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Algebra Exploration Worksheet
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Algebra Exploration Worksheet
Simplify expressions, solve equations and show your working where appropriate. Use the graphing space to plot the points you calculate.
Simplifying and Expanding Expressions
1.Simplify 7x − 3x + 6.
2.Simplify 5p + 2 − 3p + 8.
3.Simplify 8a − 2b − 3a + 5b.
4.Expand 3(x + 6).
5.Expand 4(2y − 3).
6.Expand 2(3m + 4n).
7.Which expression is equivalent to 5(x − 2) + 3x?
- 8x − 10
- 8x − 2
- 2x − 10
- 5x + 6
Linear Equations and Problem Solving
8.Solve 4x + 7 = 31. Show your working.
9.Solve 5y − 9 = 26. Show your working.
10.A bike hire shop charges a fixed fee of $8 plus $4 for each hour hired. Freya pays $28. Write an equation and work out how many hours she hired the bike.
11.A shuttle ride costs $3.50 to start, then $1.80 for each kilometre. The total fare is $17.90. Write an equation and find the distance travelled.
Linear Graphs and y = mx + c
12.For the line y = 3x − 4, state the gradient and the y-intercept.
13.Complete the table using y = 2x + 1.
x
−1
0
1
2
y
14.Plot the points from the table for y = 2x + 1 on the coordinate grid, then draw the straight line through them.
Use this space to plot and label the points, then draw the line.
15.Which equation has gradient −3 and y-intercept 5?
- y = 5x − 3
- y = −3x + 5
- y = 3x − 5
- y = −5x + 3
16.A monthly streaming plan costs $18, plus $2 for each film rented. Write a rule for the monthly cost C in dollars when f films are rented.
3 printable pages
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