Pronumerals & Language
What is the term used for a letter that represents a number in algebra?
Pronumeral (or variable)
If x = 5, evaluate 3x + 2
17
Use the index law for multiplying to simplify: x³ × x²
x⁵ (add the powers: 3 + 2)
Simplify: 5a + 3a
8a
Simplify: 4 × 3g
12g
Write an expression for "a number, y, increased by 12."
y + 12
If a = 4 and b = 7, evaluate 2a + b
15
Use the index law for dividing to simplify: m⁸ ÷ m³
m⁵ (subtract the powers: 8 − 3)
Simplify: 7x − 2x + 4x
9x
Simplify: 5a × 2b
10ab
In the expression 5ab + 3a − 7, name the coefficient of the first term, and identify the constant term.
Coefficient = 5; constant term = −7
If m = 6 and n = −2, evaluate 4m − 3n
30
Simplify: 4a² × 3a⁵
12a⁷ (multiply the numbers: 4×3=12; add the powers: 2+5=7)
Simplify: 9ab − 4a + 2ab + a
11ab − 3a
Simplify: 18x ÷ 3
6x
If x represents Tom's age now, write an expression for his age in 6 years' time, and write an expression for his sister's age if she is 4 years younger than Tom.
Tom in 6 years: x + 6. Sister's age: x − 4
If p = −3 and q = 5, evaluate 2p(q − 4)
2 × −3 × (5 − 4) = −6
Simplify: 36p⁷ ÷ 9p²
4p⁵ (divide the numbers: 36÷9=4; subtract the powers: 7−2=5)
Simplify: 3x² + 5x − 2x² + 7
x² + 5x + 7
Simplify: −4m × 3n × −2
24mn
A café orders m muffins each morning. By 10am, 15 have sold. By lunch, that number has doubled from the original 10am amount (not from m). Write an expression for how many muffins are left by lunchtime.
m − 15 − 20 = m − 35 (10am amount was m − 15; it doubling in reference to the original 10 sold... simplest accepted answer: m − 35, i.e. 15 sold by 10am plus another 20 by lunch)
The formula for the area of a triangle is A = ½bh. Calculate the area when b = 12.4 cm and h = 5 cm, giving your answer to 1 decimal place.
A = ½ × 12.4 × 5 = 31.0 cm²
Simplify fully: (6y³ × 4y⁸) ÷ (12y⁴)
2y⁷ (multiply numerator: 6×4=24, y³×y⁸=y¹¹, giving 24y¹¹; then divide by 12y⁴: 24÷12=2, y¹¹÷y⁴=y⁷)
Simplify: 4h − 6 + 3h − 2h² + 9 − h²
−3h² + 7h + 3
Simplify: 24x²y ÷ (6xy)
4x