Choice b is “five hundred twelve and sixteen hundredths.” Choice c is “five hundred twelve thousand, one hundred sixty.” Choice d is “fifty one and two hundred sixteen thousandths.” Choi
Trang 1P r a c t i c e Q u e s t i o n s A n s w e r s a n d E x p l a n a t i o n s
1 Choice a is correct The word and indicates a decimal point Therefore, the decimal point should go
after five hundred twelve and before sixteen thousandths The number 16 must end in the thousandths place, which is three digits to the right of the decimal The correct answer is 512.016
Choice b is “five hundred twelve and sixteen hundredths.”
Choice c is “five hundred twelve thousand, one hundred sixty.”
Choice d is “fifty one and two hundred sixteen thousandths.”
Choice e is “five hundred twelve and sixteen ten thousandths.”
2 Choice f is correct First, change the fractional parts of the problem to have the common denominator
of 12
4142− 1192
Subtract the numerators Since 4 is less than 9, you must borrow one whole from the whole number 4.
This means that you are adding 1122to the first fraction
31162− 1192
Subtract the fractional parts then the whole numbers The final answer is 2172
3 Choice b is correct The correct order of operations must be used to simplify the expression You may
remember this as PEMDAS or “Please Excuse My Dear Aunt Sally.” The P stands for parentheses or any grouping symbol Absolute value is a grouping symbol, so it will be done first
|−8| + 4 × 23=
8 + 4 × 23
Next, perform the exponent part
8 + 4 × 8
Then, the multiplication
8 + 32
Last, the addition
The final answer is 40
4 Choice g is correct This problem can be approached a couple of different ways The simplest way
might be to look at multiples of 4 and 5 until the multiples add to 18 If both 4 and 5 are multiplied by
2, they become 8 and 10 8 plus 10 is 18 Therefore, there are 8 boys and 10 girls in the class
The problem can also be done with an equation
4x + 5x = 18
When solved, x = 2 Multiply 4 by 2 to find that there are 8 boys.
Trang 25 Choice c is correct To find the median, place the numbers in order from least to greatest and find the
middle number In order, the numbers are:
0.008, 0.024, 0.024, 0.095, 0.1, 0.3
Since there are an even number of numbers, there are two middle numbers (0.024 and 0.095) Take the average of these two middle numbers by adding them and dividing the sum by two The answer is 0.0595
6 Choice h is correct Use the vertical line test to see if each graph is a function A graph is NOT a
func-tion if vertical lines drawn through the graph hit the graph more than once
7 Choice d is correct When multiplying by 105you move the decimal point 5 places to the right
The answer is 460,000
Another way to look at the problem is to recognize that 105= 100,000 and multiply 4.6 by 100,000 The answer is 460,000
8 Choice g is correct 35= 3 × 3 × 3 × 3 × 3 = 243 The answer is 243
9 Choice a is correct Consecutive odd integers starting with 3 are being added to find the next number.
Therefore, 11 must be added to 24 to find the next number The answer is 35
You may also notice that the numbers can be found using the expression n2− 1 where n is the place in the pattern We are looking for the sixth number, so n = 6 62− 1 = 35 The answer is 35
10 Choice h is correct First, you can eliminate choices f and i because they contain numbers that are not
prime Next, use a factor tree to determine the prime factorization
The prime factorization of 84 is 2 × 2 × 3 × 7, which can be written in exponential notation as 22× 3 ×
7 The answer is 22× 3 × 7
84
0, 3, 8, 15, 24,
+3 +5 +7 +9 +11
4.60000 = 460,000
Trang 311 Choice c is correct To easily see the slope, change the equation into the form y = mx + b The equation
is then y = 73x + 3 The coefficient of x is the slope.73is the answer
12 Choice f is correct The perimeter is twice the width plus twice the length: P = 2w + 2l Insert 20 for P
and 4 for w, then solve for l.
20 = 2(4) + 2l
20 = 8 + 2l
20 − 8 = 2l
12 = 2l
6 = l
6 is the length
13 Choice e is correct Find the lengths of the unlabeled sides by comparing them to the given sides.
Divide the shape into two rectangles as shown below Find the area of each of the regions and add together to find the total area
30 + 28 = 58 sq in
14 Choice g is correct Find the cost for one can (unit rate) by dividing the cost of five cans by 5 $6.50 ÷ 5
= $1.30 per can Multiply the cost per can by 9 cans $1.30 × 9 = $11.70 Nine cans cost $11.70
A proportion can also be used:
$65.50= 9x.
To solve the proportion, cross-multiply and divide
5x = $58.50
55x= $589.50
x = $11.70
15 Choice c is correct Find a common denominator (15x) Multiply the first fraction by 55and the second fraction by 33x x The result is 1150x+ 135x x = 101+5x3x The answer is 101+5x3x.
16 Choice i is correct The endpoints are on −1.5 and 0, so the possible choices are i and h The endpoints
are open dots (not solid) and, therefore, only < or > signs can be used (not ≤ or ≥) This information
narrows the answer choices down to only i.
17 Choice c is correct First, raise everything in the parentheses to the second power: −(62(x4)2y3)2)
When you have a power to a power you multiply the exponents Thus, −(36x8y6) Apply the negative
for the final answer of − 36x8y6
10 in
7 in
4 in
3 in 30
28
Trang 418 Choice h is correct Use substitution to solve for x and y First, solve the second equation for y.
y = 4x − 47
Next, substitute the above value for y into the first equation and solve for x.
2x + 3(4x − 47) = 55
2x + 12x − 141 = 55
14x − 141 = 55
14x = 196
x = 14
Now, substitute 14 for x in the second equation and solve for y.
4(14) = y + 47
56 = y + 47
y = 9
The solution to the system of equations is (14, 9) The problem asks you to find x − y.
14 − 9 = 5
The answer is 5
19 Choice e is correct First, eliminate choice d because the dot on the graph is open and therefore the
inequality sign must be either < or > (not ≤ or ≥) Next, solve each inequality for x remembering that
the inequality symbol must be flipped when multiplying or dividing by a negative The answer choices become:
a x > 0
b x < −14
c x < −4
e x > −4
The endpoint is on −4, so the only possibilities are choices c and e The arrow points to numbers greater than −4 The answer is choice e.
20 Choice f is correct Notice that you are taking the cube root, not the square root Break up the
expres-sion under the radical into perfect cubes
3 (8)(2)x3x2y3y
Any exponent divisible by 3 is a cube root Take out the perfect cubes and leave everything else under the radical
2xy3 2x is the answer.2y
21 Choice c is correct Substitute the value 63° for C.
F = 59(63) + 32
F = 35 + 32
F = 67
The answer is 67°F
Trang 522 Choice h is correct The equation is quadratic, so there are two ways to solve it First, try to factor the
left-hand side of the equation Since it is factorable, solve the equation using factoring
x2+ 8x + 15 = 0
(x + 5)(x + 3) = 0
Set each of the factors equal to zero and solve for x.
x + 5 = 0 x + 3 = 0
x = − 5 x = −3
The solution set is {−5, −3}
The quadratic equation can also be used to solve the equation
x =
x =
x =
x = −82± 2
x = −82+ 2 x = −82− 2
x = −26= −3 x = −210= −5
The solution set is {−5, −3}
23 Choice b is correct Solve the equation for m using inverse operations.
5k = 9m − 18
5k + 18 = 9m
5k +918 = m
Since this answer does not appear as one of the choices, you must determine if any of the choices are equivalent to it If you divide each of the numerator terms by 9 you get 59k + 2 = m, which is choice b.
24 Choice h is correct Solve the equation by moving all x terms to one side.
5x − 5x − 7 = 5x − 5x + 10
− 7 = 10
− 7 ≠ 10
Ø
The x’s cancel, leaving −7 = 10, which is not true Since −7 never equals 10, there is no solution.
25 Choice e is correct Factor the numerator.
(4x − x1+)(3x + 3)
Use the denominator as a clue when factoring the numerator Most likely, the denominator will be one
of the factors in the numerator
Cancel the x + 3 in the numerator with the x + 3 in the denominator This leaves 4x − 1.
−8 ± 64 − 60
−8 ± (8) (4)(1)( 2 − 15)
−b ± b c2− 4a
Trang 626 Choice f is correct Subtract the numbers in y from the corresponding numbers in x.
27 Choice b is correct log3x = 2 is equivalent to 32= x Therefore, x = 9.
28 Choice h is correct Factor the numerator Use the denominator as a clue Most likely, one of the
fac-tors in the numerator will be the same as the denominator Also, notice that the numerator is the dif-ference of two squares
(x − x3)−(x3+ 3)
The x − 3 in the numerator cancels with the x − 3 in the denominator leaving an answer of x + 3.
29 Choice b is correct Use the distance formula or the Pythagorean theorem to find the distance The
dis-tance formula is d = (x2− x1)2+ (y2 Substitute the x and y values for points A and C and − y1)2
solve
d = (−2 − −1)−1 − 32+ ()2
d = (−1) (−4)2+2
d = 1 + 16
d = 17
To use the Pythagorean theorem (which is what the distance formula is derived from), draw the
seg-ment on a coordinate plane and create a right triangle where A C is the hypotenuse.
The legs of the right triangle are 1 and 4 Use the Pythagorean theorem to find the length of the hypotenuse
a2+ b2= c2
12+ 42= c2
1 + 16 = c2
17 = c2
17 = c
(−1,3)
(−2,−1) 1
4
5 0
6 6
3 − ( − 2) 4 − 4
5 − ( − 1) 6 − 0