EOC Math Review
d
A triangle's base is 14 inches less than 2 times its height. If "h" represents the height in inches, and the total area of the triangle is 54 square inches, which of the following equations can be used to determine the height? a) 2h² - 14h = 54 b) 7h - h² = 54 c) 14h - 2h² = 54 d) h² - 7h = 54
b
Solve: s² + 14s + 49 = 0 a) 7,7 b) -7,-7 c) -7,7 d) -9,-1
b
The Abdul family is comparing the costs of two different high-speed Internet services. With plan A, equipment installation is $199, and the monthly fee is $50. With plan B, the installation is $50, with a $90 monthly fee. Which of the following is a function rule for Plan A? a) f(x) = 50x - 199 b) f(x) = 50x + 199 c) f(x) = 90x + 50 d) f(x) = 90x - 50
c
The directions on a turkey tell you to cook the turkey 20 minutes per pound. Which of the following is a function in function notation for this situation where x is the number of pounds? a) f(x) = 20 + x b) f(x) = 20 - x c) f(x) = 20x d) f(x) = 20/x
d
The graph of y = (1/2)ˣ is translated down 2 units. What is the equation of the translation? a) f(x) = (1/2)ˣ⁺² b) f(x) = (1/2)ˣ⁻² c) f(x) = (1/2)ˣ + 2 d) f(x) = (1/2)ˣ - 2
c
What is the apparent range of the function of x as shown? a) The set of all real numbers. b) The set of all real numbers greater than or equal to 2. c) The set of all real numbers greater than or equal to 0. d) The set of all real numbers greater than or equal to -2.
b
What is the axis of symmetry of the following quadratic equation? y = a(x - b)(x - c), assume a ≠ 0. a) x = -b/2a b) x = (b + c)/2 c) x = -(b + c)/2 d) x = b/2a
c
What is the domain of the geometric sequence an = -5ⁿ⁻¹? a) all real numbers b) all positive numbers c) all positive whole numbers d) all positive whole numbers except 1
c
What is the next term in the pattern below? 2, 4, 8, 16, 32, 64,... a) 96 b) 118 c) 128 d) 136
b
What is the vertex of the graph of the following quadratic equation? y = -4(x + 7)² - 5 a) (-4,-5) b) (-7,-5) c) (7,5) d) (-7,5)
a
When is the function f(x) symmetric about the y-axis? a) if f(-x) = f(x) b) if f(x) = -f(x) c) if -f(x) = x d) if f(x) = f(x - 1)
b
Find the common ratio of the geometric sequence. 2, -8, 32, -128,... a) 4 b) -4 c) 64 d) -64
c
The graph of y = 2ˣ is reflected over the y-axis. What is the equation of the reflection? a) y = -2ˣ b) y = 1 - 2ˣ c) y = 2⁻ˣ d) y = 2ˣ⁻¹
b
The nth term of a geometric sequence given by the rule an = 3(-5)ⁿ⁻¹. What is the common ratio of the geometric sequence? a) 3 b) -5 c) -1 d) -15
e
Which of the following is the function of the graph? a) f(x) = |x| b) f(x) = √x c) f(x) = x d) f(x) = x² e) f(x) = 1/x
d
Which of the following is the input-output table for the function y = 6x + 5 a) Input x | 1 2 3 4 5 Output y | 1 2 3 4 5 b) Input x | 1 2 3 4 5 Output y | 10 20 30 40 50 c) Input x | 1 2 3 4 5 Output y | 6 12 18 24 30 d) Input x | 1 2 3 4 5 Output y | 11 17 23 29 35
a
Which of the functions represents the input-output table? Input x | Output y 0 | -7 1 | -5 2 | -3 3 | -1 4 | 1 a) y = 2x - 7 b) y = 2x + 7 c) y = 2x + 6 d) y = x -6
d
Which of the functions represents the input-output table? Input x | Output y 0 | 6 1 | 8 2 | 10 3 | 12 a) y = 3x + 6 b) y = 2x + 7 c) y = 2x - 6 d) y = 2x + 6
b
Which type of function does this represent? f(x) = -f(-x) a) symmetric b) odd c) even d) neither odd nor even
c
Which type of function does this represent? f(x) = f(-x) a) symmetric b) odd c) even d) neither odd or even
a
Write a rule for the nth term of the geometric sequence. 24, -18, 27/2, -81/8,... a) an = 24(-3/4)ⁿ⁻¹ b) an = 24(3/4)ⁿ⁻¹ c) an = -3/4(24)ⁿ⁻¹ d) an = 3/4(24)ⁿ⁻¹
a
Write the equation in the form y = a(x - h)² + k y = x² + 6x + 11 a) y = (x + 3)² + 2 b) y = (x - 3)² + 2 c) y = (x + 3)² + 4 d) y = (x - 3)² + 4
c
Write y = (x + 2)² + 4 in standard form. a) y = x² - 4x - 8 b) y = x² - 4x + 8 c) y = x² + 4x + 8 d) y = x² + 4x - 8
b
A local gym charges nonmembers $8 per day to use the volleyball courts. Members pay a yearly fee of $150 and $2 per day to use the volleyball courts. How many days must you use the volleyball courts to justify becoming a member? a) at least 10 b) at least 25 c) at least 50 d) at least 75
b
A rectangular garden, with length four times its width, is to be expanded so that both sides are increased by 5 yards. Which expression models the area of the expanded garden? a) 5x + 10 b) 4x² + 25x + 25 c) 4x² + 10x + 25 d) 4x² + 25
d
Choose the statement that is true for the following numbers. Row A : x in x² + 4 = 13 Row B : x in x² + 3 = 19 a) The number in column A is bigger. b) The number in column B is bigger. c) The two numbers are the same. d) The relation cannot be determined from the information given.
a
Factor the expression. x² + 3x - 40 a) (x - 5)(x + 8) b) (x - f)(x - 8) c) (x + 5)(x - 8) d) (x + 5)(x + 8)
d
Factor the following terms by grouping: ra + rb + sa + sb a) (r + s) + (a + b) + (r +s) + (a + b) b) (r + s) + 2(a + b) c) 2(a + b) × (r + s) d) (r + s)(a + b)
b
Factor this polynomial completely 25s³ - 100s² - s + 4 a) (s - 1)(5s)(s - 4) b) (s - 4)(5s - 1)(5s + 1) c) 5s(5s² - 20s + 4) d) (s - 4)(5s - 20)
a
Factor this polynomial completely n³ + 5n² - 9n - 45 a) (n - 3)(n + 3)(n + 5) b) 2(n - 3)(n + 5) c) (n + 3)²(n + 5) d) n - 45(n² - 5n - 9)
b
Factor this polynomial completely x³ - 3x² - 16x + 48 a) 4(x - 1)(x - 3) b) (x + 4)(x - 4)(x - 3) c) (x² - 16)(x - 3) d) x²(x - 3) - 16(x - 3)
c
Factor this polynomial completely x⁴ - 25 a) 2(x - 5)2(x + 5) b) (x - 5)(x + 5)(x - 5)(x + 5) c) (x² + 5)(x² - 5) d) 2(x² + 5)
a
Find the common difference of the arithmetic sequence. -4.6, -5.3, -6, -6.7,... a) -0.7 b) -0.8 c) 0.7 d) 0.8
a
Find the common ratio of the geometric sequence. 125, 75, 45, 27, 81/5,... a) 3/5 b) 2/3 c) 1 1/2 d) 1 2/3
c
Find the sum of the first 12 terms of arithmetic series. -11 -8 -5 -2 +... a) 132 b) 69 c) 66 d) 63
a
Find the value of f(x) = 2x - 1/6 when x = 2. a) f(2) = 23/6 b) f(2) = 1/2 c) f(2) = 25/6 d) f(2) = -23/6
a
Find the x-intercepts of the graph of y = x² - 11x + 18. a) 2,9 b) 3,5 c) -3,-5 d) -2,-9
c
For which value of n would Sn = 248? 3 + 11 + 19 + 27 ... a) 31 b) 16 c) 8 d) 62
b
For which value of n would Sn = 256? 4 + 12 + 20 + 28 ... a) 16 b) 8 c) 32 d) 24
b
Give the first four terms of the geometric sequence for which a1 = 9 and r = 2. a) 9, 11, 13, 15 b) 9, 18, 36, 72 c) 9/2, 9/4, 9/8, 9/16 d) 18, 36, 72, 144
c
How would you transform the graph of y = 1.4ˣ to produce the graph of y = 1.4⁻ˣ? a) reflect the graph of y = 1.4ˣ over the line y = x b) reflect the graph of y = 1.4ˣ over the line y = 0 c) reflect the graph of y = 1.4ˣ over the y-axis d) reflect the graph of y = 1.4ˣ over the x-axis
a
How would you translate the graph of y = -x² to produce the graph of y = -(x - 6)²? a) translate the graph of y = - x² right 6 units b) translate the graph of y = -x² left 6 units c) translate the graph of y = -x² down 6 units d) translate the graph of y = -x² up 6 units
d
How would you translate the graph of y = 0.2x² to produce the graph of y = 0.2(x + 3)² - 4? a) translate the graph of y = 0.2x² 4 units right and 3 units up b) translate the graph of y = 0.2x² 4 units left and 3 units up c) translate the graph of y = 0.2x² 3 units right and 4 units down d) translate the graph of y = 0.2x² 3 units left and 4 units down
a
How would you translate the graph of y = 3ˣ to produce the graph of y = 3ˣ⁺⁴? a) translate the graph of y = 3ˣ left 4 units b) translate the graph of y = 3ˣ right 4 units c) translate the graph of y = 3ˣ up 4 units d) translate the graph of y = 3ˣ down 4 units
d
How would you translate the graph of y = x² to produce the graph of y = (x +5)²? a) translate the graph of y = x² up 5 units b) translate the graph of y = x² right 5 units c) translate the graph of y = x² down 5 units d) translate the graph of y = x² left 5 units
d
Kim is shipping a box. The dimensions of the box must meet the following dimensions: The length (in inches) is 4 times some value "x". The width (in inches) is "x" plus 1. The height (in inches) is the difference between 4 and x. Which equation represents the volume "V" (in cubic inches) of the box? a) (x + a)(4 - x) = V b) (x + 1)(4 - x)/4x = V c) 4x + (x + 1) + (4 - x) = V d) 4x(x + 1)(4 - x) = V
d
Multiply (4x + 1)(4x - 3) a) 16x² - 16x - 3 b) 16x² - 8x + 3 c) 16x² + 8x - 3 d) 16x² - 8x - 3
c
Multiply (x + 4)(x + 7) a) x² + 28x + 11 b) x² + 28 c) x² + 11x + 28 d) x² + 28x + 28
a
Multiply (x + 5)(x² - 2x + 3) a) x³ + 3x² - 7x + 15 b) x² - 3x + 15 c) x³ - 2x² +15 d) x³ + 3x² - 10x + 15
b
Rewrite (2x⁻²y)(3y⁻²) with a positive exponent. a) 6y⁻³/x² b) 6/x²y c) 6y/x² d) 5y/x²
a
Simplify a⁴ + 3a² - (5a - 3)(-7a). a) a⁴ + 38a² - 21a b) a⁴ - 32a² - 21a c) a⁴ + 3a² - 26a d) a⁴ + 3a² + 35a - 21
b
Simplify: (7³⋅8⁶)⁶ a) 7⁹⋅8¹² b) 7¹⁸⋅8³⁶ c) 56⁵⁴ d) 56¹⁵
a
Simplify: (p³q⁴)³ a) p⁹q¹² b) p⁶q¹² c) p⁹q⁴ d) p⁶q⁷
c
Simplify: (v⁴/w⁸)⁴ a) v⁸/w¹² b) v¹⁶/w⁸ c) v¹⁶/w³² d) v⁸/w⁸
a
Simplify: 11√25 a) 55 b) 27.5 c) 16 d) 137.5
a
Simplify: 7√121 a) 77 b) 84 c) 91 d) 70
c
Simplify: √20 a) 6 b) 4√5 c) 2√5 d) 3√15
d
Simplify: √27 a) 3 b) 4√7 c) 2√7 d) 3√3
a
Solve the equation 2x -4y = 4 for y. Write as a function of x. a) f(x) = 1/2x - 1 b) f(x) = x - 2 c) f(x) = 2x - 2 d) f(x) = 1/2x + 2
b
Solve the equation by factoring. x² + 13x +30 = 0 a) 3,10 b) -3,-10 c) 5,6 d) -5,-6
c
Solve the equation by factoring. x² - 19x + 84 = 0 a) 8,11 b) 6,14 c) 7,12 d) 2,42
b
Solve the equation by factoring. x² - 34x - 240 = 0 a) 8,30 b) -6,40 c) 2,-12 d) 1,24
b
Solve the equation by factoring. x² - 7x + 12 = 0 a) -3,-4 b) 3,4 c) 2,6 d) -6,2
b
Solve the inequality algebraically. x² + 2x ≥ 48 a) -8 ≤ x ≤ 6 b) x ≤ -8 or x ≥ 6 c) x ≤ -6 or x ≥ 8 d) -6 ≤ x ≤ 8
b
Solve: b² + 17b + 30 = 0 a) 15,2 b) -15,-2 c) -15,2 d) -2,15
a
Solve: x² + 32x + 192 = 0 a) -24,-8 b) 24, -8 c) 24,8 d) -24,8
a
Solve: x² + 4x - 21 = 0 a) -7,3 b) 7,3 c) -7,-3 d) 7,-3
b
The number of new cars purchased in a city can be modeled by the equation C = t² + 148t + 4320, where C is the number of new cars purchased and t = 0 corresponds to the number of new cars purchased in 2000. According to the table, in what year will the number of new cars purchased reach 5565? Year | # Cars 2001 | 4469 2002 | 4620 2003 | 4773 2004 | 4928 a) 2007 b) 2008 c) 2009 d) 2010
c
The rule for an arithmetic sequence is an = 4n + 2. For which value of n would the sum of the series be equal to 126? a) 9 b) 8 c) 7 d) 6
a
The sides of a rectangle have length x + 7 and width x - 3. Which equation below describes the area, "A", of the rectangle in terms of "x"? a) A = x² + 4x - 21 b) A = x² + 10x - 21 c) A = 4x + 8 d) A = 2x + 4
d
Two terms of a geometric sequence are a1 = -8 and a2 = -16. Find a rule for the nth term. a) an = -8(-8)ⁿ⁻¹ b) an = -8(1/2)ⁿ⁻¹ c) an = -8(8)ⁿ⁻¹ d) an = -8(2)ⁿ⁻¹
c
Use the quadratic formula to solve the equation. x² + 5x + 1 = 0 a) 5+√21 / 2, 5-√21 / 2 b) 5+√29 / 2, 5-√29 / 2 c) -5+√21 / 2, -5-√21 / 2 d) -5+√29 / 2, -5-√29 / 2
b
What are the first four terms of the sequence an = 2ⁿ⁻¹? a) {0, 1, 3, 7} b) {1, 2, 4, 8} c) {1/2, 1, 2, 4} d) {1, 1/2, 1/4, 1/8}
c
What are the solutions of the equation? x² + 2x - 15 = 0 a) x = -3 or x = 5 b) x = -1 or x = -15 c) x = 3 or x = -5 d) x = -1 or x = 15
a
What are the solutions of the equation? x² - 6x = 0 a) 0,6 b) 0,-6 c) -6,6 d) 1,6
a
What are the zeros of the function f(x) = 3x² + 5x - 2 a) -2 and 1/3 b) -1 and 2/3 c) -1/3 and 2 d) 2/3 and 1
Put it on my bill!
What did Daisy Duck say when she bought lipstick?
b
Where will the graphs of f(x) = 3x - 2 and g(x) = -6x + 7 intersect? a) at the origin b) at point (1,1) c) at point (2,3) d) they will not intersect, the lines are parallel
d
Where will the graphs of f(x) = 60x + 40 and g(x) = 60x + 5 intersect? a) at the origin b) at point (1,1) c) at point (2,3) d) they will not intersect
a
Where will the graphs of f(x) = x and g(x) = 2x intersect? a) at the origin b) at point (0,2) c) at point (2,4) d) they will not intersect, the lines are parallel
d
Where will the graphs of f(x) = x and g(x) = x + 3 intersect? a) at the origin b) at point (0,3) c) at point (3,3) d) they will not intersect, the lines are parallel
b
Which function does the graph represent? a) -x² b) x² c) -x² + 1 d) x² - 1
b
Which function does the graph represent? a) -x² + 1 b) x² c) x² + 1 d) -x²
b
Which function is graphed below? a) f(x) = -2ˣ b) f(x) = 2ˣ c) f(x) = -2ˣ + 1 d) f(x) = 2ˣ + 1
d
Which function rule matches the input-output table? Input x | 1 2 3 4 5 Output y | 12 16 20 24 28 a) y = 4 + 8x b) y = 5 + 7x c) y = 7 + 5x d) y = 8 + 4x
d
Which function rule matches the input-output table? Input x | 1 2 3 4 5 Output y | 9 12 15 18 21 a) y = 5 + 4x b) y = 4 + 5x c) y = 3 + 6x d) y = 6 + 3x
d
Which is equivalent to (4⁹)²? a) 36² b) 4¹¹ c) 4³⁶ d) 4¹⁸
b
Which of the following functions equals 14 when n equals 2? a) f(n) = n + 13 b) f(n) = 2(n + 5) c) f(n) = 6n d) f(n) = 15n/2
c
Which of the following is an even function? a) x³ b) x⁵ c) x⁶ d) x
a
Which of the following is an odd function? a) x b) 1 c) x² d) x⁴
b
Which of the following is equal to (7x³ - 3x² + 5x - 5) + (5x² - 8x - 3)? a) 7x³ - 11x² + 5x - 8 b) 7x³ + 2x² - 3x - 8 c) 12x³ + 2x² - 3x - 8 d) 10x³ - 3x² - 3x - 8
b
Which of the following is the difference √112 - √63, in simplified form? a) -5√7 b) √7 c) √112 - 3√7 d) √112 - 9√7
a
Which of the following is the function of the graph? a) f(x) = |x| b) f(x) = √x c) f(x) = x d) f(x) = x² e) f(x) = 1/x
b
Which of the following is the function of the graph? a) f(x) = |x| b) f(x) = √x c) f(x) = x d) f(x) = x² e) f(x) = 1/x
c
Which of the following is the function of the graph? a) f(x) = |x| b) f(x) = √x c) f(x) = x d) f(x) = x² e) f(x) = 1/x
d
Which of the following is the function of the graph? a) f(x) = |x| b) f(x) = √x c) f(x) = x d) f(x) = x² e) f(x) = 1/x
c
Write a rule for the nth term of the geometric sequence for which a1 = 7 and r = 1/3. a) an = 1/3(729)ⁿ⁻¹ b) an = 1/3(729)ⁿ⁻¹ c) an = 729(1/3)ⁿ⁻¹ d) an = 729(1/3)ⁿ⁻¹
a
Write the quadratic equation in vertex form. Then identify the vertex. y = 3x² - 36x + 101 a) y = 3(x - 6)² - 7 Vertex = (6,-7) b) y = 3(x - 6)² -7 Vertex = (-6,-7) c) y = 3(x + 6)² - 7 Vertex = (6,-7) d) y = 3(x + 6)² - 7 Vertex = (-6,-7)
b
Write y = (x - 1)² + 2 in standard form. a) y = -x² -2x + 1 b) y = x² - 2x + 3 c) y = x² + 2x + 3 d) y = -x² + 2x + 1
b
Write y = -(x - 2)² - 3 in standard form. a) y = -x² - 4x + 7 b) y = -x² + 4x - 7 c) y = -x² - 4x - 7 d) y = -x² + 4x + 7
