Simultaneous Equations: One Linear, One Quadratic (Grade 11)

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 11 · Equations and Inequalities

MEMORANDUM

Name:

Class:

Date:

Mark

/ 25

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Solve simultaneously: y = x + 1 and y = x² − 3x + 4
(4)
x² − 4x + 3 = 0 → x = 1 or 3 → (1 ; 2) and (3 ; 4)✓✓✓✓ (4)
2
Solve simultaneously: y = 2x and y = x² − 3
(4)
x² − 2x − 3 = 0 → (x − 3)(x + 1) = 0 → (3 ; 6) and (−1 ; −2)✓✓✓✓ (4)
3
Solve simultaneously: x + y = 5 and x² + y² = 17
(4)
(1 ; 4) and (4 ; 1)✓✓✓✓ (4)
4
Solve simultaneously: y − x = 2 and xy = 8
(4)
x(x + 2) = 8 → x² + 2x − 8 = 0 → (x + 4)(x − 2) = 0 → (2 ; 4) and (−4 ; −2)✓✓✓✓ (4)
5
Which equation should you rearrange first, and why?
(2)
The linear one — making a variable the subject of a linear equation is simple and never introduces a square root.✓✓ (2)
6
Solve simultaneously: y = x − 1 and y = x² − 5x + 7
(4)
x² − 6x + 8 = 0 → (x − 2)(x − 4) = 0 → (2 ; 1) and (4 ; 3)✓✓✓✓ (4)
7
The solutions of a simultaneous system are the … of the two graphs.
(1)
points of intersection✓ (1)
8
What does it mean if the resulting quadratic has a negative discriminant?
(2)
There are no real solutions, so the two graphs do not intersect.✓✓ (2)

TOTAL: 25 marks