1003020103
Level:
C
How many solutions has the inequality
\[ \frac{3x-7y}2 < x-4y-\frac12 \]
in \( \mathbb{N}\times\mathbb{N} \)? (Hint: Use the graphic solution of the inequality.)
none
infinity
\( 4 \)
\( 2 \)
C
1103020102
Level:
C
How many solutions has the inequality
\[ y\leq-\frac12x+2 \]
in \( \mathbb{N}\times\mathbb{N} \)?
\( 2 \)
\( 4 \)
infinity
none
1003020101
Level:
C
How many solutions has the inequality have in \( \mathbb{N}\times\mathbb{N} \)? (Hint: Solve the inequality graphically.)
\[ -4y\geq4x-8 \]
\( 1 \)
\( 4 \)
infinity
none
1003024704
Level:
C
Suppose the coefficient of the quadratic term (i.e. the coefficient at \( x^2 \)) in the expansion of \( (1+x)^n \) equals \( 300 \). Find the value of the exponent \( n \).
\( 25 \)
\( 24 \)
\( 30 \)
\( 20 \)
1003024703
Level:
C
Let the term with \( x^{-3} \) in the expansion of \( \left(4x^{-\frac12}-\frac12\right)^{10} \) equals \( 105 \). Find the value of \( x \).
\( 8 \)
\( 9 \)
\( 10 \)
\( 11 \)
1003024702
Level:
C
Find the constant term in the expansion of \( \left(2+3x^2\right)^{30} \).
\( 2^{30} \)
\( 2^{29} \)
\( 3\cdot2^{30} \)
\( 3\cdot2^{29} \)
1003024701
Level:
C
What is the coefficient at \( x^7 \) in the expansion of \( (1-3x)^9 \)?
\( -78\:732 \)
\( 59\:049 \)
\( -59\:049 \)
\( 78\:732 \)
1103021401
Level:
C
\( ABCD \) is a rhombus, the height \( v = 48\,\mathrm{cm} \) and the shorter diagonal \( u = 60\,\mathrm{cm} \). Determine the measure of the acute interior angle of the rhombus. Round the result to two decimal places.
\( 73.74^{\circ} \)
\( 36.87^{\circ} \)
\( 24.12^{\circ} \)
\( 27.13^{\circ} \)
1003019205
Level:
C
Adam and Eve met at the disco. They agreed to meet the next day at the same location sometime between \( 1 \) p.m. and \( 2 \) p.m. Both of them will arrive independently at random times within the hour and wait ten minutes for the other. What is the probability that they will not meet during that hour?
\( \frac{25}{36}\doteq 0{.}6944 \)
\( \frac{11}{36}\doteq 0{.}3056 \)
\( \frac{35}{36}\doteq 0{.}9722 \)
\( \frac{24}{36}\doteq 0{.}6667 \)
1003019402
Level:
C
Identify which of the given functions is neither even nor odd.
\( h(x) = \frac{x^3-7}{2x^2} \)
\( f(x) = \frac{x^2+3}{3x^4} \)
\( g(x) = \frac{5x^2-6}{x} \)
\( m(x) = \frac{x^3}{2x^2+5} \)