Download Chapter 2

Online practice assessment task for AS91027 (1.2)
From Level 1 Mathematics and Statistics Learning Workbook,
published by ESA Publications (NZ) Ltd, ISBN 978-1-927194-23-2
Apply algebraic procedures in solving problems
Externally assessed (CAT)
4 credits
Chapter 2
Practice assessment task
f.
Rearrange the formula
y=
Question 1
ax + b
to make x subject.
cx + d
a. Expand and simplify 5(2x +1) – 3(x – 4)
b. Factorise x2 + 3x – 18
4a 3 × 5a 2
c. Simplify
10a
d. Simplify fully
6x 2 – 9x
12x 2
e. The height of a trapezium of area A is given by
the formula h =
2A
where a and b are the
a+b
Question 2
a. Solve these equations
i.
1.6p + 4 = 2.4p – 6
ii. (2x + 5)(3x – 1) = 0
iii.
1
x
+
=2
2 3
lengths of the parallel sides. Find the height
of a trapezium with parallel sides of length
4.5 cm and 7.5 cm, and area 31.5 cm2.
iv. 2x = 512
2 Online practice assessment task for AS91027 (1.2) Online practice assessment task for AS91027 (1.2)
b. Manu buys lunches for her office at the
local café. One day she buys 5 coffees and
7 sandwiches, at a total cost of $49.10. If
the sandwiches cost 50 cents more than the
coffees, form and solve a pair of simultaneous
equations to find the cost of a sandwich.
Question 3
a. Simplify (3ab2)3
b. Expand and simplify (3x – 4)(2 – x)
c. One factor of 6x2 – 5x – 4 is (2x + 1). Find the
other factor.
d. Solve for a and b
3a – 2b = 8
11a + 4b = 1
c. A piece of paper is 6 cm longer than it is wide.
The piece of paper is glued onto a piece of
cardboard.
The width of the cardboard is 2 cm more than
the width of the paper.
The length of the cardboard is five times the
width of the paper.
The area of the shaded border of cardboard is
double the area of the paper.
5x
x
x+6
e. Solve for x
7x 2 + 12x – 4 = 0
x+2
Form and solve an equation to find the width
of the paper.
f.
Jack and Mia both have a bag of sweets. If Jack
gave Mia 3 sweets, then both children would
have the same number of sweets. If Mia gave
Jack 2 sweets then Jack would have twice as
many sweets as Mia.
Form and solve at least one equation to find
the total number of sweets Jack and Mia have.
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Answers
Question 1
(page 75)
a. 7x + 17 b. (x + 6)(x – 3)
c. 2a4
f.
b –y d
x= 2
y c –a
Question 2
a. i.
2x – 3
4x
d.
2
12.5
(page 75)
ii. – 2
iv. 9
e. 5.25 cm
1
1
or 2
3
iii. 3
1
3
b. 5
x + 7y = 49.1 and y = x + 0.5; a sandwich
costs $4.30
c. 5x(x + 2) – x(x + 6) = 2x(x + 6); width = 4 cm
Question 3
(page 76)
a. 27a3b6
b. –3x2 + 10x – 8
c. (3x – 4)
d. a = 1, b = –2.5
e. x = –2 or
2
7
f.
Answers will vary.
j – 3 = m + 3 and j + 2 = 2(m – 2)
Solve to get m = 12, j = 18, so 30 sweets
altogether
© ESA Publications (NZ) Ltd, Freephone 0800-372 266