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Algebra

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Practice Test on Algebraic Equations and Functions

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Algebra
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Algebra
Mathematics
Arithmetic
Factorization
polynomials
Partial fractions
Polynomial expansion
Linear differential equation

An equivalent expression to the algebraic expression 9x2 ? 4y2 is: A) 3x ? 2y B) 6(3x2 ? 2y2) C) (3x + 2y)(3x ? 2y) D) (2y + 3x)(2y ? 3x) Correct. Your answer=C, Correct answer=C Explanation: 9x2 ? 4y2 = (3x + 2y)(3x ? 2y) Factor the trinomial x2 ? 2x ? 15: A) (x ? 3)(x ? 5) B) (x + 3)(x ? 5) C) (x ? 3)(x + 5) D) (x + 3)(x + 5) Correct. Your answer=B, Correct answer=B Explanation: The numbers ?5 and 3 multiply to give ?15 and add to give ?2. x2 ? 2x ? 15 = x2 ? 5x +3x ? 15 = x (x ? 5) + 3 (x ? 5) = (x ? 5)(x + 3) Fully factored, the quadratic function y = 2x2 + 10x + 12 can be expressed as: A) y = 2(x + 6)(x + 2) B) y = 2(x + 3)(x + 2) C) y = 2(x + 6)(x + 1) D) y = 2(x + 3)(x + 1) Correct. Your answer=B, Correct answer=B Explanation: y = 2x2 + 10x + 12 y = 2(x2 + 5x + 6)

Chapter 9 Practise test

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Algebra
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Biology
biochemistry
cellular respiration
Chemistry
metabolism
Exercise physiology
Metabolic pathways
Plant physiology
Glycolysis
Pyruvic acid
Fermentation
Electron transport chain

BIOLOGY: Chapter 9-Cellular Respiration Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. ____ 1. Which of the following is the correct sequence of events in cellular respiration? a. glycolysis ? fermentation ? Krebs cycle b. Krebs cycle ? electron transport ? glycolysis c. glycolysis ? Krebs cycle ? electron transport d. Krebs cycle ? glycolysis ? electron transport ____ 2. Which of the following is released during cellular respiration? a. oxygen b. air c. energy d. lactic acid ____ 3. Cellular respiration uses one molecule of glucose to produce a. 2 ATP molecules. b. 34 ATP molecules. c. 36 ATP molecules. d. 38 ATP molecules.

6.2 Notes

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Algebra
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geometry
Elementary geometry
Quadrilaterals
Analytic geometry
Orientation
Perpendicular
Slope
line
Trapezoid
Parallelogram
Rectangle
Parallel

Unit 6 ? Linear Functions ? Slopes of Parallel & Perpendicular Lines Example 1 Plot points A(-4, 0) and B(-2, 4) and connect them. Plot points C(0, -2) and D(3, 4) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Example 2 Plot points A(1, 4) and B(-2, 3) and connect them. Plot points C(-2, 5) and D(0, -1) and connect them. a) Calculate the slope of each line segment. b) What do you notice about the lines on the graph? Parallel lines have ________________ slope. Perpendicular lines have slopes that are the ______________________ of each other. When you multiply the slopes of perpendicular lines together, the product will be ______.

5.2 Notes

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Algebra
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Mathematics
Functions and mappings
Function
Finitary relation
Computability theory
Technology

5.2 ? Functions and Function Notation Consider the following set: Domain: Range: A function is like a machine, you put a number in (input or _________), the machine mashes it, stretches it, etc. and the machine spits out a new number (output or __________). This is a special type of relation because for every input there is only one output. (eg. If you put 3 into the machine, it will always output 6) ?Every function is a relation but not every relation is a function.? Example 1 then output first Multiply by 3 Add 2 input Equation Graph Ordered Pairs Table of Values Input Output -3 -1 0 1 3 Determining whether a relation is a function: {(1, 2), (0, 5), (3, 8), (-3, 2), (5, 9)}Example 2 b) -2 3 6c)

Relations and Functions Final Review

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Algebra
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Mathematics
Analytic geometry
Elementary mathematics
Elementary algebra
equations
Functions and mappings
Linear equation
Slope
line
Continuous function
Function
Bresenham's line algorithm

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 t (Min) 1 2 3 4 5 6 d (km) 1 2 3 4 5?1?2?3?4?5 x 1 2 3 4 5 ?1 ?2 ?3 ?4 ?5 y Relations and Functions Practice Questions 1. The following distance-time graph represents the distance (in kilometres) a person bicycled during a 50-min period. Describe a possible scenario. 2. The table of values shows the cost of movie tickets at a local theatre. Number of Tickets Cost ($) 1 12 2 24 3 36 4 48 (a) Is this a linear or non-linear relationship? Explain how you know. (b) Assign a variable to represent each quantity in the relation. Which variable is the dependent variable and which is the independent variable?

Chapter 11: Relations and Functions Test

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Algebra
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Mathematics
Graph theory
Functions and mappings
Graph
Function
Diagram
Mathematical analysis
Median graph
Asymptote

Name: _______________ Date: _______________Relations and Functions Practice Test Multiple Choice (1 mark each) Use the following information to answer the next question. A farmer read a study of soil fertility and mineral absorption. It contained the graph below. The graph illustrates the relative absorption of copper by the top and bottom of a wheat plant when the plant was subjected to various solutions containing a fixed amount of copper but having different concentrations of aluminum. From this graph, the farmer concluded that the relative absorption of copper consistently decreased at the A top of a wheat as the aluminum concentration increased B top of a wheat as the aluminum concentration decreased C bottom of a wheat as the aluminum concentration increased

AHSME 1992

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Algebra
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Mathematics
Abstract algebra
Integer sequences
Number theory
Triangles
Triangle geometry
Combinatorics
Number
Prime number
Triangle
Coprime
Integer
sports

USA AIME 1992 1 Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms. 2 A positive integer is called ascending if, in its decimal representation, there are at least two digits and each digit is less than any digit to its right. How many ascending positive integers are there? 3 A tennis player computes her win ratio by dividing the number of matches she has won by the total number of matches she has played. At the start of a weekend, her win ratio is exactly .500. During the weekend, she plays four matches, winning three and losing one. At the end of the weekend, her win ratio is greater than .503. What?s the largest number of matches she could?ve won before the weekend began?

AHSME 1991

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Algebra
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Mathematics
Abstract algebra
Group theory
Number
quadratic equation
Summation

USA AIME 1991 1 Find x2 + y2 if x and y are positive integers such that xy + x+ y = 71x2y + xy2= 880. (0) Rectangle ABCD has sides AB of length 4 and CB of length 3. Divide AB into 168 congruent segments with points A = P0, P1, . . . , P168 = B, and divide CB into 168 congruent segments with points C = Q0, Q1, . . . , Q168 = B. For 1 ? k ? 167, draw the segments PkQk. Repeat this construction on the sides AD and CD, and then draw the diagonal AC. Find the sum of the lengths of the 335 parallel segments drawn. Expanding (1 + 0.2)1000 by the binomial theorem and doing no further manipulation gives ( 1000 0 ) (0.2)0 + ( 1000 1 ) (0.2)1 + ( 1000 2 ) (0.2)2 + ? ? ?+ ( 1000 1000 ) (0.2)1000 = A0 +A1 +A2 + ? ? ?+A1000, (0) where Ak = (1000 k )

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