This document contains 20 math problems with references to Khan Academy videos that provide explanations and solutions. The problems cover a range of math topics including averages, percentages, geometry, algebra, number patterns, and more. Khan Academy videos are included to help explain the concepts and steps to solve each problem.

1. 4Test.com Math Section 1 Kshn Academy references
Section I.
1) What is the average (arithmetic mean) of 4x + 5, 7x-6,and -8x+2?
https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/
old-school-equations/v/averages
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/
cc-6th-equivalent-expressions/v/adding-like-rational-terms
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/cc-6th-order-operations/
v/order-of-operations?
qa_expand_key=ag5zfmtoYW4tYWNhZGVteXJCCxIIVXNlckRhdGEiJnVzZXJfZW1haWxfa2V5X3JhZ
2hhdnRhbHJlamFAZ21haWwuY29tDAsSCEZlZWRiYWNrGAEM
2 In a classroom of 35 students, 14 are male. What percent of the classroom is male?
https://www.khanacademy.org/math/arithmetic/decimals/percent_tutorial/v/finding-percentages-
example
3. If the area of a triangle is 24 and its base is 6, what is the length of the altitude to that
base?
https://www.khanacademy.org/math/algebra/quadratics/factoring_quadratics/v/Exam
ple%204:%20Solving%20a%20quadratic%20equation%20by%20factoring
4. Lenny's average score after 3 tests is 88. What score on the 4th test would bring
Lenny's average up to exactly 90?
See the link in prob 2 about percents problems. This is a 3 step percent problem.
1. What is the total score for the 3 tests you have now?
2. What total score you need for 4 tests of 90 each?
3. What is the difference you will have to make up with your 4th test?
5. If an integer is divisible by 6 and by 9, then the integer must be divisible by which of
the following?
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/
cc-6th-lcm/v/least-common-multiple-exercise

2. 6. The equation x2 = 5x —4 has how many distinct real solutions?
1. Arrange in the standard format by getton all terms on one side, leaving them equal
to zero on the other.
2. Roots that involve a negative square root are imaginary (non-real)
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_for
mula_tutorial/v/complex-roots-from-the-quadratic-formula
7. A certain machine can make 3 widgets every 2 seconds. At this rate, how many
widgets will be made in 1 minute?
Note two question sentences. This is a two step problem.
Problem from sentence 1. Find average rate. See prob 2 kahn lesson.
Problem from sentence 2. https://www.khanacademy.org/math/cc-seventh-grade-math/
cc-7th-ratio-proportion/cc-7th-rates/v/usain-bolt-s-average-speed
8. If x + y < 10, and x - y > 12, which of the following pairs could be the values of x and
y?
If these were equalities, we could find the value of x in terms of y in the first
equation and substitute into the second, to get an equation all in y, then solve for Y and
go back and substitute to find the value of x.
9. If the positive integer x leaves a remainder of 2 when divided by 8, what will the
remainder be when x + 9 is divided by 8?
Note the comma. This is a two part question.
Step 1. https://www.khanacademy.org/math/arithmetic/multiplication-division/
long_division/v/division-3--more-long-division-and-remainder-examples
Step 2. Here we need to add some insight of our own. If we divide the 9 itself by 8,
its remainder will be added to the previous remainder, unless their sum is 8 or more (test
by trying to divide that sum by 8). This remainder is the answer!
10. B
2x +2 Error: Reference source not found
4x y
In the triangle above, if the measure of angle B is 52 degrees, then what is the value of y?
https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/
triang_prop_tut/v/sum-of-interior-angles-of-a-polygon Write the equation, then use
pemdas to solve for Y.

3. 11. If 6% of x is 7.5, then 36% of x equals?
https://www.khanacademy.org/math/algebra/ratio-proportion-topic/
ratios_algebra/v/find-an-unknown-in-a-proportion
12 In a downtown building, there are 6 floors and the number of rooms on each floor is
R. If each room has exactly C chairs, which of the following gives the total number of
chairs in the building?
Note that there are 3 sentences. This is a 3 step problem. If you don;t see how to
combine the 3 facts into a single equation, the insight is to try working from the last fact
to the first.
Step 1. Imagine one room with 6 chairs. Then go out into the hall and see that there
are, say 10 rooms on that floor. How many chairs is there on that floor?
Step 2. Now replace 10 with the algebra letter for rooms, R., and the 6 with the
algebraic letter C.
Step 3, now multiply the result by the number of floors with that many rooms that
have that many chairs.
B
13. A C
E D
In pentagon ABCDE shown above, each side is 1 centimeter. If a particle starts at point A
and travels clockwise 183 centimeters along ABCDE, the particle will stop on which
point?
Insight is required. Step1.Starting at A. How many centimeters is one complete trip
around?
Step 2.What remainder of centemeters are left after all the complete trips are done and
your are again back at A? https://www.khanacademy.org/math/arithmetic/multiplication-division/
long_division/v/division-3--more-long-division-and-remainder-examples
Step 3.Starting aroound again, how far will you get?
14. What is the greatest prime factor of 77?
https://www.khanacademy.org/math/arithmetic/factors-multiples/
prime_factorization/v/prime-factorization
Which of the factors you found that is prime is biggest?
15. A business is owned by 9 women and 1 man, each of whom owns an equal share. If

4. one of the women sells 1/2 of her share to the man, and another woman keeps 1/5 of her
share and sells the rest to the man, what fraction of the business will the man own?
There is one period and 3 commas. This is a 4 step problem.
Step1. How many total equal shares are there and what percent of the total does the man
own? https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-ratios-prop-topic/
cc-6th-percentages/v/representing-a-number-as-a-decimal--percent--and-fraction
Step 2. What percent of the total is the 1/2 share the first woman gives the man?
Step 3. What fraction of her one share does the second woman give the man, if she keeps
1/5 of her original share, and what peercent is that fraction of the total?
Step 4. Adding the two given percents of the total to the original percent the man had,
what does he have now? (percent means parts per one hundred.
16. At a bedding convention, 400 dealers sold either blankets or sheets or both. If 163
dealers sold both blankets and sheets, and 117 dealers sold only blankets, how many
dealers sold only sheets?
https://www.khanacademy.org/math/arithmetic/fractions/dividing-fractions-tutorial/
v/my-share-of-soap-as-a-mixed-number-on-a-number-line
Make a number line with 400 spaces. Mark off how many are blankets only one one
end, and then use the next part of the line to be both sheets and blankets. What does the
unmarked remainder of the line represent?
17. For all values of x, (3x + 4) (4x - 3) =
https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/
multiplying-binomials/v/multiplying-binomials
18. Steve types at an average rate of 8 pages per hour. At that rate, how many hours will
it take Jan to type 100 pages?
See the topic for problem 11. What rate can you use for Jan?
-2 -1 0 1 2
19. Error: Reference source not found
X ≠ 0
Which of the following expressions describes the indicated values on the number line
above ?
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-negative-number-topic/
cc-6th-absolute-value/v/absolute-value-and-number-lines
20. In the sequence 4, 12, 36, x, 324 ... ,what is the most likely value of x?
This requires an insight.

5. The numbers get bigger, so we hve adding or multipling, squaring etc, not
subtracting dividing, square roots, etc.
Is the difference between the first and second numbers added to the second number
to get the third?
Is it multiplied by the second to get the third?
Once you find a sequence between the first two numbers, that holds for getting the
third number, use it to get x and then test it to see if you get the next number after x..
Note that if adding and multiplying don’t work, try raising to a power. That usually is
enough to get the sequence.

6. The numbers get bigger, so we hve adding or multipling, squaring etc, not
subtracting dividing, square roots, etc.
Is the difference between the first and second numbers added to the second number
to get the third?
Is it multiplied by the second to get the third?
Once you find a sequence between the first two numbers, that holds for getting the
third number, use it to get x and then test it to see if you get the next number after x..
Note that if adding and multiplying don’t work, try raising to a power. That usually is
enough to get the sequence.