<![CDATA[SpatialMaths.com - 5th Year Class Blog]]>Tue, 03 Feb 2026 11:15:57 +0000Weebly<![CDATA[Summer Assignments]]>Mon, 15 Jun 2015 16:44:42 GMThttp://www.spatialmaths.com/5th-year-class-blog/summer-assignmentsDear Students,
I hope that you are enjoying the summer holidays. Over the past few days I have uploaded the promised summer assignments and solutions to the summer test. For most students Algebra still requires more work. It might be worthwhile looking over the solutions.

There are two summer assignments.

Assignment 1 is concerned with new material in the area of Geometry. There are 4 worksheets to be printed and completed. 

Assignment 2 looks back on some key skills/concepts from last year. This is important revision using Khan Academy Exercises.
Have a great summer,

Mr R
]]><![CDATA[Summer Assignment 2]]>Mon, 15 Jun 2015 14:27:19 GMThttp://www.spatialmaths.com/5th-year-class-blog/summer-assignment-2Assignment 2 is based on  Khan Academy Exercises. 
Complete the 68 linked Khan Academy Exercises below. These exercises revise some of the concepts covered in 5th year higher level maths. Aim to achieve as many points as you can by completing each question correctly. Enjoy and good luck.

Make sure to be signed in to the Khan Academy class before starting (instructions below if required).
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Algebra: Number Systems & Complex Numbers (8)


Classifying numbers
Quetzalcoatl » Benslandiaville » cc-ben-8-numbers-operations
Practice classifying numbers as whole, integer, rational, and irrational.

Absolute value of complex numbers
Math » Algebra II » Imaginary and complex numbers » Complex numbers
Find the absolute value of a complex number.

Complex number polar form intuition
Math » Precalculus » Imaginary and complex numbers » The complex plane
Adjust the angle and radius to plot a complex number in polar form.

Multiplying complex numbers
Math » Precalculus » Imaginary and complex numbers

Dividing complex numbers
Math » Precalculus » Imaginary and complex numbers

Complex plane operations
Math » Precalculus » Imaginary and complex numbers
Add or subtract numbers in the complex plane.

Rectangular and polar forms of complex numbers
Math » Precalculus » Imaginary and complex numbers » The complex plane

Quadratic formula with complex solutions
Math » Algebra II » Polynomial and rational functions

Number: Indices (11)


Exponents
Math » Pre-algebra » Exponents, radicals, and scientific notation
Practice taking exponents of whole numbers. All exponents in these problems are either positive or zero.

Properties of exponents
Math » Algebra I » Exponent expressions and equations
Practice applying properties of exponents.

Fractional exponents
Math » Algebra I » Exponent expressions and equations » Fractional exponents
Fractional and integer bases raised to positive and negative fractional exponents.

Simplifying expressions with exponents
Math » Algebra I » Exponent expressions and equations
Simplify expressions using exponent rules

Fractional exponents 2
Math » Algebra I » Exponent expressions and equations » Fractional exponents
Fractional bases raised to fractional exponents with non-1 numerators.

Positive and negative exponents
Math » Pre-algebra » Exponents, radicals, and scientific notation
Practice computing numbers raised to positive and negative integer exponents.

Using exponent rules to evaluate expressions
Math » Algebra I » Exponent expressions and equations
Practice evaluating expressions by adding, subtracting, or multiplying exponents.

Understanding fractional exponents
Math » Algebra I » Exponent expressions and equations » Fractional exponents

Manipulating fractional exponents
Math » Algebra I » Exponent expressions and equations » Fractional exponents

Simplifying rational expressions with exponent properties
Math » Algebra basics » Expressions with exponents » Exponent properties
Simplify the ratio of two monomials.

Whole number exponents with integer bases 2
Math » Pre-algebra » Exponents, radicals, and scientific notation
Practice raising integers to whole number powers.

Algebra: Inequalities (3)


Compound inequalities
Math » Algebra I » Linear inequalities
Solve compound inequalities.

One-step inequalities
Math » Algebra I » Linear inequalities
Practice solving inequalities in one step.

Multi-step linear inequalities
Math » Algebra I » Linear inequalities
Solve linear inequalities in multiple steps.

Number: Sequences and Series (5)


Explicit formulas for arithmetic sequences
Math » Algebra I » Sequences » Arithmetic sequences
Explicit formulas for arithmetic sequences

Evaluating geometric sequences 1
Math » Integral calculus » Sequences, series, and function approximation
Find the next term in a geometric sequence.

Evaluating geometric sequences 2
Math » Integral calculus » Sequences, series, and function approximation
Find the nth term of a geometric sequence.

Finite geometric series word problems
Math » Precalculus » Sequences, series and induction
Understanding and solving problems with the formula for a finite geometric series

Equation practice: summing integers
Math » Algebra I » Linear equations » More equation practice
Find the nth number in a sequence of consecutive numbers based on the sum.

Algebra: Quadratics & Polynomials (25)


Solutions to quadratic equations
Math » Algebra II » Polynomial and rational functions
Determine how many solutions a quadratic equation has and whether they are rational, irrational, or complex

Understanding the process for solving quadratic equations
Math » Algebra I » Quadratic equations

Using the quadratic formula
Math » Algebra II » Polynomial and rational functions
Use the quadratic formula to find the roots of a quadratic function.

Solving quadratics by completing the square 1
Math » Algebra II » Polynomial and rational functions
Find the roots of a quadratic equation by completing the square.

Solving quadratics by factoring 2
Math » Algebra II » Polynomial and rational functions » Factoring quadratics
Solve quadratics by factoring, where the leading coefficient is not 1

Solving quadratics by factoring
Math » Algebra II » Polynomial and rational functions » Factoring quadratics
Factor quadratics to find the x-intercepts.

Solving quadratics by taking the square root
Math » Algebra I » Quadratic equations
Solve quadratics by taking the square root.

Solving quadratics by completing the square 2
Math » Algebra II » Polynomial and rational functions
Find the roots of a quadratic by completing the square.

Radical equations
Math » Algebra I » Exponent expressions and equations » Radical equations
Solve equations containing square roots of variables.

Factoring quadratics with two variables
Math » Algebra I » Multiplying and factoring expressions
Factor a polynomial with two variables into expressions

Completing the square in quadratic expressions
Math » Algebra I » Quadratic equations » Completing the square

Key features of quadratic functions
Math » Algebra I » Quadratic equations » Features of quadratic functions

Systems of nonlinear equations
Math » Algebra II » Systems of equations and inequalities

Graphing parabolas in standard form
Math » Algebra I » Quadratic equations » Graphing quadratics
Graph a parabola given the equation in the form ax^2+bx+c

Graphing parabolas in vertex form
Math » Algebra I » Quadratic equations » Graphing quadratics
Graph a parabola given the equation in the form a(x+b)^2+c

Parabola intuition 3
Math » Algebra II » Conic sections » Parabolas
Find the equation of the parabola.

Dividing polynomials by binomials 1
Math » Algebra II » Rational expressions » Simplifying rational expressions
Simplify the ratio of a polynomial and a binomial.

Dividing polynomials by binomials 2
Math » Algebra II » Rational expressions » Simplifying rational expressions
Simplify the ratio of a polynomial and a binomial.

Dividing polynomials by binomials 3
Math » Algebra II » Rational expressions » Simplifying rational expressions
Simplify the ratio of a polynomial and a binomial.

Polynomial identities
Math » Algebra II » Polynomial and rational functions

Graphs of polynomials
Math » Algebra II » Polynomial and rational functions

Remainder theorem of polynomials
Math » Algebra II » Polynomial and rational functions

Equivalent forms of polynomial expressions
Math » Algebra II » Polynomial and rational functions

Dividing polynomials with remainders
Math » Algebra II » Polynomial and rational functions » Dividing polynomials

Using zeros to graph polynomials
Math » Algebra II » Polynomial and rational functions

Shifting and reflecting functions
Math » Algebra II » Functions and their graphs
Determine the equation for one graphed function in terms of another.

Algebra: Exponential functions (5)


Rewriting and interpreting exponential functions
Math » Algebra II » Exponential and logarithmic functions

Modeling with exponential functions
Math » Algebra II » Exponential and logarithmic functions

Evaluating functions
Math » Algebra II » Functions and their graphs » Function introduction
Evaluate functions written with function notation

Understanding logarithms as inverse exponentials
Math » Algebra II » Logarithms » Logarithm basics

Using logarithms to solve exponential equations
Math » Algebra II » Exponential and logarithmic functions

Probability (11)


Probability with permutations and combinations
Math » Probability and statistics » Probability and combinatorics
Probability questions using permutations and combinations of objects

Probabilities of compound events
Math » Precalculus » Probability and combinatorics
Practice using sample space diagrams to find probabilities.

Independent probability
Math » Precalculus » Probability and combinatorics

Dependent probability
Math » Precalculus » Probability and combinatorics » Dependent events

Making predictions with probability
Quetzalcoatl » Content improvement » Middle school content
Practice predicting the number of times a certain event will happen.

Constructing probability distributions
Math » Probability and statistics

Multiplying dependent probabilities
Math » Probability and statistics » Independent and dependent events

Expected value with empirical probabilities
Math » Probability and statistics

Expected value with calculated probabilities
Math » Probability and statistics

Using probability to make fair decisions
Math » Probability and statistics » Probability and combinatorics

Expected value
Math » Probability and statistics
Compute the expected value given a set of outcomes, probabilities, ...

]]><![CDATA[Summer Assignment 1]]>Sat, 13 Jun 2015 10:45:17 GMThttp://www.spatialmaths.com/5th-year-class-blog/summer-assignment-1Complete the 4 PDF Worksheets below.
The Geometry part of the LC HL syllabus builds on the Junior Cert Syllabus. It requires students to:
  • Be able to perform 22 constructions
  • Prove 3 theorems
  • Understand enlargements
All support materials required are on the Geometry Page.
LCHL Geometry
The 1st (and main) part of this assignment involves printing and completing the 3 worksheets below.
There are also 2 constructions in the number strand that must be practiced: The construction of root 2 and root 3 on a number line.
The supporting videos for these constructions are on the Number systems page.
LCHL Number Systems
The 2nd part of this assignment is to complete the 2 constructions in the worksheet below.
Irrational No. Constructions PDF
Completed work is to be presented in class in August.
]]><![CDATA[Solutions to the Summer Test ]]>Fri, 12 Jun 2015 12:48:50 GMThttp://www.spatialmaths.com/5th-year-class-blog/solutions-to-the-summer-test
5hl_test_may15.pdf
File Size: 4267 kb
File Type: pdf
Download File
]]><![CDATA[May 21st, 2015]]>Thu, 21 May 2015 14:45:54 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-21st-2015
Revision questions on Probability handed out.
We worked through questions on this worksheet.

We also discussed Summer Assignments which will be expanded after the exams in this blog.
probability_revision_questions.pdf
File Size: 1768 kb
File Type: pdf
Download File
]]><![CDATA[May 20th, 2015]]>Wed, 20 May 2015 14:30:20 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-20th-2015Revision Questions on 
]]><![CDATA[May 19th, 2015]]>Tue, 19 May 2015 14:57:17 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-19th-2015
Today we revised some complex number questions.
For HW go through revision questions 3-8
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Argand diagram
]]><![CDATA[May 18th, 2015]]>Mon, 18 May 2015 10:50:00 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-18th-2015Began correction of Algebra Worksheet. Showed Revision Resources on this website. For HW complete and correct this worksheet.
]]><![CDATA[May 15th, 2015]]>Fri, 15 May 2015 13:04:56 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-15th-2015Finished Probability Chapter 2
HW: Worksheet on Algebra
algebra_revision_questions_lchl_(lsms).pdf
File Size: 2406 kb
File Type: pdf
Download File
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]]><![CDATA[May 12th, 2015]]>Tue, 12 May 2015 14:58:34 GMThttp://www.spatialmaths.com/5th-year-class-blog/may-12th-2015
We did two leaving cert questions on Probability.

Then we looked at a standardising question on Normal distributions (see below).
t&t5_3.6_normal_distribution_12-5-2012.pdf
File Size: 251 kb
File Type: pdf
Download File
2012_lchl_sample_p.2_q.1_&_2.pdf
File Size: 248 kb
File Type: pdf
Download File
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