- IBDP Maths AA SL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IBDP Maths AA SL- IB Style Practice Questions with Answer-Topic Wise-Paper 2
- IB DP Maths AA HL- IB Style Practice Questions with Answer-Topic Wise-Paper 1
- IB DP Maths AA HL- IB Style Practice Questions with Answer-Topic Wise-Paper 2

### IBDP Maths analysis and approaches IB Style questions HL Paper 1

__HL-Paper 1__

- Duration: 1 hour 30 minutes (80 marks)
- This paper consists of section A, short-response questions, and section B, extended-response questions
- No marks deducted from incorrect answers
- NO CALCULATOR ALLOWED
- Formula booklet provided
- 40% weight

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

- Topic : SL 1.1
- Topic : SL 1.2
- Topic : SL 1.3
- Topic : SL 1.4
- Topic : SL 1.5
- Topic : SL 1.6
- Topic : SL 1.7
- Laws of exponents with rational exponents.
- Laws of logarithms.
- Change of base of a logarithm.
- log
_{a}x = \(\frac{log_bx}{log_ba}\) for a, b, x > 0

- log
- Solving exponential equations, including using logarithms

- Topic : SL 1.8
- Topic : SL 1.9

**Topic 1: Number and algebra****– AH**L content

- Topic : AHL 1.10
- Topic : AHL 1.11
- Topic : AHL 1.12
- Topic : AHL 1.13
- Topic : AHL 1.14
- Topic : AHL 1.15
- Topic : AHL 1.16

### 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
^{−1}(x).

- Topic: SL 2.3
- Topic: SL 2.4
- Topic: SL 2.5
- Topic: SL 2.6
- Topic: SL 2.7
- Topic: SL 2.8
- Topic: SL 2.9
- Exponential functions and their graphs
- Logarithmic functions and their graphs:

- Exponential functions and their graphs
- Topic: SL 2.10
- Solving equations, both graphically and analytically.
- Use of technology to solve a variety of equations, including those where there is no appropriate analytic approach.
- Applications of graphing skills and solving equations that relate to real-life situations

- Topic SL 2.11

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

- Topic: AHL 2.12
- Topic: AHL 2.13
- Topic: AHL 2.14
- Topic: AHL 2.15
- Solutions of \(g\left( x \right) \geqslant f\left( x \right)\) both graphically and analytically
- Graphical or algebraic methods, for simple polynomials up to degree 3.
- Use of technology for these and other functions.

- Topic: AHL 2.16

### 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 3.2
- 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
- Topic SL 3.4
- Topic SL 3.5
- Definition of \(\cos \theta \) , \(\sin \theta \) in terms of the unit circle and \(\tan \theta \) 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 3: Geometry and trigonometry-AHL content

- Topic : AHL 3.9
- Topic : AHL 3.10
- Topic : AHL 3.11
- Topic : AHL 3.12
- Concept of a vector; position vectors; displacement vectors.
- Representation of vectors using directed line segments.
- Base vectors i, j, k.
- Components of a vector: \(v = \left( {\begin{array}{*{20}{c}} {{v_1}} \\ {{v_2}} \\ {{v_3}} \end{array}} \right) = {v_1}i + {v_2}j + {v_3}k\) .
- Algebraic and geometric approaches to the following:
- sum and difference of two vectors.
- the zero vector \(0\), the vector \( – v\) .
- multiplication by a scalar, \(kv\) , parallel vectors
- magnitude of a vector, \(\left| v \right|\) .unit vectors=\(\frac{\vec{v}}{\left | \vec{v} \right |}\)
- position vectors \(\overrightarrow {OA} = a\) .
- displacement vector \(\overrightarrow {AB} = b – a\) .

- Proofs of geometrical properties using vectors.

- Topic : AHL 3.13
- Topic : AHL 3.14
- Topic : AHL 3.15
- Topic : AHL 3.16
- The definition of the vector product of two vectors.
- Properties of the vector product: \({\text{v}} \times {\text{w}} = – {\text{w}} \times {\text{v}}\) ; \({\text{u}} \times ({\text{v}} + {\text{w}}) = {\text{u}} \times {\text{v}} + {\text{u}} \times {\text{w}}\) ; \((k{\text{v}}) \times {\text{w}} = k({\text{v}} + {\text{w}})\) ; \({\text{v}} \times {\text{v}} = 0\) .
- Geometric interpretation of \({\text{v}} \times {\text{w}}\) .

- Topic : AHL 3.17
- Topic : AHL 3.18

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

- Topic: SL 4.1
- Topic: SL 4.2
- Topic: SL 4.3
- Topic: SL 4.4
- Linear correlation of bivariate data. Pearson’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: SL 4.5
- Topic: SL 4.6
- Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities.
- Combined events: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
- Mutually exclusive events: P(A ∩ 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: SL 4.7
- Topic: SL 4.8
- Topic: SL 4.9
- Topic: SL 4.10
- Topic: SL 4.11
- Topic: SL 4.12

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

- Topic: AHL 4.13
- Topic: AHL 4.14

### Topic 5: Calculus-SL content

- Topic SL 5.1
- Topic SL 5.2
- 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^{n−1}+ …., where n ∈ ℤ, n ≠ − 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

### Topic 5: Calculus-AHL content

- Topic: AHL 5.12
- Informal understanding of continuity and differentiability of a function at a point.
- Understanding of limits (convergence and divergence).
- Higher derivatives.

- Topic: AHL 5.13
- Topic: AHL 5.14
- Topic: AHL 5.15
- Derivatives of \(\tan x\), \(\sec x\) , cosec x , \(\cot x\) , \({a^x}\) , \({\log _a}x\) , \(\arcsin x\) , \(\arccos x\) and \(\arctan x\) .
- Indefinite integrals of the derivatives of any of the above functions. The composites of any of these with a linear function.
- Use of partial fractions to rearrange the integrand.

- Topic: AHL 5.16
- Topic: AHL 5.17
- Topic: AHL 5.18
- Topic: AHL 5.19