Expressions, Structure & Units — Practice
Before you manipulate an expression, read it. Its structure tells you what it means and what you are allowed to do.
What these questions cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Rate — A ratio of two different units, like miles per hour or dollars per pound.
- Coefficient — The number multiplying a variable — the 3 in 3n.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Perfect square — A number that is some whole number squared: 1, 4, 9, 16, 25, …
- Factor — A number that divides evenly into another.
- GCF — Greatest common factor — the largest number dividing both.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
- Difference of squares — a2 - b2 = (a - b)(a + b).
Problem 1
How many terms are in 4x2 - 7x + 2?
Worked answer
3
4x2, -7x, +2
Three terms
Problem 2
What is the coefficient of x in 9 - 5x?
Worked answer
-5
The term is -5x
So the coefficient is -5
Problem 3
What is the degree of 3x4 - x2 + 8?
Worked answer
4
Exponents are 4, 2, 0
The degree is 4
Problem 4
Evaluate 3a - 2b when a = 5 and b = 4.
Worked answer
7
3(5) - 2(4)
= 15 - 8 = 7
Problem 5
Evaluate x2 - 3x when x = -2.
Worked answer
10
(-2)2 = 4
-3(-2) = 6
4 + 6 = 10
Problem 6
Simplify 6x + 93.
Worked answer
2x + 3
6x3 = 2x
93 = 3
2x + 3
Problem 7
Simplify 5(2x - 3) - 4x.
Worked answer
6x - 15
10x - 15 - 4x
= 6x - 15
Problem 8
Factor x2 - 49 using structure.
Worked answer
(x - 7)(x + 7)
x2 - 72
= (x - 7)(x + 7)
Problem 9
A car uses 9 litres per 100 km. How many litres for 250 km?
Worked answer
22.5
9 L100 km × 250 km
= 22.5 L
Problem 10
Convert 72 km/h to metres per second.
Worked answer
20
72 × 1000 = 72000 m per hour
72000 ÷ 3600 = 20
20 m/s
Problem 11
Which is equivalent to 4x + 84?
- x + 2
- x + 8
- 4x + 2
- x
Worked answer
x + 2
4x4 + 84
= x + 2
Cancelling only the first 4 would be wrong
Problem 12
Evaluate 2a + ba - b when a = 5 and b = 3.
Worked answer
6.5
Top: 10 + 3 = 13
Bottom: 5 - 3 = 2
13 ÷ 2 = 6.5
Problem 13
Factor x4 - 16 completely.
Worked answer
(x - 2)(x + 2)(x^2 + 4)
(x2)2 - 42 = (x2 - 4)(x2 + 4)
x2 - 4 = (x-2)(x+2)
x2 + 4 does not factor
Problem 14
A recipe needs 34 cup per serving. How many cups for 14 servings?
Worked answer
10.5
34 × 14 = 424
= 10.5 cups
Problem 15
Write 16x2 - 24x as a product of two factors.
Worked answer
8x(2x - 3)
GCF of 16x2 and 24x is 8x
8x(2x - 3)
Problem 16
If P = 2l + 2w with P = 46 and l = 14, find w.
Worked answer
9
46 = 28 + 2w
2w = 18
w = 9