Prep for Honors Geometry
Are you ready? Prep Packet for Honors GeometryName:
In order to be successful in Honors Geometry, you will need the following:
•Strong Algebra skills (i.e. solving quadratics and systems of equations),
•Critical thinking skills to apply learned concepts to a variety of different problems,
•Regular homework/study habits,
•Ability to take good notes and reference them later,
•Self-motivation,
•Interest in being challenged in math.
PART 1: The following problems are examples of Algebra problems you should be able to solve without a calculator in a timely manner.All answers in Honors Geometry should be in simplest form. Answers should be exact and not decimal approximations, unless otherwise noted.
*You may need a separate sheet of paper to show work.
Solve each equation.
1.r – 21 = -37 2.14 + c = -5 3.-27 = -6 – p 4. b + (-14) = 6
5.r + (-11) = -21 6.d – (-1.2) = -7.3 7. 6x = -428.
9.(-3/5)y = -5010. 11.4t – 7 = 5 12. 6 = 4x + 2
13.14. 15.16.
17.18. 4(3 + 5w) = -11 19.20.3x – 2(x + 3) = x
Solve each system.Solve each quadratic equation by factoring.
1. x – 5y = 0 and 1. y² + 11y = 0
2x – 3y = 7
2. 2a² - 9a = 0
2. x – 2y = 5 and
3x – 5y = 83. y² + 13y + 40 = 0
3. 6x + 7y = 5 and 4. n² = -17n
2x – 3y = 7
5. 2m² + 13m = 24
4. 5m + 2n = -8 and
4m + 3n = 26. 25r² + 4 = -20r
5. 3s + 6r = 33 and Multiplying polynomials: Find each product.
6r – 9s = 211. (2a – 1)(a + 8)
6. 12x – 9y = 114 and 2. (x + 4)(x – 8)
7y + 12x = 82
3. (5b – 3)(2b + 1)
Simplifying Radicals: Simplify completely and rationalize answers when necessary.
1. 2. 3. 4.
5. 6. 7. 3 + 48. 5 + 10
9. 10. 3 ∙ 811.12.
Pythagorean Theorem: . If a, b, and c represent the sides of a right triangle, where c is the length of the hypotenuse, find each missing side. Simplify answers completely.
1. a = 30, b = 16, c = ?2. a = 10, c = 15, b = ?3. b = 3, c = 5, a = ?
Quadratic formula: Solve each equation by using the quadratic formula. Simplify answers completely.
1. 2y² + 3 = -8y2. x² + 4x – 3 = 03. 2n² - 3 = 7n
PART 2: Honors Geometry also requires the ability to solve different types of problems. Often, problems you will be asked to solve will not look exactly like anything you have been taught. The problems require critical thinking, logic, and reasoning skills.
1.How many rectangles are in the figure?
(Note: a square is also considered a rectangle.)
2.What would the shape drawn below look like
if it is rotated 270° clockwise?
3.What is the next picture in the pattern?
4.You have a 3 gallon jug and a 5 gallon jug. You need to measure out exactly 7 gallons of water. How can you do it?
5.You are on the bank of a river. You have to get a fox, a hen, and corn to the other side of the river. If left alone, the fox will eat the hen, the hen will also eat the corn if left alone. The boat is only big enough to take you and one of the three to the other side.How do you get all 3 across intact?
6.A man is looking at a photograph of someone. His friend asks who it is. The man replies, "Brothers and sisters, I have none. But that man's father is my father's son." Who was in the photograph?
7.Your sock drawer contains 24 white socks and 30 black socks. The lights in your room are off, so you cannot see the color of the socks. How many socks must you grab to ensure to have at least one matching pair?
Solutions:
Equations:(Ans: -16, -19, 21, 20, -10, -8.5, -7, -30, 250/3, 10, 3, 1, -153, 136, 11, 2, 65/7, -23/20, 40, no sol.)
Systems: (Ans: (5,1); (-9, -7); (2, -1); (-4, 6); (5, 1); (8, -2) )
Quadratics: (Ans: 0, -11 ; 0, 4.5; -5, -8; 0, -17; -8, 3/2; -2/5)
Radicals: (Ans: 4; 11; 10;; 6;, 7, 20, , 240, , 48)
Pythagorean Theorem: (34, 5, 4)
Quadratic formula: (Ans: , ,)
Multiplying polynomials: (Ans: 2a² + 15a – 8; x² - 4x – 32; 10b² - b – 3)
1.2. 3. Solution:
Explanation:
Grey box 1 rotates 2 clockwise, box 2 rotates 2 counter-clockwise, the dot rotates 2 clockwise.
4.Fill the 5 gallon jug, pour it into the 3 gallon jug until the 3 gallon is full, leaving 2 gallons in the 5 gallon jug. Now pour the 3 gallon jug out. Pour the remaining 2 gallons from the 5 gallon into the empty 3 gallon jug. Now fill the 5 gallon from the faucet. You now have exactly 7 gallons.
5. First take the hen across. Leave the hen. Go back and get the fox. Take the fox to the other side. Leave the fox there, but take the hen with you back to get the corn. Leave the hen and take the corn to the other side. Drop the corn off with the fox, then go back to get the hen. Bring the hen to the other side. All 3 make it fully intact!
6. His son.
7. Three. In the worst case, the first two socks you take out will consist of one black sock and one white sock. The next sock you take out is guaranteed to match one or the other.