Victoria University of Wellington
School of Mathematics, Statistics
Te Kura Mātai Tatauranga
MATH 132
Introduction to mathematical thinking
2017
Assignment 2
Due by 1pm on Friday, 24/3/2017.
(1) Draw tree diagrams for these formulae.
2x + 3
4−x 1
(a)
−4
+
(b) 10 + 2
5
5
3
(2) Fill in the seven boxes in Figure 1.
+
4(x − 1)
2x
−
x
1
Figure 1. Tree for assignment question 2
(3) (a) Solve using substitution, they both have integer solutions.
(i) x + 3y =− 4 and x = 2y − 9
(ii) 2x − 4y = 10 and x = y + 1
(b) Solve using elimination, they both have integer solutions.
(i) x + 2y = 4 and x + 5y = 16
(ii) x − 3y = 8 and 2x + y = 2
(c) Solve using any method, one has a solution involving fractions, the other
has no solution.
(i) y = 4x − 3 and y = 6x − 2
(ii) 2x − 4y = 6 and x = 2y − 1
Assignment continues over the page
1
2
(4) Expand the brackets and then simplify.
(c) (b + 2)(b − 2)
(d) (c − 4)(c + 2)(c + 3)
(a) (x1 + x2 )(y1 + y2 )
(b) (a + 3)(a − 5)
(5) Factorise the following expressions. Make sure to put in the step described
in the lecture.
(a) x2 + 6x + 8
(b) x2 − 6x + 8
(c) x2 − 2x − 8
(d) x2 + 2x − 8
(6) In each equation, solve for x. Make sure to put in the step described in the
lecture.
(a) (x + 5)(x + 3) = 0
(b) (x − 2)(x + 1) = 0
(7) In each equation, solve for x.
(a) (x + 1)2 = 32
(b) (x − 2)2 = 42
(c) (x + 4)2 = 02
(d) (x − 1)2 = (− 2)2
(c) (x + 2)(x + 2) = 0
3
Tutorial exercises Don’t hand these in, they are practice exercises.
(1) Draw tree diagrams for these formulae (hint: grafting is in order, the first
appears in the second).
(a) x+1
(b) 4 x+1
−7
3
3
(2) Fill in the boxes in Figure 2, on page 3.
x2 + 3(x − 6)
+
∧
×
2
x−6
Figure 2. Tree for tutorial exercise 2
(3) Solve these simultaneous equations.
(a) Using substitution, they both have integer solutions.
(i) x − 2y = 5 and x = 3y + 1
(ii) 3x + 4y = 7 and y = 3 − x
(b) Using elimination, they both have integer solutions.
(i) x + y = 8 and x − y = 12
(ii) x − 2y = 5 and 2x + 3y =− 4
(c) Using any method, one has a fractional solution, the other has no solution.
(i) 4x + 2y = 6 and y = 2 − 2x
(ii) y = 2x − 1 and x = 2y + 1
Tutorial continues over the page
4
(4) Expand the brackets and then simplify.
(a) (p1 + q1 )(p2 + q2 )
(b) (a − 6)(a + 2)
(c) (b + 5)(b − 5)
(d) (c + 5)(c − 3)(c + 1)
(5) Factorise the following expressions. Make sure to put in the step described
in the lecture.
(a) x2 − x − 6
(b) x2 + x − 6
(6) In each equation, solve for x. Make sure to put in the step described in the
lecture.
(a) (x − 3)(x + 1) = 0
(b) (x − 4)(x − 4) = 0
(7) In each equation, solve for x.
(a) (x − 3)2 = 22
(b) (x + 1)2 = (− 5)2