Test - Expressions using letters and numbers

Translating Word Statements to Algebraic Expressions

1. Write an algebraic expression for: "10 subtracted from the product of 4 and a number $z$.
2. Write an algebraic expression for: "15 more than a number $y$."
3. Write an algebraic expression for: "7 less than 3 times a number $x$."
4. Write an algebraic expression for: "Half of a number $k$, increased by 9."
5. Write an algebraic expression for: "The sum of a number $p$ and 4, multiplied by 6."

Write a real life situation

1. Describe a real-life situation that could correspond to the expression $20x + 10y$.
2. Describe a real-life situation that could correspond to the expression $100 - 5m$
3. Imagine you’re in a place where the temperature drops by 5°C each hour. If the temperature is currently at 8°C, write an expression which denotes the temperature after $h$ hours.

Mind the Mistake, Mend the Mistake

1. Statement: "If $p = -2$, then $12 + p = 14$."
2. Statement: "If $g = 4$ and $h = 2$, then $3g - 2h = 0$."
3. Statement: "If $z = 0$, then $5z + 7 = 57$.
4. Statement: "If $a = 6$ and $b = 2$, then $4a - 3b = 6$."

Evaluate the expression

1. Simplify the algebraic expression: $15m - 4m + 8n - 3n$.
2. Calculate the total score for a game if the score is calculated by the expression $10p - 5q$, where the number of correct answers $p = 6$ and incorrect answers $q = 3$.
3. Simplify the following expression by grouping the like terms: $7a + 4b - 2a + 3b$.
4. Evaluate the expression $12(p - 2)$ when $p = 5$.

Formula machine

1. Observe the machine outputs for $(a, b)$ and determine the formula for this machine:

• $(10, 2) \rightarrow 5$
• $(15, 3) \rightarrow 5$
• $(8, 4) \rightarrow 2$

1. A machine processes inputs $(m, n)$ as follows:

• $(5, 2) \rightarrow 15$
• $(4, 1) \rightarrow 11$
• $(6, 3) \rightarrow 19$ What is the algebraic formula for this machine?

Patterns

1. A pattern of shapes repeats every 3 positions: Circle, Square, Triangle. Write the formula for the position where the Triangle appears for the $n$th time and for square and circle too.

2. A repetitive border design uses a specific floral motif at positions 2, 7, 12, 17… Find the formula for the $n$th occurrence of this motif.