For [[2x+5y=20]], state the slope and [[y]]-intercept.

Slope [[-\frac{2}{5}]]; [[y]]-intercept [[4]]

Is [[\{(1,4),(2,7),(1,9)\}]] a function? Explain.

No; input [[1]] has two outputs

A line of best fit is [[y=1.8x+12]]. Interpret [[1.8]] if [[x]] is hours studied and [[y]] is test score.

The predicted score rises [[1.8]] points per additional study hour

Explain why [[2^{3}\times2^{4}]] is not [[4^{7}]].

Same-base powers add exponents: [[2^{7}=128]], while [[4^{7}]] is much larger

Free printable summer review

8th Grade Summer Math Review

A 40-problem Algebra 1 preparation packet for students finishing 8th grade, with typeset equations, functions, exponents, radicals, systems, visual geometry, and a full answer key.

40 problems8 skill areasAbout 95 minutesAnswer key included

Download the free worksheet PDF

What this review measures

This review is intentionally algebra-heavy. It checks the habits Algebra 1 uses every week: maintaining equality, reading slope as a rate, moving among tables, graphs, and equations, applying exponent rules, and explaining what a solution means in context. Mathematical expressions are typeset consistently so notation supports rather than distracts from the reasoning.

For parents and educators

Students should show one algebra step per line. If an answer is wrong but the written method is sound, focus on arithmetic; if no equation appears, focus on translating the situation first.

Preview the complete review

Every question below appears in the printable packet. Students should show their work and simplify answers unless directed otherwise.

Linear equations

Solve equations with distribution, variables on both sides, and rational coefficients.

1Solve $\displaystyle 4(2x-3)+5=3x+18$ .
2Solve $\displaystyle \frac{x-4}{3}=6$ .
3Solve $\displaystyle 0.6x+2.4=9.6$ .
4Solve $\displaystyle 7-2(3x+1)=5x-9$ .
5Solve $\displaystyle \frac{2}{3}x-5=9$ .
6Solve $\displaystyle 5(x-2)=3x+14$ .

Lines and slope

Find slope and write linear equations from multiple forms.

7Find the slope through $\displaystyle (-2,5)$ and $\displaystyle (4,-7)$ .
8Write the equation of the line with slope $\displaystyle 3$ through $\displaystyle (2,-1)$ .
9For $\displaystyle 2x+5y=20$ , state the slope and $\displaystyle y$ -intercept.
10Are $\displaystyle y=-3x+8$ and $\displaystyle 6x+2y=1$ parallel, perpendicular, or neither?
11Use the table to find the slope and write the linear rule.
x y
0 1
2 5
5 11
12Points A and B are shown. Find the slope of the line through them.

x	y
0	1
2	5
5	11

Functions

Identify functions and evaluate rules.

13Evaluate $\displaystyle f(-3)$ for $\displaystyle f(x)=2x^{2}-5$ .
14Is $\displaystyle \{(1,4),(2,7),(1,9)\}$ a function? Explain.
15A linear function has $\displaystyle f(2)=7$ and $\displaystyle f(6)=19$ . Find its rule.
16Use the table to decide whether the relation is a function.
input output
-2 5
0 1
3 -5
17For $\displaystyle g(x)=-4x+9$ , solve $\displaystyle g(x)=-15$ .

input	output
-2	5
0	1
3	-5

Exponents and radicals

Apply exponent rules and estimate square roots.

18Simplify $\displaystyle (3x^{4})(2x^{3})$ .
19Simplify $\displaystyle \frac{a^{9}}{a^{4}}$ for $\displaystyle a\neq0$ .
20Write $\displaystyle 0.00072$ in scientific notation.
21Between which two consecutive integers is $\displaystyle \sqrt{70}$ ?
22Solve $\displaystyle x^{2}=121$ .

Systems

Solve pairs of linear equations and interpret intersections.

23Solve $\displaystyle y=2x+1$ and $\displaystyle y=-x+10$ .
24Solve $\displaystyle 2x+y=11$ and $\displaystyle x-y=1$ .
25How many solutions do $\displaystyle y=4x-2$ and $\displaystyle 8x-2y=4$ have?
26Adult tickets cost $12 and student tickets cost $8. Thirty tickets bring in $296. How many of each are sold?

Geometry and transformations

Use the Pythagorean theorem, similarity, and coordinate transformations.

27Find the hypotenuse of the right triangle.
28A 6-foot person casts an 8-foot shadow. A tree casts a 30-foot shadow. Find the tree's height.
29Reflect $\displaystyle (-4,3)$ across the $\displaystyle y$ -axis.
30Points P and Q are shown. Find their exact distance.
31The angle shown and its supplement form a linear pair. Find the supplement.
32Find the volume of the rectangular prism.
33The rectangle is dilated by a scale factor of $\displaystyle \frac{3}{2}$ . Find the new area.

Algebra readiness problems

Translate situations into linear models.

34Plan A costs $25 plus $4 per month. Plan B costs $10 plus $7 per month. After how many months are the costs equal?
35A line of best fit is $\displaystyle y=1.8x+12$ . Interpret $\displaystyle 1.8$ if $\displaystyle x$ is hours studied and $\displaystyle y$ is test score.
36The perimeter of a rectangle is $\displaystyle 54$ . Its length is $\displaystyle 3$ more than twice its width. Find both dimensions.
37A phone battery begins at $\displaystyle 92\%$ and loses $\displaystyle 7\%$ per hour. Write a linear model for the remaining percent after $\displaystyle h$ hours.
38A sequence begins $\displaystyle 5,11,17,23,\ldots$ . Write an explicit rule for the $\displaystyle n$ th term.

Challenge

Recognize equivalent structures.

39Without expanding, solve $\displaystyle (x-5)^{2}=49$ .
40Explain why $\displaystyle 2^{3}\times2^{4}$ is not $\displaystyle 4^{7}$ .

View the complete answer key

Open-ended explanations may use different wording while showing the same reasoning.

Linear equations

1. $\displaystyle x=5$

2. $\displaystyle x=22$

3. $\displaystyle x=12$

4. $\displaystyle x=\frac{14}{11}$

5. $\displaystyle x=21$

6. $\displaystyle x=12$

Lines and slope

7. $\displaystyle -2$

8. $\displaystyle y=3x-7$

9. Slope $\displaystyle -\frac{2}{5}$ ; $\displaystyle y$ -intercept $\displaystyle 4$

10. Parallel

11. Slope $\displaystyle 2$ ; $\displaystyle y=2x+1$

12. $\displaystyle 2$

Functions

13. $\displaystyle 13$

14. No; input $\displaystyle 1$ has two outputs

15. $\displaystyle f(x)=3x+1$

16. Yes; each input has exactly one output

17. $\displaystyle x=6$

Exponents and radicals

18. $\displaystyle 6x^{7}$

19. $\displaystyle a^{5}$

20. $\displaystyle 7.2\times10^{-4}$

21. $\displaystyle 8$ and $\displaystyle 9$

22. $\displaystyle x=\pm11$

Systems

23. $\displaystyle (3,7)$

24. $\displaystyle (4,3)$

25. Infinitely many; the equations describe the same line

26. 14 adult tickets and 16 student tickets

Geometry and transformations

27. $\displaystyle 15$

28. $\displaystyle 22.5$ feet

29. $\displaystyle (4,3)$

30. $\displaystyle 2\sqrt{13}$ units

31. $\displaystyle 43$ degrees

32. $\displaystyle 120$ cubic cm

33. $\displaystyle 135$ square units

Algebra readiness problems

34. $\displaystyle 5$ months

35. The predicted score rises $\displaystyle 1.8$ points per additional study hour

36. Width $\displaystyle 8$ ; length $\displaystyle 19$

37. $\displaystyle B(h)=92-7h$

38. $\displaystyle a_n=6n-1$

Challenge

39. $\displaystyle x=12$ or $\displaystyle x=-2$

40. Same-base powers add exponents: $\displaystyle 2^{7}=128$ , while $\displaystyle 4^{7}$ is much larger

What this review measures

For parents and educators

Preview the complete review

Linear equations

Lines and slope

Functions

Exponents and radicals

Systems

Geometry and transformations

Algebra readiness problems

Challenge

Linear equations

Lines and slope

Functions

Exponents and radicals

Systems

Geometry and transformations

Algebra readiness problems

Challenge

Keep reviewing