IB Questionbank

Updates to Questionbank

User interface language: English | Español

Date	November 2017	Marks available	4	Reference code	17N.2.AHL.TZ0.H_1
Level	Additional Higher Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	H_1	Adapted from	N/A

Question

Boxes of mixed fruit are on sale at a local supermarket.

Box A contains 2 bananas, 3 kiwifruit and 4 melons, and costs $6.58.

Box B contains 5 bananas, 2 kiwifruit and 8 melons and costs $12.32.

Box C contains 5 bananas and 4 kiwifruit and costs $3.00.

Find the cost of each type of fruit.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

let $b$ $b$ be the cost of one banana, $k$ $k$ the cost of one kiwifruit, and $m$ $m$ the cost of one melon

attempt to set up three linear equations (M1)

$2 b + 3 k + 4 m = 658$ $2b + 3k + 4m = 658$

$5 b + 2 k + 8 m = 1232$ $5b + 2k + 8m = 1232$

$5 b + 4 k = 300$ $5b + 4k = 300$ (A1)

attempt to solve three simultaneous equations (M1)

$b = 36, k = 30, m = 124$ $b = 36,{\text{ }}k = 30,{\text{ }}m = 124$

banana costs ($)0.36, kiwifruit costs ($)0.30, melon costs ($)1.24 A1

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 1—Number and algebra » AHL 1.16—Solution of systems of linear equations

22M.1.AHL.TZ1.11b.i:
Verify that the point $P (1, - 2, 0)$ $P (1, - 2, 0)$ lies on both $\prod_{1}$ $\prod_{1}$ and $\prod_{2}$ $\prod_{2}$ .
18N.1.AHL.TZ0.H_4b:
Find the solution of the system of equations when $a = 2$ $a = 2$ .
22M.1.AHL.TZ1.11b.ii:
Find a vector equation of $L$ $L$ , the line of intersection of $\prod_{1}$ $\prod_{1}$ and $\prod_{2}$ $\prod_{2}$ .
22M.1.AHL.TZ1.11c:
Find the distance between $L$ $L$ and $\prod_{3}$ $\prod_{3}$ .
19N.1.AHL.TZ0.H_3:
Three planes have equations:

$2 x - y + z = 5$ $2x - y + z = 5$

$x + 3 y - z = 4$ $x + 3y - z = 4$ , where $a{\text{, }}b \in \mathbb{R}$ .

$3x - 5y + az = b$

Find the set of values of $a$ and $b$ such that the three planes have no points of intersection.
18N.1.AHL.TZ0.H_4a:
Find the value of $a$ for which the system of equations does not have a unique solution.
22M.1.AHL.TZ1.11a:
Show that the three planes do not intersect.

Topic 1—Number and algebra