### Paper 1

**Â New IBDPÂ Mathematics: Analysis and Approaches SL- Syllabus**

**Â New IBDPÂ Mathematics: Analysis and Approaches SL- Syllabus**

__SL__

- Time: 45 minutes (30Â marks)
- 30 multiple – choice questions (core)
- No marks deducted from incorrect answers
- NO CALCULATOR ALLOWED
- Data booklet provided
- 20% weight

### IB Diploma Maths analysis and approaches IB Style questions SL Paper 1

**Topic 1: Number and algebra****– **SL content

- Topic : SL 1.1
- Topic : SL 1.2
- Arithmetic sequences and series. Use of the formulae for the n
^{th}term and the sum of the first n terms of the sequence. - Use of sigma notation for sums of arithmetic sequences.
- Applications.
- Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
- approximate common differences.

- Arithmetic sequences and series. Use of the formulae for the n
- Topic : SL 1.3Â
- Geometric sequences and series Use of the formulae for the nth term and the sum of the first n terms of the sequence.
- Use of sigma notation for the sums of geometric sequences.
- Applications
- Examples include the spread of disease, salary increase and decrease and population growth

- Topic : SL 1.4
- Topic : SL 1.5
- Topic : SL 1.6
- Simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side (LHS to RHS) proof. The symbols and notation for equality and identity.

- Topic : SL 1.7
- Laws of exponents with rational exponents.
- Laws of logarithms.
- log
_{a}xy = log_{a}x + log_{a}y - loga\(\frac{x}{y}\)=logax – log
_{a}y - log
_{a}x^{m}= mlog_{a}x for a, x, y > 0

- log
- Change of base of a logarithm.
- log
_{a}x = \(\frac{log_bx}{log_ba}\)Â for a, b, x > 0

- log
- Solving exponential equations, including using logarithms

- Topic : SL 1.8
- Topic : SL 1.9

- Â

### Topic 2: Functions**– **SL content

- Topic: SL 2.1
- Topic: SL 2.2
- Concept of a function, domain, range and graph. Function notation, for example f(x), v(t), C(n). The concept of a function as a mathematical model.
- Informal concept that an inverse function reverses or undoes the effect of a function. Inverse function as a reflection in the line y = x, and the notation f
^{âˆ’1}(x).

- Topic: SL 2.3
- Topic: SL 2.4
- Topic: SL 2.5
- Composite functions.
- (f âˆ˜ g)(x) = f(g(x))

- Identity function.
- Finding the inverse function f
^{âˆ’1}(x)- (f âˆ˜ f
^{âˆ’1})(x) = (f^{âˆ’1}âˆ˜ f)(x) = x

- (f âˆ˜ f

- Composite functions.
- Topic: SL 2.6
- Topic: SL 2.7
- Topic: SL 2.8
- Topic: SL 2.9
- Topic: SL 2.10
- Topic SL 2.11

### Topic 3: Geometry and trigonometry-SL content

- Topic : SL 3.1
- The distance between two points in three dimensional space, and their midpoint.
- Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.
- The size of an angle between two intersecting lines or between a line and a plane.

- Topic SL 3.2Â
- Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.
- The sine rule including the ambiguous case.
- \(\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}\)

- The cosine rule.
- \(c^2 = a^2 +b^2-2abcosC;\)
- \(cosC =\frac{a^2+ b^2-c^2}{2ab}\)

- Area of a triangle as \(\frac{1}{2}ab\sin C\) .

- Topic SL 3.3
- Applications of right and non-right angled trigonometry, including Pythagorasâ€™s theorem.
- Angles of elevation and depression.
- Construction of labelled diagrams from written statements.

- Topic SL 3.4
- Topic SL 3.5
- Definition of \(\cos \theta \) , \(\sin \theta \) in terms of the unit circle and \(\tan \theta \)Â as \(\frac{sin\theta }{cos\theta }\).
- Exact values of \(\sin\), \(\cos\) and \(\tan\) of \(0\), \(\frac{\pi }{6}\), \(\frac{\pi }{4}\), \(\frac{\pi }{3}\), \(\frac{\pi }{2}\) and their multiples.
- Extension of the sine rule to the ambiguous case

- Topic SL 3.6
- Topic : SL 3.7
- Topic : SL 3.8

**Topic 4 : Statistics and probability-SL content**

- Topic: SLÂ 4.1
- Concepts of population, sample, random sample and frequency distribution of discrete and continuous data.
- Reliability of data sources and bias in sampling.
- Interpretation of outliers.
- Sampling techniques and their effectiveness

- Topic: SLÂ 4.2
- Topic: SLÂ 4.3
- Topic: SLÂ 4.4
- Linear correlation of bivariate data. Pearsonâ€™s product-moment correlation coefficient, r.
- Scatter diagrams; lines of best fit, by eye, passing through the mean point.
- Equation of the regression line of y on x.
- Use of the equation of the regression line for prediction purposes.
- Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b.

- Topic: SLÂ 4.5
- Topic: SLÂ 4.6
- Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities.
- Combined events: P(A âˆª B) = P(A) + P(B) âˆ’ P(A âˆ© B).
- Mutually exclusive events: P(A âˆ© B) = 0.
- Conditional probability; the definition \(P\left( {\left. A \right|P} \right) = \frac{{P\left( {A\mathop \cap \nolimits B} \right)}}{{P\left( B \right)}}\).
- Independent events; the definition \(P\left( {\left. A \right|B} \right) = P\left( A \right) = P\left( {\left. A \right|B’} \right)\) .

- Topic: SLÂ 4.7
- Topic: SLÂ 4.8
- Binomial distribution. Mean and variance of the binomial distribution.

- Topic: SLÂ 4.9
- Topic: SLÂ 4.10
- Equation of the regression line of x on y.
- Use of the equation for prediction purposes.

- Topic: SLÂ 4.11
- Formal definition and use of the formulae:
- \(P\left( {\left. A \right|P} \right) = \frac{{P\left( {A\mathop \cap \nolimits B} \right)}}{{P\left( B \right)}}\).
- \(P\left( {\left. A \right|B} \right) = P\left( A \right) = P\left( {\left. A \right|B’} \right)\) .

- Formal definition and use of the formulae:
- Topic: SLÂ 4.12
- Standardization of normal variables (z- values).
- Inverse normal calculations where mean and standard deviation are unknown.

### Topic 5: Calculus-SL content

- Topic SL 5.1
- Topic SL 5.2
- Increasing and decreasing functions.
- Graphical interpretation of f â€²(x) > 0, f â€²(x) = 0, f â€²(x) < 0.

- Topic SL 5.3
- Topic SL 5.4
- Topic: SL 5.5
- Introduction to integration as anti-differentiation of functions of the form f(x) = ax
^{n}+ bx^{nâˆ’1}+ …., where n âˆˆ â„¤, n â‰ âˆ’ 1. - Anti-differentiation with a boundary condition to determine the constant term.
- Definite integrals using technology.
- Area of a region enclosed by a curve y = f(x) and the x -axis, where f(x) > 0.

- Introduction to integration as anti-differentiation of functions of the form f(x) = ax
- Topic: SL 5.6
- Topic: SL 5.7
- Topic: SL 5.8
- Topic SL 5.9
- Topic SL 5.10
- Topic SL 5.11