Based on 4test.com ACT practice test

1. 4Tests.com Math Section III Kahn remediation if question was missed.
1. At Joes Steakhouse the hourly wage for a chef is 20% greater than that of a dishwasher, and
the hourly wage of a dishwasher is half as much as the hourly wage of a manager. If a managers
wage is $8.50
2.
3. hour, how much less than a manager does a chef earn each hour?
Insight. There are 2 commas and a period. This will be a 3 step problem.
Step 1, From the first phrase: C=100% +20% of D, = 1.2D
Step 2. From phrase 2: D= 1/2M
Step 3.
M= 8.5 Now answer the question “how much less (subtraction) does C make than M” or
what is M-C? 8.5- (1.2)(1/2) (8.5)
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-multistep-
word-probs/v/multistep-word-problems-example-3
2. A florist buys roses at $0.50 a piece and sells them for $1.00 a piece. If there are no
other expenses, how many roses must be sold in order to make a profit of $300?
Insight: How much profit is there for each rose? What are the units of this number? Does she have any
other types of costs or income? Is the answer asked for in units of $ or Roses? What do you have to do to
get the units you have to give the units you need in the answer?
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-fractions-decimals/cc-7th-multistep-
word-probs/v/multistep-word-problems-example-2
3. A certain pump can drain a full 375-gallon tank in 15 minutes. At this rate, how many
more minutes would it take to drain a full 600-gallon tank?
https://www.khanacademy.org/math/algebra/ratio-proportion-topic/ratios_algebra/v/find-an-
unknown-in-a-proportion-2
Insight: you have a ratio of 375 gallons in 15 minutes. What are the units of the
unknown? Form the ratio on the other side of the = sign using a letter to stand for the
unknown.
4. If n is an even integer, which of the following must be an odd integer?
3n-2
3(n+1)
n-2
n/3
n^2

2. Insight: test each answer, using the even integer 2 for n. Only one will always be
odd. (If you get more than one possible answer, try another even number, for example,
10).
5. Cindy has a collection of 80 records. If 40 percent of her records are jazz records, and
the rest are blues records, how many blues records does she have?
https://www.khanacademy.org/math/arithmetic/decimals/percent_word_probs/v/solvi
ng-percent-problems
Insight: Her whole collection is 100%. Is she only collects two things, and 40% are
one thing, what percent will be the other? With 80 total records, how many are Blues?
6. Six cups of flour are required to make a batch of cookies. How many cups of flour are
needed to make enough cookies to fill 12 cookie jars, if each cookie jar holds 1.5
batches?
Insight:This problem has a period and a comma, so we need two steps. The first
sentence says 6C = 1B The last statement says 1J = 1.5B. Substitute 6F for B from the
first equation into the second equation to learn how many Cs it takes to do 1.5 batches
(one jar), and multiply by the number of jars you need to get the C you need for 12 times
that many jars.
7. How many even integers are there between 2 and 100, not including 2 and 100?
Insight: Count the number of integers in one of the sets of 10 (use 11-20). There are
10 of these sets between 1 and 100, so multiply by 10. However, you cant use the first
one or the last one (2 and 100) so subtract 2 to get the answer.
8. If the sum of two numbers is -15 and their product is 56, then these two numbers are
roots of which of the following equations? Error: Reference source not found
x2 + 7x + 8
2x2 + 7x + 8
x2 - 15x + 56
x2 + 15x + 56
None of the above
https://www.khanacademy.org/math/algebra/quadratics/quadratic_odds_ends/v/ca-algebra-
i--factoring-quadratics
Insight: Roots are the negatives of the factors of quadratic equations. All of the
proposed equations have one for the multiple of the first term, except the second one,
which needed to have each term divided by 2. Now, the sum of the two roots will be +15
and the product will be (minus times minus [ +) 56. The last equation fits the givens.

3. 9 What is the smallest positive number that leaves a remainder of 2 when the number is
divided by 3, 4, or 5? Error: Reference source not found
42
82
22
62
122
Test the proposed answers to see. Start with the smallest number, since finding a larger
number that works is useless. For example, 22 has a remainder of 2 when divided by 5
and 4, but not when divided by 3. He math to check an answer is often easier than the
math to get the answer in the first place. Since they give the answer along with 4 wrong
ones, on average you will only need to check 3 “answers” to find the right one,.
10. Which is greater?
Column A Column B
3-5+6-8-4+7 -2
This is easy if you and your calculator are best friends. With paper and pencil, add all
the positive numbers, then adding all the negative numbers and taking the difference.
Switching back and forth between adding and subtracting causes mistakes.
11. Which is greater?
Column A Column B
one square yard 1600 square inches
We need to add two facts, the number of inches in 1 yard (36), and the fact that both
numbers must be squared to get the ratio of square inches to square yards.
12. Which is greater?
Column A Column B
(1.2)-1 1
Here, you need to know how to evaluate a negative exponent.
https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-
algebra/v/negative-and-positive-exponents
13. Which is greater?
Column A Column B

4. (10/4) / (3/2) * (3/7) (3/4) * (10/7) / (3/2)
https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/mul
tiplying-a-fraction-by-a-fraction
14. The hypotenuse of an isosceles right triangle is 2"
Column A Column B
length of one leg of the triangle 1"
http://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-geometry/cc-7th-constructing-
slicing-geometric-shapes/v/constructing-right-isosceles.
Use the rules of equal length legs and of right triangles to get the length of the legs of
an isosceles right triangle with a 2 inch hypotenuse. Is this greater or less than 1 inch?
15. Which of the following has a graph that is symmetric to the x-axis? Error: Reference
source not found
y = x
y2 = x
y = x3 - x
y = x2 + 3
Since it is easier to check formulas than create them, test each one. By creating a few
number pairs (set x = -1,0,1 and find each y to start). Symmetry around the x axis means
it mirrors above and below the x (horizontal) axis. Note that I get answer C, not B.
16. If a die is tossed twice the probability of getting a 3 on both tosses is:
http://www.khanacademy.org/math/probability/independent-dependent-probability/
independent_events/v/events-and-outcomes-2
Rolling one die two times is the same as rolling two of them once. Only one of the
6x6= 36 possible outcomes is a match with the requirement, so we have 1/35.
We say that the probability of multiple independent events is the product of their
individual probabilities (1/6 x 1/6= 1/36)
17. A student received test grades of 10, 7, 8, 9, 6, 9, 8, 7, 6 in a math class. Her median
score was:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/
cc-7th-central-tendency/v/mean-median-and-mode
I suggest making flashcards with the definitions of average (mean), median, and
mode on them, and reviewing them during the week before the SAT test, while btushing
your teeth. You will be tested with a simple question on each one.

5. 18. A test shows that 10 out of 100 gadgets are defective. In a random sample of two
gadgets are chosen, the probability that both are defective it is:
This is called sampling without replacement. The first sample out of 100 had 10
chances of being defective = 1/100. Now there are only 99 items, and since the one
already taken was defective, only 9 defective. This is 9/99. Multiplying (see problem 16),
we get 10/100 x 9/99 = .090909.... If you don’t have a calculator that will convert this to
a fraction, (and give answers in fraction form) buy one for less than $16. However, all is
not lost. Convert the answers give to decimal by doing them as division problems and see
which is the same in decimal form as the answer you got on your junky calculator.
19. Two cards are simultaneously drawn from an ordinary deck. The probability that
they're not both the same suit is:
To answer this you must know that there are 52 cards in a deck. 13 of them are
marked with a spade symbol, 13 with a heart symbol, 13 with a diamond symbol, and 13
with a club symbol (4 “suits” of 13 cards each). In each of these sets of 13, there are cards
numbered 2 through 10 and a jack, queen , king, and an ace. (4 of each of these values)
Review problem 16. Again, think of drawing two cards at once as sampling one at a
time without replacement It is easiest to calculate the chance they are both the same suit,
and subtract that from 1.00
The chance they are both a spade is 13/52 x 13/51. But you can add to that the
chance they are both Hearts, or diamonds or clubs. (4 times the chance they are both
spades).
20. The prime factors of 96 are: Error: Reference source not found
2 and 3
6 and 8
2, 3 and 4
8 and 12
3 and 9
https://www.khanacademy.org/math/arithmetic/factors-multiples/
prime_numbers/v/prime-numbers
It is easiest to check the ansers, instead of come p with your own. However, note first
that 6 and 8, 4 , 12 and 9 are not prime, so only the first answer can be correct.

6. 21. The area of a square is 100. The length of its diagonal is approximately __.
You need the formula for the lenght of the sides, given the area of a square, and the
formula for hypotenuse of a triangle formed with legs being two sides of that square.
(draw a sketch first, any time you can. A picture is worth 1000 words, even when they are
in writing.)
If you haven’t memorized the formula for area of a square, and hypotenuse of a right
triangle, look up the reference formula page (“cheat sheet” provided by 4 tests.com.
Make flash cards of all the formulas given and practice them when brushing your teeth,
then review them for the week before the SAT exam.
22. If x + 1 < 3x + 5, then Error: Reference source not found
x > -2
x < -2
x = 0
x < 2
x > 2
With inequalities, it is best to test the proposed answers by making up an example
number.
For X>-2, try -1. For x<-2, try -3. There will only be one that is true. The easiest to
try is x = 0, so try that first. Note that it happens to be correct! The test writers are kind!
23. Which of the numbers cannot be represented by a repeating decimal? Error:
Reference source not found
11/9
23/7
Square Root of 3
4 1/3 2
https://www.khanacademy.org/math/arithmetic/order-of-operations/rational-irrational-
numbers/v/recognizing-irrational-numbers
24. The probability of obtaining all heads or tails when three coins are tossed
simultaneously is:
http://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-probability-statistics/
cc-7th-basic-prob/v/basic-probability. Now, unlike earlier, we have
replacement.

7. http://www.khanacademy.org/math/probability/independent-dependent-probability/
independent_events/v/compound-probability-of-independent-events
25. Suppose 3 of a dozen oranges are bruised and 2 are chosen at random from the dozen.
The probability that both are bruised is__
Non replacement. See problem 16. 3 dozen = 3 x 12 =36. Drawing one has a 3/36 chance
of being bruised. For the second to ALSO be bruised, you have 2/35. The product is