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Algebra Transformations Review

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Algebra Transformations Review

A pop-up game stall is testing its pricing rules before opening day. Complete each algebra challenge, show your working where you can, and check that your answers make sense.

Substitute and calculate

Replace each letter with its given value, then follow the order of operations.

1.The score rule is 3x + 4. If x = 5, what is the score?

2.A prize costs 5a − 2 dollars. Find its cost when a = 6.

3.For the expression 2p + 3q, use p = 4 and q = 2. Show the substitution and find the value.

Rounds, n

Tokens, t

4.Use t = 4n + 1 to complete the token table above. Write the token totals in order for n = 0, 1, 2 and 5.

Transform expressions

Use the distributive property and collect like terms to rewrite each expression.

5.Expand 3(x + 4). Which expression is equivalent?

3x + 4
3x + 12
x + 12
7x

6.Expand and simplify 2(y + 5) + 3y. Show both steps.

7.Simplify 7m − 2m + 6. Explain which terms can be combined.

8.A friend says 4(a + 2) = 4a + 2. Is the statement true or false? Correct it if needed.

TrueFalse

Build and use rules

Turn descriptions and patterns into algebra, then use the rule to solve a real problem.

9.Write an expression for “seven more than twice a number k”.

10.A number pattern follows a linear rule, so y increases by a constant amount each time x increases by 1. When x = 1, y = 6; when x = 2, y = 9; when x = 3, y = 12. Find the rule connecting x and y, then use it to find y when x = 8.

11.At a games stall, entry costs $4 and each game costs $2.50. Write a formula for the total cost C for g games, then calculate the cost of playing 6 games.

12.Which transformation turns 5x + 5 into 5(x + 1)? Choose the best description.