Practice Test 10 - PSAT Math

20 questions. Answer them in any order, then submit to see your score and every explanation.

A line passes through the points $(-2, 7)$ and $(4, -5)$ . What is the slope of the line?
A gym tracked 50 members for 6 months and recorded whether they attended at least 3 classes per week and whether they renewed their membership. The gym posted the table and claimed, "Taking at least 3 classes per week makes members renew." Which statement is best supported by the table?
At a grocery store, $3.2$ pounds of apples cost $5.76. At the same price per pound, what is the cost of $7$ pounds of apples?
A line graph shows total cost versus number of tickets purchased. The line passes through $(0,0)$ and $(6,54)$ . What is the unit rate, in dollars per ticket, represented by the slope of the line?
A car travels $200$ kilometers on $16$ liters of fuel. At the same rate of fuel consumption, about how many liters would be needed for the car to travel $350$ kilometers?
Consider the scatter plot shown. If the additional point (10, 90) were added to the data set, how would the correlation coefficient $r$ most likely change?
A line is modeled by $y=-4x+7$ . If $x$ decreases by 3, by how much does $y$ change?
A bank account earns 5% interest compounded monthly, with no deposits or withdrawals. If the initial balance is $1,000, which model best represents the balance $B$ after $m$ months?
Which expression is equivalent to $3(2x-5)-4(x+1)+7$ ? Be careful to distribute the negatives and then combine like terms so the final result is written in the form $ax+b$ .
In the diagram, two parallel lines are cut by a transversal. An alternate interior angle is labeled $x$ and its alternate interior partner is labeled $64^\circ$ . What is $x$ ?
A cubic polynomial has x-intercepts at $x=-2$ and $x=3$ , and the graph touches (bounces off) the x-axis at $x=3$ rather than crossing it. Which polynomial could represent this graph, assuming the leading coefficient is positive?
The graph of the linear function $h$ is shown in the $xy$ -plane. If $h(x)=mx+b$ , what is the value of $h(b)-h(m)$ ?
A local newspaper reports that neighborhoods with more parks have lower crime rates, based on citywide data collected in the same year. The paper concludes, "Building more parks will reduce crime." Which evaluation is most appropriate?
Based on the scatter plot shown, which statement best characterizes the relationship between daily study time and quiz score for the 12 students?
The table shown gives values of a linear function $f$ at selected inputs. If $f(x)=ax+b$ , what is the value of $a+b$ ?
A coordinate plane shows the graph of a quadratic function $f(x)$ . The parabola opens upward and has a vertex at $(-1,-4)$ . It crosses the $x$ -axis at $x=-3$ and $x=1$ . Which equation matches the graphed function? Choose the equation whose graph has the same vertex and intercepts.
The graph of the exponential function $f(x) = a \cdot b^x + c$ is shown. What is the value of $a + b + c$ ?
The figure below shows the graphs of three lines: $\ell_1$ , $\ell_2$ , and $\ell_3$ . Lines $\ell_1$ and $\ell_2$ intersect at $(1, 4)$ ; lines $\ell_2$ and $\ell_3$ intersect at $(5, 2)$ ; and lines $\ell_1$ and $\ell_3$ intersect at $(-1, -2)$ . If the equation of $\ell_2$ is $y = mx + b$ , what is the value of $m + b$ ?
A function $f$ satisfies $f(0)=10$ and $f(1)=14$ . Which of the following possible values of $f(3)$ would indicate that $f$ is growing exponentially rather than linearly?
A store owner buys an item for $c$ dollars. To set a selling price, the owner marks up the cost by 50%. After two weeks, the item has not sold, so the owner offers a 20% discount off the current selling price. If the final price after the discount is $\$36, what was the original cost,$ c$$?

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