Systems of equations: IB Mathematics: Applications & Interpretation questions with answers
Free Systems of equations questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Number & algebra. Each question has the answer and the marking points an examiner would look for.
The height of a ball, h metres, t seconds after it is hit is modelled by h(t) = at2 + bt + c. When t = 0, h = 1.5; when t = 1, h = 16.6; when t = 2, h = 21.9.
(a)
Write down three equations in a, b and c, and hence find a, b and c.
[3]
(b)
Find the maximum height of the ball.
[2]
(c)
Find the time at which the ball hits the ground.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
a = −4.9, b = 20, c = 1.5
three correct equations (M1) GDC to solve (M1) a = −4.9, b = 20, c = 1.5 A1
3
(b)
21.9 m
t = 2.04 (M1) 21.9 m A1
2
(c)
4.16 s
h(t) = 0 (M1) 4.16 s A1
2
Question 2Structured · 5 marks
A cinema sells adult, child and senior tickets at $x, $y and $z respectively.
Day
Adults
Children
Seniors
Total takings ($)
1
23
23
15
412
2
23
24
15
416
3
31
17
13
456
Table 2.1
(a)
Write down a system of three equations to represent this information.
[2]
(b)
Find the price of each type of ticket.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
equations
one correct equation, e.g. 23x + 23y + 15z = 412 A1 all three correct A1
2
(b)
$10, $4, $6
use of GDC to solve (M1) x = 10, y = 4 A1 z = 6 A1
3
Question 3Structured · 4 marks
A cinema sells adult, student and child tickets.
3 adult, 2 student and 1 child ticket cost $31; 1 adult, 3 student and 2 child tickets cost $31; 2 adult, 1 student and 4 child tickets cost $32. Find the price of each ticket.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
adult $5, student $6, child $4
three equations (M1) GDC solution (M1) two correct A1 all three A1
4
Question 4Structured · 7 marksA* challenge
The height of a ball, h metres, t seconds after it is hit is modelled by h(t) = at2 + bt + c. When t = 0, h = 2.5; when t = 1, h = 17.5; when t = 2, h = 22.5.
(a)
Write down three equations in a, b and c, and hence find a, b and c.
[3]
(b)
Find the maximum height of the ball.
[2]
(c)
Find the time at which the ball hits the ground.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
a = −5, b = 20, c = 2.5
three correct equations (M1) GDC to solve (M1) a = −5, b = 20, c = 2.5 A1
3
(b)
22.5 m
t = 2.00 (M1) 22.5 m A1
2
(c)
4.12 s
h(t) = 0 (M1) 4.12 s A1
2
Question 5Structured · 4 marks
A cinema sells adult, student and child tickets.
3 adult, 2 student and 1 child ticket cost $33; 1 adult, 3 student and 2 child tickets cost $30; 2 adult, 1 student and 4 child tickets cost $30. Find the price of each ticket.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
adult $6, student $6, child $3
three equations (M1) GDC solution (M1) two correct A1 all three A1
4
Question 6Structured · 7 marksA* challenge
The height of a ball, h metres, t seconds after it is hit is modelled by h(t) = at2 + bt + c. When t = 0, h = 2; when t = 1, h = 21.0; when t = 2, h = 30.0.
(a)
Write down three equations in a, b and c, and hence find a, b and c.
[3]
(b)
Find the maximum height of the ball.
[2]
(c)
Find the time at which the ball hits the ground.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
a = −5, b = 24, c = 2
three correct equations (M1) GDC to solve (M1) a = −5, b = 24, c = 2 A1
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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in