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Skills available for Singapore higher 1 maths curriculum
IXL's higher 1 skills will be aligned to the Singapore Mathematics Syllabus soon! Until then, you can view a complete list of higher 1 objectives below.
Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.
H1 Pure Mathematics
H1.1 Functions and graphs
H1.1.1 Exponential and logarithmic functions and Graphing techniques
Include:
H1.1.1.a concept of function
H1.1.1.b use of notation such as f(x) = x² + 5
H1.1.1.c functions e to the x power and ln x and their graphs
H1.1.1.d laws of logarithms
H1.1.1.e equivalence of = e to the x power and x = ln y
H1.1.1.f use of a graphic calculator to graph a given function
H1.1.1.g characteristics of graphs such as symmetry, intersections with the axes, turning points and asymptotes
Exclude:
H1.1.1.a concepts of domain and range
H1.1.1.b the use of notation f: →5 x² + 5
H1.1.2 Equations and inequalities
Include:
H1.1.2.a solving simultaneous equations, one linear and one quadratic, by substitution
H1.1.2.b conditions for a quadratic equation to have real or equal roots
H1.1.2.c solving quadratic inequalities
H1.1.2.d conditions for ax² + bx + c to be always positive (or always negative)
H1.1.2.e solving inequalities by graphical methods
H1.1.2.f formulating an equation from a problem situation
H1.1.2.g finding the numerical solution of an equation using a graphic calculator
H1.2 Calculus
H1.2.1 Differentiation
Include:
H1.2.1.a derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point
H1.2.1.b use of standard notations f '(x) and dy/dx
H1.2.1.c derivatives of x^{n} for any rational n, e to the x power, ln x, together with constant multiples, sums and differences
H1.2.1.d use of chain rule
H1.2.1.e graphical interpretation of f' (x) > 0, f' (x) = 0 and f' (x) < 0
H1.2.1.f stationary points (local maximum and minimum points and points of inflexion)
H1.2.1.g finding the numerical value of a derivative at a given point using a graphic calculator
H1.2.1.h finding equations of tangents and normals to curves
H1.2.1.i solving practical problems involving differentiation
Exclude:
H1.2.1.a differentiation from first principles
H1.2.1.b derivatives of products and quotients of functions
H1.2.1.c use of dy/dx = 1/dx/dy
H1.2.1.d differentiation of functions defined implicitly or parametrically
H1.2.1.e finding non-stationary points of inflexion
H1.2.1.f problems involving small increments and approximation
H1.2.1.g relating the graph of y = f '(x) to the graph of y = f(x)
H1.2.2 Integration
Include:
H1.2.2.a integration as the reverse of differentiation
H1.2.2.b integration of n x^{n} , for any rational n, and e to the x power, together with constant multiples, sums and differences
H1.2.2.c integration of (ax +b)^{n} , for any rational n, and e to the (ax +b) power
H1.2.2.d definite integral as the area under a curve
H1.2.2.e evaluation of definite integrals
H1.2.2.f finding the area of a region bounded by a curve and lines parallel to the coordinate axes, between a curve and a line, or between two curves
H1.2.2.g finding the numerical value of a definite integral using a graphic calculator
Exclude:
H1.2.2.a definite integral as a limit of sum
H1.2.2.b approximation of area under a curve using the trapezium rule
H1.2.2.c area below the x-axis
H1 Statistics
H1.3 Probability
H1.3.1 Probability
Include:
H1.3.1.a addition and multiplication of probabilities
H1.3.1.b mutually exclusive events and independent events
H1.3.1.c use of tables of outcomes, Venn diagrams, and tree diagrams to calculate probabilities
H1.3.1.d calculation of conditional probabilities in simple cases
H1.3.1.e use of P(A') = 1– P(A), P(A∪B) = P(A) +P(B) –P(A∩B), P(A|B)= P(A∩B)/P(B)
H1.4 Binomial and normal distributions
H1.4.1 Binomial distribution
Include:
H1.4.1.a knowledge of the binomial expansion of (a + b)^{n} for positive integer n
H1.4.1.b use of the notations n! and (n r)
H1.4.1.c concept of binomial distribution B(n,p) and use of B(n,p) as a probability model
H1.4.1.d use of mean and variance of a binomial distribution (without proof)
H1.4.1.e solving problems involving binomial variables
Exclude:
H1.4.1.a calculation of mean and variance for other probability distributions
H1.4.2 Normal distribution
Include:
H1.4.2.a concept of a normal distribution and its mean and variance; use of N(μ,σ²) as a probability model
H1.4.2.b standard normal distribution
H1.4.2.c finding the value of P (X < x1) given the values of x1, μ, σ
H1.4.2.d use of the symmetry of the normal distribution
H1.4.2.e finding a relationship between x_{1} , μ, σ given the value of P(X < x_{1} )
H1.4.2.f solving problems involving normal variables
H1.4.2.g solving problems involving the use of E(aX + b) and Var(aX + b)
H1.4.2.h solving problems involving the use of E(aX + bY) and Var(aX + bY), where X and Y are independent
H1.4.2.i normal approximation to binomial
Exclude:
H1.4.2.a finding probability density functions and distribution functions
H1.4.2.b calculation of E(X) and Var(X) from other probability density functions
H1.5 Sampling and hypothesis testing
H1.5.1 Sampling
Include:
H1.5.1.a concepts of population and sample
H1.5.1.b random, stratified, systematic and quota samples
H1.5.1.c advantages and disadvantages of the various sampling methods
H1.5.1.d distribution of sample means from a normal population
H1.5.1.e use of the Central Limit Theorem to treat sample means as having normal distribution when the sample size is sufficiently large
H1.5.1.f calculation of unbiased estimates of the population mean and variance from a sample
H1.5.1.g solving problems involving the sampling distribution
H1.5.2 Hypothesis testing
Include:
H1.5.2.a concepts of null and alternative hypotheses, test statistic, level of significance and p-value
H1.5.2.b tests for a population mean based on:
H1.5.2.b.1 a sample from a normal population of known variance
H1.5.2.b.2 a large sample from any population
H1.5.2.c 1-tail and 2-tail tests
Exclude:
H1.5.2.a testing the difference between two population means
H1.6 Correlation and Regression
H1.6.1 Correlation coefficient and linear regression
Include:
H1.6.1.a concepts of scatter diagram, correlation coefficient and linear regression
H1.6.1.b calculation and interpretation of the product moment correlation coefficient and of the equation of the least squares regression line
H1.6.1.c concepts of interpolation and extrapolation
Exclude:
H1.6.1.a derivation of formulae
H1.6.1.b hypothesis tests
H1.6.1.c use of a square, reciprocal or logarithmic transformation to achieve linearity