Difference between revisions of "1963 TMTA High School Algebra I Contest Problems"
Coolmath34 (talk | contribs) (Created page with "== Problem 1== If <math>4a - x = 3a - 4x,</math> then <math>x = </math> <math>\text{(A)} \quad -a \quad \text{(B)} \quad 7a/5 \quad \text{(C)} \quad a/5 \quad \text{(D)} \qua...") |
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<math>\text{(A)} 5.3 \times 10^7 \quad \text{(B)} \quad 6.3 \times 10^7 \quad \text{(C)} \quad 6.3 \times 10^{12} \quad \text{(D)} \quad 5.3 \times 10^1 \quad \text{(E) NOTA}</math> | <math>\text{(A)} 5.3 \times 10^7 \quad \text{(B)} \quad 6.3 \times 10^7 \quad \text{(C)} \quad 6.3 \times 10^{12} \quad \text{(D)} \quad 5.3 \times 10^1 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 4 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 4 | Solution]] | ||
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<math>\text{(A)} \quad 8 \quad \text{(B)} \quad 8/9 \quad \text{(C)} \quad 2/5 \quad \text{(D)} \quad 8/41 \quad \text{(E)} \quad 6</math> | <math>\text{(A)} \quad 8 \quad \text{(B)} \quad 8/9 \quad \text{(C)} \quad 2/5 \quad \text{(D)} \quad 8/41 \quad \text{(E)} \quad 6</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 5 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 5 | Solution]] | ||
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<math>\text{(D)} \quad 12x^2-7x-10 \quad \text{(E) NOTA}</math> | <math>\text{(D)} \quad 12x^2-7x-10 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 6 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 6 | Solution]] | ||
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<math>\text{(A)} \quad \frac{(a+b)^2}{ab} \quad \text{(B)} \quad \frac{1}{ab} \quad \text{(C)} \quad ab \quad \text{(D)} \quad \frac{ab}{(a+b)^2} \quad \text{(E)} a+b</math> | <math>\text{(A)} \quad \frac{(a+b)^2}{ab} \quad \text{(B)} \quad \frac{1}{ab} \quad \text{(C)} \quad ab \quad \text{(D)} \quad \frac{ab}{(a+b)^2} \quad \text{(E)} a+b</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 8 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 8 | Solution]] | ||
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<math>\text{(E)} \quad \frac{(ab)^3}{a^3} = b^3</math> | <math>\text{(E)} \quad \frac{(ab)^3}{a^3} = b^3</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 10 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 10 | Solution]] | ||
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<math>\text{(A)} \quad x>6 \quad \text{(B)} \quad x=6 \quad \text{(C)} \quad x=-6 \quad \text{(D)} \quad x<6 \quad \text{(E) NOTA}</math> | <math>\text{(A)} \quad x>6 \quad \text{(B)} \quad x=6 \quad \text{(C)} \quad x=-6 \quad \text{(D)} \quad x<6 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 13 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 13 | Solution]] | ||
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<math>\text{(D)} \quad 16(x^2+y^2)(x-y)(x+y) \quad \text{(E) can't be factored}</math> | <math>\text{(D)} \quad 16(x^2+y^2)(x-y)(x+y) \quad \text{(E) can't be factored}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 14 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 14 | Solution]] | ||
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<math>\text{(A)} \quad 24 \quad \text{(B)} \quad 16 \quad \text{(C)} \quad -6 \quad \text{(D)} \quad 6 \quad \text{(E)} \quad 4</math> | <math>\text{(A)} \quad 24 \quad \text{(B)} \quad 16 \quad \text{(C)} \quad -6 \quad \text{(D)} \quad 6 \quad \text{(E)} \quad 4</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 17 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 17 | Solution]] | ||
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<math>\text{(A)} \quad 75 \quad \text{(B)} \quad 225 \quad \text{(C)} \quad 150 \quad \text{(D)} \quad 25 \quad \text{(E) NOTA}</math> | <math>\text{(A)} \quad 75 \quad \text{(B)} \quad 225 \quad \text{(C)} \quad 150 \quad \text{(D)} \quad 25 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 18 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 18 | Solution]] | ||
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<math>\text{(A)} \quad 28\frac{1}{2} \quad \text{(B)} \quad 31 \quad \text{(C)} \quad 32 \quad \text{(D)} \quad 31\frac{1}{2} \quad \text{(E)} 30</math> | <math>\text{(A)} \quad 28\frac{1}{2} \quad \text{(B)} \quad 31 \quad \text{(C)} \quad 32 \quad \text{(D)} \quad 31\frac{1}{2} \quad \text{(E)} 30</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 20 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 20 | Solution]] | ||
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<math>\text{(A)} \quad A \quad \text{(B)} \quad B \quad \text{(C)} \quad C \quad \text{(D)} \quad D \quad \text{(E)} \quad E</math> | <math>\text{(A)} \quad A \quad \text{(B)} \quad B \quad \text{(C)} \quad C \quad \text{(D)} \quad D \quad \text{(E)} \quad E</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 21 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 21 | Solution]] | ||
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<math>\text{(A)} \quad A \quad \text{(B)} \quad B \quad \text{(C)} \quad C \quad \text{(D)} \quad D \quad \text{(E)} \quad E</math> | <math>\text{(A)} \quad A \quad \text{(B)} \quad B \quad \text{(C)} \quad C \quad \text{(D)} \quad D \quad \text{(E)} \quad E</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 22 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 22 | Solution]] | ||
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<math>\text{(D)} \quad N-5=\frac{1}{5}N \quad \text{(E)} \quad 5N-25=1</math> | <math>\text{(D)} \quad N-5=\frac{1}{5}N \quad \text{(E)} \quad 5N-25=1</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 24 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 24 | Solution]] | ||
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<math>\text{(A)} \quad -2.25 \quad \text{(B)} \quad -2.35 \quad \text{(C)} \quad -2.15 \quad \text{(D)} \quad -2.20 \quad \text{(E)} \quad -2.50</math> | <math>\text{(A)} \quad -2.25 \quad \text{(B)} \quad -2.35 \quad \text{(C)} \quad -2.15 \quad \text{(D)} \quad -2.20 \quad \text{(E)} \quad -2.50</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 25 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 25 | Solution]] | ||
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<math>\text{(A)} \quad 9 \quad \text{(B)} \quad 6 \quad \text{(C)} \quad 36 \quad \text{(D)} \quad -9 \quad \text{(E) NOTA}</math> | <math>\text{(A)} \quad 9 \quad \text{(B)} \quad 6 \quad \text{(C)} \quad 36 \quad \text{(D)} \quad -9 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 28 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 28 | Solution]] | ||
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<math>\text{(A)} \quad 2 \quad \text{(B)} \quad -1 \quad \text{(C)} \quad 1 \quad \text{(D)} \quad -2 \quad \text{(E) NOTA}</math> | <math>\text{(A)} \quad 2 \quad \text{(B)} \quad -1 \quad \text{(C)} \quad 1 \quad \text{(D)} \quad -2 \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 31 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 31 | Solution]] | ||
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<math>\text{(E)} \quad \{3, 5, 7, 9\}</math> | <math>\text{(E)} \quad \{3, 5, 7, 9\}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 32 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 32 | Solution]] | ||
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<math>\text{(D)} \quad \frac{HC-2A}{H} \quad \text{(E)} \quad H-2A+C</math> | <math>\text{(D)} \quad \frac{HC-2A}{H} \quad \text{(E)} \quad H-2A+C</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 33 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 33 | Solution]] | ||
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<math>\text{(D)} \quad \frac{6}{2-x} \quad \text{(E)} \quad \frac{6}{x-2}</math> | <math>\text{(D)} \quad \frac{6}{2-x} \quad \text{(E)} \quad \frac{6}{x-2}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 35 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 35 | Solution]] | ||
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<math>\text{(A)} \quad 2\% \quad \text{(B)} \quad 4\% \quad \text{(C)} \quad 3\frac{1}{2}\% \quad \text{(D)} \quad 5\% \quad \text{(E) NOTA}</math> | <math>\text{(A)} \quad 2\% \quad \text{(B)} \quad 4\% \quad \text{(C)} \quad 3\frac{1}{2}\% \quad \text{(D)} \quad 5\% \quad \text{(E) NOTA}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 37 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 37 | Solution]] | ||
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<math>\text{(A)} \quad 37; \quad \text{(B)} \quad 19; \quad \text{(C)} \quad 29; \quad \text{(D)} \quad 42; \quad \text{(E)} \quad \text{none of these}</math> | <math>\text{(A)} \quad 37; \quad \text{(B)} \quad 19; \quad \text{(C)} \quad 29; \quad \text{(D)} \quad 42; \quad \text{(E)} \quad \text{none of these}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 38 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 38 | Solution]] | ||
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<math>\text{(A)} \quad 9; \quad \text{(B)} \quad 4; \quad \text{(C)} \quad 2; \quad \text{(D)} \quad 6; \quad \text{(E)} \quad \text{none of these}</math> | <math>\text{(A)} \quad 9; \quad \text{(B)} \quad 4; \quad \text{(C)} \quad 2; \quad \text{(D)} \quad 6; \quad \text{(E)} \quad \text{none of these}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 39 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 39 | Solution]] | ||
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<math>\text{(D)} \quad 16x^{2}-8xy+4y^{2} \quad \text{(E)} \quad \text{none of these}</math> | <math>\text{(D)} \quad 16x^{2}-8xy+4y^{2} \quad \text{(E)} \quad \text{none of these}</math> | ||
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[[1963 TMTA High School Algebra I Contest Problem 40 | Solution]] | [[1963 TMTA High School Algebra I Contest Problem 40 | Solution]] | ||
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+ | ==See Also== | ||
+ | {{Succession box | ||
+ | |header=1963 TMTA High School Algebra I Contest ([[1963 TMTA High School Algebra I Contest Problems|Problems]]) | ||
+ | |before=First Contest | ||
+ | |title=[[TMTA High School Mathematics Contest]] | ||
+ | |after=[[1964 TMTA High School Mathematics Contests]] | ||
+ | }} | ||
+ | *[[TMTA High School Mathematics Contest Past Problems/Solutions]] |
Latest revision as of 13:08, 2 February 2021
Contents
- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 Problem 26
- 27 Problem 27
- 28 Problem 28
- 29 Problem 29
- 30 Problem 30
- 31 Problem 31
- 32 Problem 32
- 33 Problem 33
- 34 Problem 34
- 35 Problem 35
- 36 Problem 36
- 37 Problem 37
- 38 Problem 38
- 39 Problem 39
- 40 Problem 40
- 41 See Also
Problem 1
If then
Problem 2
The number of dimes in half dollars is:
Problem 3
Which of the following has a negative root?
Problem 4
The product of and is:
Problem 5
is equal to:
Problem 6
is equal to:
Problem 7
is equal to
Problem 8
is equal to
Problem 9
Combine:
Problem 10
Which of the following is true?
Problem 11
factored into real primes is
Problem 12
Divide by
Problem 13
If a "solution set" is the set of all numbers which satisfy a statement, which is the solution set of
Problem 14
factored into its real prime factors is equal to:
Problem 15
is equal to
Problem 16
The factors of are
Problem 17
If the graph if the equation passes through the point what is the value of
Problem 18
A dealer packed basketballs in barrels and boxes. Later he packed basketballs in barrels and boxes. Find the number of basketballs that a barrel will hold.
Problem 19
If the symbol is read "the absolute value of " and is equal to when and is equal to when which of the following is always true?
Problem 20
If a piece of cloth inches long will shrink to inches when washed, to what length in inches will a inch piece of the same cloth shrink after washing?
Problem 21
On the graph chart which point has coordinates
Problem 22
On the graph chart which point has zero for its ordinate?
Problem 23
On the graph chart, if the lines and were graphed, at which point would they intersect?
Problem 24
When is subtracted from a certain number, of the number remains. The equation which expresses this relationship is:
Problem 25
If the value of to the nearest hundredth is:
Problem 26
If sulfuric acid is chemically pure, how many quarts of water must be added to one quart of acid to make a mixture?
Problem 27
If varies directly as and if when then the value of when is:
Problem 28
If we add its square to a certain number, the sum is Find the number.
Problem 29
A mechanic agreed to work for days at for each day that he worked, forfeiting for each day that he was idle. At the end of the days he received How many days had he worked?
Problem 30
If is positive, which of the following is always less than one?
Problem 31
Solve for when
Problem 32
A mathematical set is a collection of elements which satisfy a specified condition or conditions and braces {} are used to indicate a set. Which of the following is the set of all positive prime numbers between one and ten?
Problem 33
From the formula the value of in terms of and is:
Problem 34
An acre of wheat yielded pounds more of straw than of grain. The weight of the grain was of the total weight of grain and straw. How many pound bushels of grain were produced?
Problem 35
Combine and simplify
Problem 36
Find the fraction which equals 1/4 when 3 is subtracted from the numerator, but equals 1/2 when 2 is added to the denominator.
Problem 37
A man has invested at and at The annual interest on the investments totals Find the rate.
Problem 38
A farmer sold hogs for Some were sold for , and the remainder were sold for each. How many were sold at each?
Problem 39
The length of service a chair cover will give varies directly as the strength of the fabric and inversely as the amount of wear it receives. If one fabric, which is twice as strong as a second fabric and receives three times as much wear, lasts for 4 years, how long will the second fabric last?
Problem 40
If is divided by , the quotient will be:
See Also
1963 TMTA High School Algebra I Contest (Problems) | ||
Preceded by First Contest |
TMTA High School Mathematics Contest | Followed by 1964 TMTA High School Mathematics Contests |