ACCUPLACER REVIEW * PERRY HIGH SCHOOL APRIL 2015 * The information in this packet is based on the practice tests available at: http://www.riosalado.edu/testing/placement/Pages/Math-Practice-Placement.aspx 1 (http://www.learnnc.org/reference/number+sense) 2 http://dl.uncw.edu/digilib/mathematics/algebra/mat111hb/pandr/quadratic/quadratic.html 3 https://partiallyderivative.wordpress.com/2013/12/04/function-transformations-card-matching-activity/ https://secure-media.collegeboard.org/digitalServices/pdf/accuplacer/accuplacer-texas-success-initiative-assessment-sample-questions.pdf ANOTHER REVIEW CAN BE FOUND AT: http://www.ccm.edu/admissions/placementTesting/cal/mathreviewsheets.aspx THINGS TO REMEMBER: http://regentsprep.org/regents/math/algtrig/formulasheetalgebra2trig.pdf NUMBER SENSE: An intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations. 1 Write < or > between the pair of numbers to make the statement true. -43, -41 > < Write < or > between the pair of numbers to make the statement true. -46.8 ___________ -46.08 If x ≠ 0, then = -4x - 4x If x ≠ 0, then 10 320 . Explain why x cannot equal 0: Which of the following number sentences is true? -6 < 0 < 3 < < -3 -6 > -5 > -3 -3 > 0 > -5 Order the following from least to greatest: 48/3 9.1 √75 15 3 7 5 8 Which of the following is the greatest? 3 ÷ (-4) 3 × (-4) 3 - (-4) 3 + (-4) Which is greatest? 7 + (-12) -7 - (-12) 7 - (-12) -7 + (-12) = 6 15 14 -5 −12 + (−13) 5 Which of these expressions is negative? -(2 - 3) 3(2 - 3) 3 - (2 - 1)
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ACCUPLACER REVIEW - Chandler Unified School … REVIEW* ... SOLVE: ... Graph the functions using the x- and y-intercepts. Then, identify the slope of the line. 6x + 4y = 12
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ACCUPLACER REVIEW*
PERRY HIGH SCHOOL APRIL 2015
* The information in this packet is based on the practice tests available at: http://www.riosalado.edu/testing/placement/Pages/Math-Practice-Placement.aspx
ANOTHER REVIEW CAN BE FOUND AT: http://www.ccm.edu/admissions/placementTesting/cal/mathreviewsheets.aspx
THINGS TO REMEMBER: http://regentsprep.org/regents/math/algtrig/formulasheetalgebra2trig.pdf
NUMBER SENSE: An intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations. 1 Write < or > between the pair of numbers to make the statement true. -43, -41
> <
Write < or > between the pair of numbers to make the statement true.
QUADRATIC FUNCTIONS: A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are
numbers with a not equal to zero. The graph of a quadratic function is a curve called a parabola. 2
GENERAL _____________________ VERTEX: __________________ FACTORED: _____________________
HOW TO FACTOR: HOW TO GRAPH: y = x2+8x+7
y = 3x2 -5x -2 1. Identify the vertex (find axis of symmetry and corresponding y value.)
2. Find the x and y-intercepts. 3. Connect the points.
What is the quadratic formula?
What is the discriminant? What does it tell us?
Find the roots of the functions (solve by factoring, quadratic formula, or complete the square, you choose)
f(x) = 4x2 + 20 f(x) = 3x2 + 6x - 8 375 2 xxxg
Re-write the function 223 xxf in standard form.
Given that g(x) = x2 + 6x + 10 and f(x) = -3x-4, determine the solutions to g(x) = f(x)
Given that g(x) = 3x2 + 5x + 1 and f(x) = 4x+5, determine the solutions to g(x) = f(x)
Solve x2+8x+7=0 by…
….Factoring …Completing the Square …Quadratic formula
Find the discriminant. State the number and type of solutions. 882 2 xxy
Identify the vertex. State whether it is a maximum or minimum.
y = x2 + 8x +7 y=5(x-4)2 + 6
____ Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the
parabola in vertex form.
a. c.
b. d.
What is the maximum or minimum value of the function? What is the range?
____
a. minimum value: – 9
range:
c. minimum value: – 9
range:
b. minimum value: –1
range:
d. minimum value: 1
range:
If 6x2 + 5x - 21 = (2x - 3)(ax + b). What is the value of a + b?
-11 -4
7 10
Factor
21x2 – 8x - 5
x2 - 4x - 5 = 0 when x =
4 or -1 1 or 9
-1 or 5 1 or 5
4x2 -7x -2 = 0 when x =
(5x - 3)2 =
25x2 - 30x + 9
25t2 -15t + 9
25x2 + 9
5t2 - 3
(7x + 10)2
x2 - =
Factor:
(49x2 –1
16)
(2t - 3)(t + 4) =
2t2 + 5t – 12 2t2 + t – 12
t2 + t – 12 2t2 - 5t - 12
(5x + 4) (x -7)
r2 - 25 =
(r - 5)(r - 5) (r - 5)(r + 5)
(5 + r)(5 - r) (5 - r)(5 - r)
Factor
(9x2 – 121)
Factor: (x + 2)2 - 4y2
(x + 2 - 2y)(x + 2 + 2y) (x + 2 - 2y)2
(x + 2 - 4y)(x + 2 + 4y) (x + 2 + 2y)2
x2 + 4 - 4y2
Factor: 25a2 – 9b2
If a = 3b , what is the value of 9(b - 1)2 in terms of a?
3a2 - 6a + 9 a2 - 3a + 1
a2 - 6a + 9 a2 - 3a + 9 27a2 - 9
If a = 5x, what is the value of 25(x+2)2 in terms of a?
If f is a quadratic function with no real zeros, which of these is f?
x2 + x + 12 x2 + x – 12
x2 - 3 x2 + x x2 - 3x + 2
If f is a quadratic function with exactly one real zero, which of these is f?
a) x3 – 2x2 –x + 2 b) x2 + 5x + 4 c) 9x2 -6x +4 d) x2 + 2x + 3
POLYNOMIAL FUNCTIONS:
A polynomial function is a function with whole number integer powers. It has one or more
roots (x-intercepts). You should know:
1. The first term determines the end behavior. How?
2. To graph, identify the end behavior, y-intercept, and x-intercepts. Then, connect the
dots.
3. Not all polynomial equations can be solved by factoring in the traditional sense. When
you cannot factor by another method, you may have to use synthetic division to factor.
Consider the leading term of each polynomial function. What is the end behavior of the graph?
Write the polynomial in factored form & identify the roots of the function: 4x3 + 8x2 – 96x x3 + 9x2 + 18x Use synthetic division and factor the equation completely and then graph the function. Note: x = 5 is one root. f(x) = x3 – 5x2 +16x -80
If x3 + ax – 8 is divided by x - 1, the remainder is -4. what is the value of a?
7 -76 3 8 -7
Use synthetic division to evaluate f(2) if f(x) = 3x4 -5x2 + 2.
PROBABILITY
Your friend is having a party and has 15 games to chose from. There is enough time to play 4 games. In how
many combinations of 4 games can games be chosen?
How many different numbers can be made using any three digits of 12,378?
Find the mean, mean, mode, and range of the data: 4, 8, 6, 7, 5, -4, 4, 6, 7, 7, 9, 10
Ryan has grades of 87%, 78%, and 95% on his last 3 tests. What is the minimum grade he can get on his 4th test in order
to get an A average (90% or above) on his tests?
Kyle has grades of 85, 92, 96, and 89% on his first tests. What score does he need on his final test to have an average of
92? (assume all tests are weighted equally).
In a school election, there are 3 candidates for president, 4 for vice-president and 4 for treasurer. How many different outcomes are there for the election?
48 12 24 11 10
Teresa has 5 shirts, 3 pairs of shorts and 2 hats. How many different outfits can she wear consisting of one of each?
15. There are 20 children in the cast of a class play, and 8 of the children are boys. Of the boys, 4 have a speaking part in the play, and of the girls, 8 do not have a speaking part in the play. If a child from the cast of the play is chosen at random, what is the probability that the child has a speaking part? A. 2/5 B. 1/2 C. 3/5 D. 3/4
City High Temp
A t°F
B 87°F
C 81°F
D 62°F
E 93°F The table above shows the high temperature last Thursday for five cities, A through E. If the median of the Thursday high temperatures for these cities was 81 F, ° which of the following could NOT have been the high temperature last Thursday for City A ? A. 85 F° B. 75 F° C. 65 F° D. 55 F
IMAGINARY NUMBERS
What are imaginary numbers?
Simplify the following:
(4+10i)(3-2i) – 𝟒𝒊(𝟐 + 𝟑𝒊) − √−𝟑𝟔
𝟓 + √−𝟏𝟔 √−𝟓𝟐 𝟒
𝟑−𝒊
If (2 + i)(3 + i) = a + bi, what is the value of a + b?
3 2 10 5 9
If (-6+i)(4+7i) = a + bi, what is the value of a + b?
COMPOSITE & INVERSE FUCNTIONS
1. What is a composite function?
2. How do you find an inverse function?
3. How can you prove that two functions are inverse functions using composite functions?
1) Given: f(x) = 3x + 5 g(x) = 4x2 +3 2) Find the inverse of 3) Are f(x) and g(x) inverse functions?
f + g g – f 𝑓(𝑥) =𝑥−3
5 f(x) = 3x + 5 𝑔(𝑥) =
1
3𝑥 − 5
f(g(x)) g(f(x))
Given the following table, find f-1(-2).
If f(x) = 2x + 1 and g(x) = x2 + 1, then f(g(x)) =
The difference of two numbers is seven and their sum is 23. What is the product of the two numbers?
120 56 184 161
The difference of two number is 95. The product of the two numbers is -2226. What are the two numbers?
If 10x - 6 = 7, then x =
1
3x – 8 = 24
If y = 2x - 3 and x = 2y, then what is the value of x?
-2 -3 2 1
If 2y = 3x -14 and x = 3y. Then, x =
Use the given values of the variables to find the value of the expression. 6x + 2y for x = 5, y = 9
72 40 48 64
Evaluate -8y + 7z for x = -3 and y = 2
If = a + b , then a + b =
7 4 11 3 9
If f(x) = x2 + 2(x + 1), then f(2) =
12 16 8 4 20
If g(x) = 3x2 + 7x-1, find g(3)
If , what is the value of a?
5 3 -2 7 4
What is the value of y?
For the given system of 3 equations, find x.
-1 1 2 3
Solve the system:
{
𝑥 + 2𝑦 + 𝑧 = 16−𝑦 + 3𝑥 = 5
𝑧 + 𝑦 = 9
Which of the following functions contains the points (0, 1), and (2, 1)?
Which of the following represent a function that passes through (2,3) and (4, 2)?
a. y = 0.5x +3 c. y =|x-1| b. x - 2y = 4 d. –x -2y = 4
GEOMETRY & TRIGONOMETRY
SOH CAH TOA
1. The angle of depression from a ship to a rock
on the ocean floor is 21 . After sailing 245 m,
the ship is directly above the rock. At this point,
what’s the distance between the rock and the
ship?
2. The angle of elevation from a leaf on the
ground to the top of a tree is 23 . The leaf is
54m from the base of the tree. How tall is the
tree?
Draw the angle and find a coterminal angle that is less than 360°: Find the csc30° 530° 23∏/4
Find the tan135° Graph the function sinϴ
Graph the points (1,2) and (7, 10). Find the distance between the two points and label the midpoint. Find the volume of a sphere with diameter 20. Find the volume of a sphere with radius of 6 and height of 9.
ABC is equilateral with each side having length 6, and DEFG is a square.
If D and E are the midpoints of AB and AC, the the perimeter of DEFG is
24 18 12 20 16
Given AC = 42, CB = 46, AB = 48. D, E, F are midpoints. Find the perimeter of triangle DEF.
In a right triangle, the cscϴ= 9/4, find the cotϴ.
What is the difference between the largest and the
smallest y values of the function y = ?
4 2 0 1
Complete a table of values for the function 𝑦 =𝑐𝑜𝑠𝜃.
What is the difference between the largest and smallest y values of the function?
If cos θ = , then θ could not be
420 300 -60 60 30
If csc θ is undefined, then sin θ =
Which of the following functions contains the
point ?
y = 2sin x y = csc x y = tan x
y = 2sec x y = 2cot x
Evaluate: sec 𝜋
3
Arithmetic Review
Four people are going to equally share a lunch tab of $38.40. How much does each person owe?
1.2 × 0.03 =
22.3 - 8.46 =
Which of these is not equivalent to 45/100?
0.55 0.45 45%
1.025 x 0.04 1580 × 0.044 is closest to
A runner's time for a 100 meter race improved from 18.3 seconds to 16.4 seconds. By how many seconds did he reduce his time?
70% of the animals in the zoo are mammals. If there are 80 mammals. How many animals are there in the class?
A car gets 42 miles to the gallon. How many miles will it be able to go on 6.5 gallons?
In Mr. Smith's math class, 2/3 of the 27 students are girls. How many girls are in the class?
Karl’s average time to finish a book was 3.5 weeks. After completing a speed reading course, his average time to finish was 2 weeks. By how much did he improve his reading time?
Use long division to find:
0.5488 ÷ 5.6
73.5 × 125 is closest to
100 1,000
10,000 100,000
What is 85% of 200? The distance
between and is
An item originally priced at $120 is sold at a 20% discount. What is the new price?
$96 $24 $100 $240
What percent is 14 of 35?
21 40 35 25
20% of a number is 15. What is the number?
75 300 30 3
+ =
÷ =
22
5÷ 3
is equivalent to
3.75% 3.8% 37.5%0.375%
÷ =
-
6
Which of these inequalitites is false?
0.04 < 0.045 < 0.05
0.1 < (0.4)2 < 0.2
0.1 < 0.2 < 0.25
1 < 1.25 < 1.2
The bill for 8 people to eat pizza was $54.70. Since Tommy bought a special glueten-free meal, he paid his own dinner of $8.50. Everyone else split the remaining bill evenly. How much does each person owe?
13.2 × 0.2 =
15.4 2.64 0.264 26.4
=
+ is closest to
4 13 5 3
LOGARITHMIC FUNCTIONS & EXPONENTIAL EQUATIONS
Logarithmic functions are the inverse “undo” exponential functions.
3 Rules for Condensing: Rules for solving: Product – 1. Condense into one log function on either side of equal sign. Quotient Rule – 2. Use the Power Rule to move variables out of the exponent Power Rule - 3. Solve for the variable.
Write the equation in logarithmic form. Write the equation in exponential format: log3x+4 = 16
Evaluate the logarithms:
log81 3
Write the expression as a single logarithm.
Expand the logarithmic expression.
Solve the exponential/logarithmic equation.
Does the function represents exponential growth or exponential decay?
In a particular region of a national park, there are currently 330 deer,
and the population is increasing at an annual rate of 11%.
a. Write an exponential function to model the deer population.
b. Explain what each value in the model represents.
c. Predict the number of deer that will be in the region after five years. Show your work
INTEREST EQUATIONS:
Continuously By Period A = Pert A = P(1+ r/n)nt
If Carlos has $8,000 to invest for the next 5 years, should he put it in account A or B?