IB Mathematics AA

Conducting Body: International Baccalaureate (IB)
For: IB Diploma students aiming for degrees in STEM, economics, or mathematics
Levels: Standard Level (SL) and Higher Level (HL)
Papers: Paper 1 (no calculator), Paper 2 (calculator), plus Paper 3 for HL
Question Types: Short response and extended response
Total Duration: 3 hours for SL; 5 hours for HL
Held: Twice a year (May and November sessions)
Also Includes: A written Internal Assessment (IA) project

IB Mathematics: Analysis and Approaches (AA) is one of two mathematics courses available to students in the International Baccalaureate Diploma Programme. It is offered at both Standard Level (SL) and Higher Level (HL) and is intended for students with a strong background in mathematics who enjoy the subject's abstract and theoretical aspects. Universities often require it for admission into degrees with significant mathematical content, such as engineering, the physical sciences, and economics.

The final examination is split into multiple papers. A distinctive feature is the non-calculator paper, which tests a student's fundamental understanding and procedural fluency with algebra, trigonometry, and calculus. The other papers permit the use of a graphic display calculator to tackle more complex, application-based problems. Higher Level students also sit a third paper that focuses on extended problem-solving, requiring them to synthesize knowledge from across the syllabus.

The difficulty of the AA exam lies in its emphasis on formal logic and rigorous proof. The non-calculator paper in particular can be demanding, as it requires speed and accuracy in algebraic manipulation without technological aids. Students must not only memorize formulas but also understand their underlying concepts to adapt them to unfamiliar questions, all under strict time constraints.

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JEE Advanced 2024

A straight line drawn from the point $P(1, 3, 2)$ , parallel to the line $\frac{x-2}{1} = \frac{y-4}{2} = \frac{z-6}{1}$ , intersects the plane $L_1 : x - y + 3z = 6$ at the point $Q$ . Another straight line which passes through $Q$ and is perpendicular to the plane $L_1$ intersects the plane $L_2 : 2x - y + z = -4$ at the point $R$ . Then which of the following statements is (are) TRUE?

Introduction to Three Dimensional Geometry A straight line drawn from the point

P(1, 3, 2)

, parallel to the line

\frac{x-2}{1} = \frac{y-4}{2} = \frac{z-6}{1}

, intersects the plane

L_1 : x - y + 3z = 6

at the point

Q

. Another straight line which passes through

Q

and is perpendicular to the plane

L_1

intersects the plane

L_2 : 2x - y + z = -4

at the point

R

. Then which of the following statements is (are) TRUE?

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$P(1,3,2),\quad \text{direction of } PQ=(1,2,1)$ $L_1:\ x-y+3z=6 \quad (Q = \text{line} \cap L_1)$ $L_2:\ 2x-y+z=-4$ $QR \perp L_1 \Rightarrow \text{direction } (1,-1,3);\quad R \in L_2$ $\text{Check: } (1)\ PQ=\sqrt{6},\qquad (2)\ R=(1,6,3)$ $(3)\ \text{centroid}=\left(\dfrac{4}{3},\dfrac{14}{3},\dfrac{5}{3}\right),\quad (4)\ \text{perimeter}=\sqrt2+\sqrt6+\sqrt{11}$ $\text{Plan: }1.\ \text{line } P+t(1,2,1)\ \cap L_1 = Q$ $2.\ \text{line } Q+s(1,-1,3)\ \cap L_2 = R$ $3.\ \text{find } PQ,\ R,\ \text{centroid},\ \text{perimeter}$ $P(1,3,2),\quad \text{direction } (1,2,1)\ \text{(given)}$ $L_1:\ x-y+3z=6,\qquad L_2:\ 2x-y+z=-4$ $\text{line: } (x,y,z)=(1,3,2)+t(1,2,1)$ $x=1+t,\quad y=3+2t,\quad z=2+t$ $\text{put in } L_1:\ (1+t)-(3+2t)+3(2+t)=6$ $4+2t=6 \Rightarrow t=1$ $Q(2,5,3)$ $PQ=|t|\cdot|(1,2,1)|=1\cdot\sqrt{6}=\sqrt{6}$ $(1)\ \textbf{TRUE}$ $QR \perp L_1 \Rightarrow \text{direction } (1,-1,3)$ $\text{line: } (x,y,z)=(2,5,3)+s(1,-1,3)$ $\text{put in } L_2:\ 2(2+s)-(5-s)+(3+3s)=-4$ $2+6s=-4 \Rightarrow s=-1$ $R(1,6,0)$ $R=(1,6,0)\ \neq\ (1,6,3)$ $(2)\ \textbf{FALSE}$ $\bar{x}=\dfrac{1+2+1}{3}=\dfrac{4}{3},\quad \bar{y}=\dfrac{3+5+6}{3}=\dfrac{14}{3},\quad \bar{z}=\dfrac{2+3+0}{3}=\dfrac{5}{3}$ $(3)\ \textbf{TRUE}$ $QR=|s|\cdot|(1,-1,3)|=1\cdot\sqrt{11}=\sqrt{11}$ $RP=|(0,3,-2)|=\sqrt{13}$ $\text{Perimeter}=\sqrt6+\sqrt{11}+\sqrt{13}\ \neq\ \sqrt2+\sqrt6+\sqrt{11}\ \Rightarrow\ (4)\ \textbf{FALSE}$ $\text{TRUE statements: } (1)\ \text{and}\ (3)$

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