots and cube roots
• Simplifying surds
• Fractional indices
• Exponential Equations

Percentages, Ratios, Rates, and Proportions:

• Percentages
• Proportions
• Factorization
• Polynomials
• Pair of linear equations in two variables
• Quadratic equations
• Rational equations
• Relations and functions
• Domain and range of functions
• Arithmetic progressions

Coordinate Geometry:

• Equation of a line
• Graphing a line
• Distance formula
• Midpoint formula
• Triangle theorems
• Circle theorems
• Constructions

Trigonometry:

• sin, cos, tan
• csc, sec, cot
• Trigonometric ratios of special angles
• Finding missing sides and angles in a right triangle

Mensuration:

• Areas of circles and sectors
• Surface areas and volumes

Statistics and Probability:

• Mean, median, and mode of grouped data
• Cumulative frequency graph
• Median, lower quartile , and upper quartile
• Box and Whisker plot
• Scatter plots
• Probability of independent and dependent events
• Mutually exclusive events

Developing Year 10 Maths Skills

Year 10 maths has lots of newly introduced topics such as surds, polynomials, special right-angled triangles in trigonometry, grouped data, probability of independent events, etc. To develop the skill in these topics, it is important to understand the theory part first.

Surds: Year 10 maths newly introduces surds and various operations on surds. Surds involve mixed concepts of square roots, cube roots, and irrational numbers. Surds simplification further involves laws of exponents as well.

Polynomials: In year 10, the student learns the relationship between the zeros and coefficients of polynomials. Also, it involves simple problems on the division algorithm.

Trigonometry: In year 10 trigonometry, some special right triangles with 30°-60°-90° and 45°-45°-90° are introduced. Students need to solve right triangles using these special angles.

Statistics: In year 10 statistics, the topics that are newly introduced are finding the measures of central tendency of grouped data, box and whisker plots, probability of independent and dependent events, etc.

Year 10 Maths Tips and Tricks

Here are some tips for a year 10 student to excel in maths.

• Do not rote learn the formulas/concepts. Understand the theory first and then try to memorize the formulas.
• Work on more and more exam-style questions. It is the key to improving speed and accuracy during the exam.
• Work on the exam-style questions under exam conditions. i.e., keep a timer while solving.
• Work on the mistakes.

FAQs on Year 10 Maths

What math do students learn in year 10.

The following are the topics of year 10 maths :

• Number system
• Percentages, Ratios, Rates, and Proportions
• Coordinate geometry
• Trigonometry
• Mensuration
• Statistics and probability

In this page, the subtopics under each of these topics are also mentioned in detail.

Is Maths in Year 10 Hard?

No, it is not hard. It is just that there are a few new topics introduced such as coordinate geometry , exponential equations, etc. These topics are not difficult as long as the student manages to understand the topic and solved some practice questions.

What Does Algebra of Year 10 Have?

In the algebra of year 10, the student gets to study polynomials, quadratic equations, rational equations, relations and functions, linear equations in two variables, and arithmetic progressions .

What Key Stage is Year 10 Maths?

Key stage 4 (KS4) is comprised of years 10 and year 11. Thus, year 10 belongs to KS4.

What are the New Topics in Year 10 Maths?

Some new topics in year 10 maths are polynomials, functions , more statistics like quartiles, box and whisker plots, and more probability like the probability of independent and dependent events.

Addvance Maths

Free online maths revision for gcse, a-level and ib maths..

End of Year 10 Practice Exam

Below is a printable practice exam for the end of Year 10.

It covers a mix of topics from Year 10 . Perfect for end of year practice!

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• Performing transformations
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• Right triangles & trigonometry
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• Analytic geometry
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• Polynomial factorization
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• Polynomial graphs
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• Non-right triangles & trigonometry
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• Analyzing categorical data
• Displaying and comparing quantitative data
• Summarizing quantitative data
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• Study design
• Probability
• Counting, permutations, and combinations
• Random variables
• Sampling distributions
• Confidence intervals
• Significance tests (hypothesis testing)
• Two-sample inference for the difference between groups
• Inference for categorical data (chi-square tests)
• Advanced regression (inference and transforming)
• Analysis of variance (ANOVA)
• Scatterplots
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• Normal distributions
• Displaying and describing quantitative data
• Inference comparing two groups or populations
• Chi-square tests for categorical data
• More on regression
• Prepare for the 2020 AP®︎ Statistics Exam
• AP®︎ Statistics Standards mappings
• Polynomials
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• Probability and combinatorics
• Limits and continuity
• Derivatives: definition and basic rules
• Derivatives: chain rule and other advanced topics
• Applications of derivatives
• Analyzing functions
• Parametric equations, polar coordinates, and vector-valued functions
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• Differentiation: definition and basic derivative rules
• Differentiation: composite, implicit, and inverse functions
• Contextual applications of differentiation
• Applying derivatives to analyze functions
• Integration and accumulation of change
• Applications of integration
• AP Calculus AB solved free response questions from past exams
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• AP Calculus BC solved exams
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• Green’s, Stokes’, and the divergence theorems
• First order differential equations
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• Laplace transform
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Maths champions – a winning programme, eef blog: connecting with early maths, eef blog: developmental progressions in early maths.

International Journal of Learning, Teaching and Educational Research

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A Socio-Constructivist Perspective on Problem-Solving Approaches in Mathematics: Perceptions of Future Primary Education Teachers

This study investigates the perceptions of future primary education teachers regarding the implementation of a problem-solving teaching approach from a socio-constructivist perspective. Although previous research has shown the benefits of problem-solving in mathematics education, few studies have yet focused on preservice teachers in primary education, particularly within a socio-constructivist framework. Therefore, this study addresses this gap by exploring the effectiveness and challenges of the Building Thinking Classrooms approach developed by Peter Liljedahl. The study was conducted through a case study design involving 36 first-year preservice teachers enrolled in a mathematics didactics course at a public university in Chile. Qualitative and quantitative data were collected through surveys, field logs, and classroom observations. The data analysis included descriptive statistics and content analysis to understand the students’ perceptions of problem difficulty, engagement, and the overall approach. The findings reveal that the problem-solving approach was positively perceived by the participants, highlighting its role in fostering critical thinking, collaboration, and a deep understanding of mathematical concepts. However, challenges were identified, particularly regarding group work and the autonomy required in solving problems. Furthermore, the study identified areas in which additional support could enhance the effectiveness of problem-solving approaches. This research underlines the importance of integrating problem-solving approaches into teacher education programmes and highlights the need for future research on the long-term impacts and strategies needed to support autonomy and collaborative learning.

https://doi.org/10.26803/ijlter.23.9.12

Bailey, J., & Taylor, M. (2015). Experiencing a mathematical problem-solving teaching approach: Opportunities to identify ambitious teaching practices. Mathematics Teacher Education and Development, 17(2), 111?124. https://eric.ed.gov/?id=EJ1085902

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Cohen, D. K., & Hill, H. C. (2001). Learning policy: When state education reform works. Yale University Press.

Csikszentmihalyi, M. (2003). Fluir: Una psicología de la felicidad [Flow: A psychology of happiness] (9th ed.). Kairós.

Darling-Hammond, L. (2010). The flat world and education: How America’s commitment to equity will determine our future. Teachers College Press.

Darmawati, Y., & Mustadi, A. (2023). The effect of problem-based learning on the critical thinking skills of elementary school students. Journal of Prima Edukasia, 11(2), 142?151. https://doi.org/10.21831/jpe.v11i2.55620

Delgado-Rodríguez, S., Carrascal, S., & García-Fandino, R. (2023). Design, development, and validation of an educational methodology using immersive augmented reality for STEAM education. Journal of New Approaches in Educational Research, 12(1), 19–39. https://doi.org/10.7821/naer.2023.1.1250

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Frederick-Jonah, T. M. (2022). The implications of social constructivism as a philosophical theory in the professional training of the mathematics teacher. International Journal of Science and Research, 11(1), 23–27. https://www.ijsr.net/getabstract.php?paperid=SR211229000631

Fukuzawa, S., Boyd, C., & Cahn, J. (2017). Student motivation in response to problem-based learning. Collected Essays on Learning and Teaching, 10, 175–188. https://doi.org/10.22329/celt.v10i0.4748

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Jiang, P., Zhang, Y., Jiang, Y., & Xiong, B. (2022). Preservice mathematics teachers’ perceptions of mathematical problem solving and its teaching: A case from China. Frontiers in Psychology, 13, Article 998586. https://doi.org/10.3389/fpsyg.2022.998586

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Lee, N. H., Wong, Z. Y., Lee, J., & Cheng, L. P. (2022). The effect of constructivist instruction on learning engagement in mathematics lessons: A flow theory perspective. The Mathematician Educator, 3(2), 133?153. https://ame.org.sg/2022/12/29/tme2022-vol-3-no-2-pp-133-153/

Lester, F., & Cai, J. (2016). Can mathematical problem solving be taught? Preliminary answers from 30 years of research. In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems (pp. 117–135). Springer. https://doi.org/10.1007/978-3-319-28023-3_8

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Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K–12: 14 teaching practices for enhancing learning. Corwin Press.

Liljedahl, P., Santos-Trigo, M., Malaspina, U., & Bruder, R. (2016). Problem solving in mathematics education. Springer. https://doi.org/10.1007/978-3-319-40730-2_1

Martinez-Roig, R., Iglesias-Martínez, M. J., & Cabezas, I. L. (2023). Las emociones percibidas por el profesorado en activo en el uso de metodologías activas en el aula [The emotions perceived by active teachers in the use of active methodologies in the classroom]. Research in Education and Learning Innovation Archives, (30), 39?59. http://hdl.handle.net/10045/131285

Mason, J. (2015). When is a problem? Contribution in honour of Jeremy Kilpatrick. In E. Silver, & C. Keitel-Kreidt (Eds.), Pursuing excellence in mathematics education (pp. 55–69). Springer. https://doi.org/10.1007/978-3-319-11952-6_4

Mason, J. (2016). When is a problem…? “When” is actually the problem! In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems (pp. 263–285). Springer. https://doi.org/10.1007/978-3-319-28023-3_16

Mendaglio, S. (2003). Qualitative case study in gifted education. Journal for the Education of the Gifted, 26(3), 163–183. https://doi.org/10.1177/016235320302600302

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Nurhayati, Rahmat, P. S., & Suryani, Y. (2024). The effect of using problem based learning model on critical thinking ability with moderator variable of learning motivation. Eduvest–Journal of Universal Studies, 4(8), 7294–7311. https://doi.org/10.59188/eduvest.v4i8.1722

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Fox45: math problem, 31% of maryland students score in lowest level on state test.

The Maryland State Department of Education recently released revised results of the 2024 state test known as MCAP, the Maryland Comprehensive Assessment Program. FOX45 News analyzed the numbers, and many of the results are alarming.

When students take the MCAP test, their scores place them in one of four levels. Level 1 is the lowest level, considered beginning learners. Level two is developing. Level three is proficient, and level four is distinguished.

Statewide 475,269 students took the state math test last year. Overall, 24.1% scored proficient, a slight improvement from the previous year. But more than 31% of students tested scored in level 1 — meaning there were more students who scored at the lowest level than scored proficient.

Meanwhile, just 2% of students scored in level four. That means, throughout Maryland, around 150,000 students last year scored in the lowest level for math and about 9,000 scored in the highest level.

The data also shows that 27 schools statewide had zero students among those tested who scored proficient in math. Most of those schools are alternative schools or for students with disabilities. However, eight schools that would be considered traditional schools had zero students test proficient in math. All eight are in Baltimore City.

The school level data was made available following a year-long Fox45 News investigation.

In February 2023, FOX45 broke the news that in 23 Baltimore City schools, none of the students tested received proficient scores. After that story aired, the state changed the way it reports test scores to the public by replacing many results with asterisks for the state’s lowest performing schools. At the time, the state claimed the move was necessary to protect student privacy.

But that decision, which kept parents and taxpayers from seeing how poorly many schools were performing, sparked criticism from the community. When FOX45 tried to question then State Superintendent of Schools Mohammed Choudhury about it, he locked himself behind a door.

When Carey Wright took over as the new State Superintendent, Project Baltimore asked if she would reverse Choudhury’s decision. The change was officially made, and the revised test score results were released, in September.

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