RevisionDojo

AHL 1.16—Solution of systems of linear equations - IB Questionbank | RevisionDojo

Practice AHL 1.16—Solution of systems of linear equations with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

Solve the following simultaneous equations:

$2x + y = 7 \\ 3x - y = 3$

[5]

Question 2

HLPaper 1

Solve the following simultaneous equations:

$2x + 3y - z = 15 \\ x - 2y + 4z = 80 \\ 3x + y + 2z = 75$

[6]

Question 3

HLPaper 1

Solve the following simultaneous equations:

$x + y + z = 6 \\ 2x - y + 3z = 9 \\ x + 2y - z = 2$

[6]

Question 4

HLPaper 1

Given that P = $\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}$ and Q = $\begin{pmatrix} 1 & -3 \\ 5 & 0 \end{pmatrix}$ . Find

P + 3Q

[3]

Question 5

HLPaper 1

The line $y = x+1$ intersects the curve $x^2 + y = 7$ at points $A$ and $B$ .

Calculate the coordinates of $A$ and of $B$ .

[6]

Question 6

HLPaper 1

Solve the following system using Gaussian elimination:

\begin{gathered} x+2 y-z=4 \\ 2 x+y+z=5 \\ 3 x+3 y=9 \end{gathered}

[4]

Question 7

HLPaper 1

A bookstore sells two types of books: novels and textbooks. A novel costs $ 12 and a textbook costs $20. A customer buys a total of 5 books and spends $ 76. How many novels and textbooks did the customer buy?

[5]

Question 8

HLPaper 1

Consider the rational function $f(x) = \frac{2x^2 + 3x + 1}{(x+1)^2(x-2)}$ .

Express $f(x)$ as a sum of partial fractions.

[7]

Hence, or otherwise, find $\int\!f(x)dx$ with only one $\ln$ term

[4]

Question 9

HLPaper 1

Consider the rational function $g(x) = \frac{3x^2 + 5x + 2}{(x-1)^2(x+2)}$ .

Express $g(x)$ as a sum of partial fractions.

[8]

Hence, or otherwise, compute $\int_0^2\! g(x)dx$

[5]

Question 10

HLPaper 1

Solve the following system:

\begin{aligned} & \frac{1}{2} x+\frac{1}{3} y=1 \\ & \frac{2}{3} x-\frac{1}{4} y=0 \end{aligned}

[4]

AHL 1.16—Solution of systems of linear equations Questionbank