Name:________________________________________________________________ Date:_____________________
Silver Spring
International
Middle School
Honors Geometry
Summer Math Packet
To help you be successful next year in Honors Geometry, make sure you are able to complete the
problems in this packet. These are skills that are prerequisites for Honors Geometry.
1|Page
Part 1: Solving Equations
Directions: Solve for x in each equation. Be sure to show all your work for each problem.
1. 4x – 8 = 24
2. (6x – 8) – (5x + 9) = 3
3. 7x – 8x + 4 = 5x – 2
4. 3(x – 2) = 18
5. 3(x + 2) – 2(x + 4) = 7
6.
7. -63 – x = -82
8. -6.11 + x = 14.321
9. 5x + 1 = 3x – 3
𝒙
𝟏𝟖
=𝟔
2|Page
Part 2: Finding Slope
Directions: Find the slope of each line (rise/run).
1.
2.
3.
4.
5.
6.
Δy rise
=
Δx run
Find the slope of the line that passes through each pair of points.
m=
7. A(1, -5), B(6, -7)
8. C(7, -3), D(8, 1)
9. E(7, 2), F(12, 6)
10. G(8, -3), H(11, -2)
11. J(5, -9), K(0, -12)
12. L(-4, 6), M(5, 3)
3|Page
Part 3: Equation of a Line
Directions: Graph the equation of the line in slope-intercept form. y = mx + b
Graph an Equation in Slope-Intercept Form
1. Graph y =
2
x+1
3
4. Graph y = -4x + 1
2. Graph y = 3x + 1
5. Graph y =
1
x
2
3. Graph y = x – 2
1
6. Graph y = - x – 3
3
4|Page
Directions: Graph the equation of the line in slope-intercept form. y = mx + b
1. ____________________
2. ____________________
3. ____________________
4. ____________________
5. ____________________
5. ____________________
7. ____________________
8. ____________________
9. ____________________
5|Page
Part 4: Quadratic Equations
Directions: Graph each quadratic function below. Identify the a, h, and k values and
describe how they transform the parabola. y = a(x – h)2 + k
1. y = (x – 3)2 +4
!
2. y = –(x + 5)2 + 2
3. y = (x – 2)2 – 4
!
a=
a=
a=
h=
h=
h=
k=
k=
k=
Write the equation of each parabola in vertex form.
4.
a=
5.
h=
k=
a=
6.
h=
k=
a=
h=
Vertex:
Vertex:
Vertex:
Equation:
Equation:
Equation:
k=
6|Page
Part 5: Pythagorean Theorem & Distance Formula
Directions: Use the Pythagorean theorem to solve for the missing side of each triangle.
a2 + b2 = c2
Directions: Use the distance formula (𝑑 = 𝑥! − 𝑥! ! + 𝑦! − 𝑦! ! ) to find the distance
between each pair of points. Round your answers to the nearest hundredth if necessary.
Show all work!
1. (0, 3) and (2, 1)
2.
(9, 17) and (4, 5)
4. (4, 10) and (6, 13)
5. (7, -3) and (3, 2)
3. (-1, 3) and (2, 5)
6. (4, -2) and (0, 5)
7|Page
Part 6: Multiplying Binomials
Directions: Multiply each pair of binomials using FOIL or the BOX Method. Show your work.
1. (5r – 7) (4r + 3)
2. (4a – 3) (a + 4)
3. (3x – 5)(3x + 5)
4.(x – 6)2
5. (2h + 3) (2h + 3)
6. (3x + 4)(5x + 6)
8|Page
Part 7: Building the Perfect Square
Multiply using an area model.
1.
2. ( x + 4)
( x + 7 )( x + 7 )
2
Fill in the number that completes the square. Then write the trinomial in factored form.
3. x 2 + 16 x + ______
4. x 2 + 18 x + ______
5. x 2 − 6 x + _______
6. x 2 − 10 x + _______
7. x 2 + 12 x + _______
8. x 2 + 15 x + _______
Find the value of “b,” that will make a perfect square expression. Then write the expression in
factored form.
9. x 2 + ______ x + 64 2
10. x + ______ x + 25
11. x 2 − ______ x + 49
9|Page