Rising Geometry

Students

Summer Skills

Workbook

June 2018

Name_____________

This booklet is a review of the main Algebra

I concepts. You should complete each page.

Turn this booklet in the first day back to

school.

Please be sure to not

use the calculator

when you see this symbol.

For questions or comments, please email

Rising Geometry Students Summer Skills Work Page 1

Evaluate the following when x = 4, y = -2, and z = 5. Show all work.

Evaluate means to substitute the value in for each variable and simplify the expression.

1) 3x – y 2) 𝑥𝑥 + z 3) 4𝑥 – 3𝑥

4) 𝑥𝑥𝑥 5) x – 2y + 3z 6) x (y – 2z)

7) 8) 9)

10) 11) 12)

Rising Geometry Students Summer Skills Work Page 2

Simplify the following by combining like terms. Like terms have the same variable and

exponent. These terms can be combined with addition and subtraction without changing the

exponent of each term.

1) 5x – 3x 2) 4y – 7y 3)

4) 5x – 3y – x + 7 5) 7y – 12 – 3y 6) 2x – 4 + 3x + 8

7) 5y + 3x – 2z – 3y + 6x + 8 8) 4(x – 2) – 3(x + 7)

9) 4 – 3(x – 5) + 2x 10)

11) 12)

13) 5(x – 2y + 3) – 2(2y + 3x + 7) 14)

Rising Geometry Students Summer Skills Work Page 3

Use order of operations (PEMDAS) to simplify the following.

1) 8 + 6 – 3 2) 15 – (7 – 2) – 3 3) 5(4) – 10

4) 24 – 21 ÷ 3 5) 18 – 12 ÷ 4 6) 12 – (4 + 7)

7) 7(3 + 4) 8) 12 ÷ 3 · 4 9) (11 + 4) ÷ 5

10) (12 · 4) ÷ (2 · 2) 11) 30 ÷ 6 – 1 12) 42 ÷ (5 + 2) · 3

13) 4 + 3(7 – 2) 14) 5(6 – 8) 15) 15 – 2(8 + 3)

16) 2 – 8 ÷ 4 17) 4 – 8 + 6 18) 10 - 3(4)

Rising Geometry Students Summer Skills Work Page 4

Simplify the following:

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

Rising Geometry Students Summer Skills Work Page 5

Simplify the following using the rules for exponents:

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

13) 14)

15) 16)

Rising Geometry Students Summer Skills Work Page 6

Solve for x. Show all work.

1) .5x = 3.5 2) 3)

4) 3x – 4 = -22 5) 5 – x = 12 6)

7) 5(x – 3) = -20 8) -3(4 – x ) = 12 9)

10) 4(x – 3) = 3(x + 7) 11) 5(2x + 3) = 7(x – 3)

12) 2(x – 3) – 4 = 10 13) 5(x – 2) – 3(x + 4) = -20

14) 5x – 13 = 2x + 14 15) 12 – 7x = -3x – 8

Rising Geometry Students Summer Skills Work Page 7

Solve the following multi-step equations:

1) 2x + 4 = 8x - 26 2) 3x – 9 = 2x + 8

3) x - 12 = 5x 4) 7x – 9 = 4x

5) 3x – 8 = x + 12 6) 4x + 8 = 2x + 7

7) 4(x – 3) = -12 8) 5(2x + 7) = -15

9) 4(x + 6) = 2(x – 4) 10) 3(2x – 7) = 6 + 2(x – 3)

11) 12)

Rising Geometry Students Summer Skills Work Page 8

The slope m of a line describes how steep it is. The slope is calculated by finding

the quotient of the vertical change (change in y) and the horizontal change (change

in x). Formula:

Find the slope of the line that contains each pair of points.

1) (2, 4), (4, 6)

2) (3, 2), (-2, -8)

3) (-1, 3), (-2, 5)

4) (8, -3), (10, 0)

5) (0, 0), (6, -3)

6) (3, 4), (-1, 4)

7) (-4, 7), (-7, 15)

8) (2, -2), (6, 5)

9) (4, 3), (4, -5)

10) (2, 8), (7, -7)

Rising Geometry Students Summer Skills Work Page 9

The number 18 is not a perfect square, but it does have a perfect square factor.

should be further simplified to . Simplify the following radicals.

Think of the largest perfect square that can be simplified.

1) 2) - 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

13) 14) 15)

Rising Geometry Students Summer Skills Work Page 10

Multiply the following either using Distributive Property or FOIL:

1) 2)

3) 4)

5) 6)

7) 8)

9) 10)

11) 12)

13) 14)

Rising Geometry Students Summer Skills Work Page 11

Factor the following trinomials.

1) 2) 3)

4) 5) 6)

7) 8) 9)

10) 11) 12)

13) 14) 15)

16) 17) 18)

19) 20) 21)

Rising Geometry Students Summer Skills Work Page 12

Factor the following trinomials.

1) 2𝑥2 + 5𝑥 + 2 2) 3𝑥2 + 5𝑥 + 2 3) 2𝑥2 + 9𝑥 − 5

4) 3𝑥2 − 7𝑥 + 2 5) 2𝑥2 − 11𝑥 + 15 6) 9𝑥2 + 6𝑥 − 8

7) 8𝑥2 − 2𝑥 − 10 8) 6𝑥2 + 9𝑥 − 27 9) 60𝑥2 + 4𝑥 − 8

10) 20𝑥2 + 55𝑥 + 30 11) 12𝑥 − 27 12) 4𝑥3𝑥 − 8𝑥2𝑥2

13) 𝑥2 − 121 14) 𝑥2 − 25𝑥2 15) 𝑥3 + 16𝑥2 + 64𝑥

16) 𝑥2 − 6𝑥 − 27 17) 6𝑥2 − 28𝑥 + 32 18) 4𝑥2 + 4𝑥 − 80

19) 3𝑥3 − 21𝑥2 + 2𝑥 − 14 20) 𝑥3 − 9𝑥2𝑥 + 𝑥𝑥 − 9𝑥2