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| LEVEL 1 | ||
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Chapter 1 - Terms, Sets, Functions
1. How much is 3a + 4a? 2. How much is 7b - b? 3. How much is 2b - (-5b)? 4. How much is (-4b) * (-1)? 5. There is a set A = {1, 2, 3} and B = {3, 4, 5}. What is the intersection of A and B? 6. Given a function f(x) = 2x + 4, what is the value of f(7)? 7. The number -2 is an element of which set of numbers? |
Chapter 2 - The Cartesian Plane and Intro to Equations
1. Find x in this equation: x - 7 = 9 2. Find x in this equation: x + 9 = 2 3. Find x in this equation: 3x = 12 4. Find x in this equation: 5x = -10 5. Find x in this equation: 4x + 1 = 9 6. Find x in this equation: 4x - 3 = 17 7. Find the value of f(10) for f(x) = x + 4 |
Chapter 3 - Slope and Intercept
1. What is the slope formula for two points (x1,y1) and (x2,y2) on the coordinates plane? 2. Find the slope of the line through the points (1,2) and (3,4) 3. Find the slope of the line through the points (-2, -3) and (2, 2) 4. Find the slope of the line through the points (5, -3) and (2, 1) 5. What is the slope of the line perpendicular to function f(x) = 2x - 3 6. What is the intercept of f(x) = 3x + 5? 7. Write an equation, in the slope intercept form, of the line with slope 7 and passing through the point (0, -8). |
| LEVEL 2 | ||
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Chapter 4 - Fractions
1. How much is 3/4 * 2/3? 2. How much is a/3 * b/5? 3. How much is a/b * c/d? 4. How much is (-2b)/3 * (-2)/5? 5. How much is 1/5 divided by 1/2? 6. How much is a/4 divided by 2/b? 7. How much is -(a/3) divided by 2/b? |
Chapter 5 - More Fractions and Polynomials
1. How much is 2^4 (2 to the power of 4)? 2. Find the sum: 3/7 + 4/7 3. How much is 5/11 + 2/11 - 3/11? 4. How much is 2/9 + 2/3? 5. How much is 13/18 - 7/12? 6. How much is 5a/2 + a/5? 7. Reduce the fraction 3/9 |
Chapter 6 - Polynomials Operations
1. If we have a function f(x) = 4x - 5, how much is f(9)? 2. Execute the sum: 5a - 3a + 4b - b 3. How much is 5a * 2a - 3b * 4? 4. How much is 4 * (5p - 3q)? 5. How much is 3a/4b + b/3a? 6. How much is (3a - 2)(3a - 2b)? 7. How much is (36a^2 - 25)/(6a + 5)? |
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Chapter 7 - More complex Linear Equations
1. Solve the equation 4x/7 = 2/5 2. Solve the equation x/3 + 2/5 = 3/5 3. Solve (x + 1)/3 = x/4 4. How much is x? (x + 2)/2 = (x-1)/3 5. Simplify this fraction: (4a + 16ab) / (1 + 4b) 6. Simplify this fraction: 2b(a+2) - (a+2) / (2b-1) 7. Solve the equation: (x+2)/3 + (x-2)/2 = (2x+5)/7 |
Chapter 8 - Exponents and Radicals
1. How much is 2 to the power of 8? (2^8 = ?) 2. How much is a to the power of three times a to the power of 4? (a^3) * (a^4) 3. (a^8) / (a^2) = ? 4. 4^(-2) = ? 5. (b^2)^7 = ? 6. How can we write 140,000,000 using power of 10 7. How can we write 0.00000005 using power of 10 8. How much is 36 to the power of 1/2? (36^1/2) 9. How much is square root of 72? ( V72 ) 10. How much is square root of a to the power of 6? ( Va^6 ) |
Chapter 9 - Quadratic Functions and Equations
1. What is the y-intercept for f(x) = x^2 - 3x + 4? 2. What are the vertex coordinates for f(x) = x^2 + 4x - 1? ( hint: x = -b/(2a) ) 3. Find the roots by factoring: 9x^2 - 16 4. Find the roots by factoring: x^2 + 7x + 6 5. Find the roots by factoring: x^2 + 13x - 14 6. Find the roots using the quadratic formula: x^2 - 4x - 20 7. Find the roots using the quadratic formula: 2x^2 + 3x - 9 |
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Chapter 10 - Inequalities
1. Which is bigger: -10 or -11 ? 2. What is the range for x on this inequality? x-4 > 1 3. Find the range for z on this inequality: 4z - 2 < 6 4. Find the range for y on this inequality: 5 - 2y < 1 5. Find the range for x on this compound inequality: -12 < 2x < 10 6. Find the range for x if (1-3x) > (x-1) 7. Find the range for x if |x+1| > 3 |
Chapter 11 - Systems of Equations
1. If x + y = 10 and 2x + y = 23, what is the value of x and y? 2. If 5x + y = 21 and 6x - y = 23, what is the value of x and y? 3. If 4x - 5y = 12 and 6y - 3x = -6, what is the value of x and y? 4. If x - y < 4 and 3x + 2y > 10, the origin point (0,0) will be located on the shaded area of (y = x-4) line. True or false? 5. Related to problem 4, the origin point (0,0) will be located on the shaded area of (y = -3/2x+5) line. True or false? 6. Each sheep has 4 legs and each chicken has 2 legs. If a farm boy counts 50 heads and 120 feet, how many sheep are there? 7. James has $1.70. If he only has quarters and nickels and he has 10 coins total, how many nickels does he have? |
Chapter 12 - Exponentials and Logarithms
1. 4^x = 256. Find x. 2. Solve the equation: 4^x = 2^6 3. Solve the equation: 5^2x = 625 4. 4^5x = 8^(4x-1). Solve for x. 5. Solve: 25^(-x+5) = 125^(6x-10) 6. Find x in 3^x = 15 7. Find x in 4^x = 11 |
| LEVEL 3 | ||
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Chapter 13 - Polynomials Advanced
1. Simplify this polynomial: : 8ab - 3b + 2ab - 7ac - b + 2ac 2. Multiply: (5x-7)(4x+1) 3. Simplify: (16x^2 - 25) / (4x + 5) 4. Factor and reduce: (8ab - 4a + 24ac) / 4a 5. Factor and reduce: (5x + 10xy + 1 + 2y) / (5x + 1) 6. Divide (5x^2 - 12x - 9) : (x - 3) 7. Factor and reduce (x^2 + 10x + 24) / (x + 6) |
Chapter 14 - Sets, Functions and Quadratics
1. Add the complex numbers: (3-2i) + (5+7i) 2. Multiply the complex numbers: (8-i)*(2-3i) 3. If y=(2x-3)/4, find x in relation to y. 4. Solve the quadratic equation by grouping: 3x^2 + 10x + 3 5. Solve the quadratic equation by factoring: x^2 - 10x + 9 6. Solve the quadratic equation by completing the square: x^2 + 10x + 9 7. Solve this equation using the quadratic formula: 3x^2 - 5x + 12 |
Chapter 15 - Inequalities Advanced
1. Solve the inequality: 4x - 12 > 0 2. Solve the inequality: 5x - 9 < 11 3. Solve the inequality: 3x + 6 < 11x - 10 4. Solve: -3x-20 < 4(5+3x)+5x 5. Solve the quadratic inequality: x^2 -17x > -16 6. Solve the rational inequality: (4x-12) / (x^2-4) < 0 7. Solve this exponential inequality: 4^(3x+2) > 64 |
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Chapter 16 - Matrices
1. Matrix A = [-3 11] [ 12 9] What is the element a12? 2. Give the determinant of the matrix [8 -2] [9 12] 3. Add [23 -4] + [-5 39] [-5 17] [-12 -11] 4. Evaluate 5* [2 7 -3] [-7 -4 16] 5. 5*[7 -2 12] = 4*[-x -7 2y]. Calculate (x+y). 6. Let A = [ 3 6] [-2 7] and B = A^(-1). Evaluate b12. 7. Let A = [15 18] [14 x] What value of x makes A a matrix without an inverse? |
Chapter 17 - Combinatorics and Probabilities
1. One die is thrown. What is the probability to get a 5? 2. In one bag there are 20 marbles: 3 red, 5 blue and 12 green. What is the probability to draw 1 blue marble? 3. A bag contains 3 red, 4 green and 3 blue balls. One ball is drawn at random. What is the probability that the ball is not blue? 4. A bag of jellybeans has 15 watermelon jellybeans, 20 sour apple jellybeans, 25 orange jellybeans and 15 cotton candy jellybeans. If you reach in and grab one jelly bean, what is the probability that it will be watermelon flavored? 5. Mike has a bag of marbles, 5 white, 9 blue, and 6 red. He pulls out one marble from the bag and it is red. He leaves it outside the bag. What is the probability that the second marble he pulls out of the bag is white? 6. If given two dice, what is the probability that the sum of the two numbers rolled will equal 7? 7. A coin is flipped 5 times. What is the probability of getting 5 heads in a row? |
Chapter 18 - Data Analysis
1. Find the Mean of this dataset (5, 8, -3, 12) 2. Find the Median of this dataset (5, 8, -3, 12, 8, 11, 9) 3. Find the Mode: (3, -2, 1, 4, 5, 9, 6, 4, 7) 4. Find the first quartile of this dataset: (2, -3, 5, 8, 2, 1, 5) 5. Find the mean, median and mode (in this order): (3, -3, 5, 11, 8, 3, 2, 3, 2) 6. Find the quartiles Range in this dataset: (3, -3, 5, 11, 8, 3, 2, 3, 2) 7. Find the Median and the Mode in the following Stem-and-Leaf: 1|18 2|357 3|1589 4|233468 5|3444479 6|4599 7|112 |
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Chapter 19 - Polynomials Revisited
1. Find the degree of the polynomial: x^3-3x^5+7 2. Simplify: 6x^7y^3z^9 / 3x^6y^3z 3. Divide x^3+125y^3 by x+5y. 4. Find the product: (x^4−5x+7)(x^4+2x+1) 5. Simplify the following expression: (2q^2+4q+7)-(3q^2-5) 6. Subtract 2x^2-3x+6 from 4x^2+10x-11. 7. If the polynomial x^5+x^4-x^3-x^2 is divided by x-2, what is the remainder? 8. Simplify (4x^2 - 25) / (2x + 5) 9. Simplify (49x^2 - 14x + 1) / (7x - 1) 10. Simplify (x^4 - 14x^2 - 32) / (x - 16) |
Chapter 20 - Exponents Revisited
1. If (300)(5000) = 15 * 10^p, p = ? 2. (3x10^3) x (2x10^5) x (2x10^11) = ? 3. If 4^x = 64, then 3^(x-1) = ? 4. Find the value of x such that: 2^(x-2) = 8^(5-x) 5. (x^3)^5 * x^(–4) = 6. If a and b are positive integers and 4^2a(4^2b)=256, what is the value of a+b? 7. (b^2 * b^3 * b^7)^(1/2)/(b^4 * b^x) = b, find x = ? 8. If x^2 = 11 and y^2 = 9 then x^4 + y^4 = ? 9. Solve for x: 5^2 + 12^(x-1) = 13^2 10. Solve 100^(3x-1) = 10^(2x+1) |
Chapter 21 - Sets and Functions Revisited
1. What is the domain of the given function? f(x)=(x+5) / (x+4)^2 2. Which of the following represents the domain of the function f(x)=V(2x+10)? 3. f(x)=x^2+24x-10. What is f(4)? 4. If F(x) = 2x^2 + 5 and G(x) = x - 1, what is F(G(x))? 5. If a(x) = 5x^3 + 2x, and b(x) = -3x, what is a(b(3))? 6. f(x)=x^2+1 and g(x)=x-3. Find g(f(2)). 7. If the average of two numbers is 4y and one of the numbers is 2y+z, what is the other number, in terms of y and z? 8. If f(x)=2x^2+4x+1, what does f(x+4) equal? 9. If f(x)=5x+21, what is f(2x^2+3x)? 10. Find f(g(x)) when f(x)=x^2, g(x)=3x-2, and x=4. |
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Chapter 22 - Equations Advanced
1. If a line has an equation of 3y=4x+3, what is the slope of a line that is perpendicular to the line? 2. If 5x + 3 = 12x + 4 - 2x - 7, then x = ? 3. If 3x^2 * (4-x)(2x+3) = 0, then what is the sum of all of the possible values of x? 4. John has 15 coins consisting of nickels and dimes that total $0.85. How many dimes does John have? 5. What is the sum of all the values of x that satisfy: x^2-5x=2x-6? 6. Solve for x : 3x^2-13x+16=4+2x^2 7. What is x^(-2) / x(-3)? 8. What is the y-intercept of y = 5 * (3^x)? 9. Solve: 4*[2^(x-1)] = 1/2 10. Solve for x in the following equation: log3(27) - log3(3)= logx(16) |
Chapter 23 - Systems and Inequalities Advanced
1. Find a+b from this system: 5a+6b=21 and 3a-5b=4 2. An amusement park charges both an entrance fee, and a fee for every ride. This fee is the same for all rides. Jenny went on 5 rides and paid 120 dollars. John went on only 4 rides and paid 100 dollars. What was the entrance fee? 3. The cost of buying 1 shirt and 2 pants is $90 and cost of buying 3 shirts and 4 pants is $300. Assume that all shirts have the same cost and all pants have the same cost. What is the cost of one shirt and one pair of pants in dollars? 4. If a+3b=4c and a+3b+4c=80, what is the value of c? 5. In a bakery, 3 scones and 4 donuts cost $10. Also 3 scones and 5 donuts cost $12. How much do donuts cost at the bakery? 6. The product of two positive numbers is 80. One number is 6 less than twice the value of the other number. What is the sum of the two numbers? 7. We have x^2-16 < 0, find the solution set for this inequality. 8. Solve: -5(x+4) >= 25+3x 9. What is the solution set for x^2 < 8x+9? 10. Give the solution set of the inequality: x^2+7x-18x-12 >= 0 |
Chapter 24 - Final Lessons and Review
1. Multiply: (2a - b - 3ab)(a - 2b + 1) 2. Find slope: 2x+5=-3y+4 3. Solve (1/3)x - 3/4 = 4x + 1 4. Solve for x: (x^2+2x-45)/(x+3)=10 5. Find x: 5^(2x-1) = 25^[(x^2-3x-4)/4] 6. Twelve people and only 10 chairs. How many arrangements are possible? 7. Box with marbles: 4 white, 5 red, 6 green. Extract one marble at a time and don't replace. First is green, second is red. What is the probability for the third to be green? 8. Find mean, median and mode for this set (-10,8,3,6,8,8,9,12,8,2). 9. Find a and b from this system: 2/a+3/b=13 and 3/a-2/b=0 10. What is the solution set for x2<12-11x? |
