Expressions, Structure & Units — Drills
Expressions, Structure & Units has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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).
Parts of the whole
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the degree in 6x2 + 3x + 10?
Worked answer
2
Terms: 6x2, 3x, 10
Answer: 2
Problem 2
What is the constant in 8x4 + 3x - 2?
Worked answer
-2
Terms: 8x4, 3x, -2
Answer: -2
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate 5a - 5b when a = 7 and b = 0.
Worked answer
35
5(7) = 35
5(0) = 0
35 - (0) = 35
Problem 2
Evaluate 6a - 4b when a = 0 and b = -3.
Worked answer
12
6(0) = 0
4(-3) = -12
0 - (-12) = 12
Simplifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Simplify 30x + 605.
Worked answer
6x + 12
30x5 = 6x
605 = 12
6x + 12
Problem 2
Simplify 35x + 427.
Worked answer
5x + 6
35x7 = 5x
427 = 6
5x + 6
Structure
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Factor x2 - 9 using structure.
Worked answer
(x - 3)(x + 3)
x2 - 32
= (x - 3)(x + 3)
Problem 2
Factor x2 - 36 using structure.
Worked answer
(x - 6)(x + 6)
x2 - 62
= (x - 6)(x + 6)
Units
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Convert 22 m/s to kilometres per hour.
Worked answer
79.2
22 × 3600 = 79200 m per hour
÷ 1000 = 79.2
79.2 km/h
Problem 2
Convert 18 m/s to kilometres per hour.
Worked answer
64.8
18 × 3600 = 64800 m per hour
÷ 1000 = 64.8
64.8 km/h