10 Hard SAT Math Questions (Part - 5)

Question 1 :

y + k = x + 26

y – k = x² – 5x

In the given system of equations, k is a constant. The system has exactly one real solution. What is the value of k?

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Question 2 :

The scatterplot shows the relationship between two variables x and y. A line of best fit is also shown. For what fraction of the data points in the scatterplot is the y-value predicted by the line of best fit less than the actual y-value?

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Question 3 :

In the given system of equations, a and b are constants and a > 0. The system has infinitely many solutions. What is the value of a – b?

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Question 4 :

The equation above gives the power in an electrical circuit, P, in Watts a function of the Voltage, V in Volts and the resistance, R, in ohms. An electrical engineer is measuring two circuits. The first circuit has a voltage of v Volts and a resistance of r Ohms. The second circuit has a voltage of 12v Volts and a resistance of 3r Ohms. The numbers v and r are positive constants. Which of the following could represent the ratio of the power in the second circuit to the power in the first circuit?

A) 3 to 1

B) 4 to 1

C) 48 to 1

D) 81 to 1

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Question 5 :

Point Q is the center of the circle. Point A, point B and point C all lie on the circle. Point D lies on segment AC as shown. Segment BD is perpendicular to segment AC. In the figure shown, AB = 58 and AD = 40. If a point within the figure is selected at random, what is the probability that the point is within the shaded region? (Express your answer as a decimal or fraction, not as a percent.) Round your answer to the nearest thousandth.

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Question 6 :

In the given equation, k is a constant. The equation has exactly one real solution. What is the value of 56k? (Round your answer to the nearest tenth)

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Question 7 :

For the function f, for each increase in the value of x by 1/4, the value of f(x) increases by a factor of m. Which of the following equivalent forms displays m as a constant or coefficient?

A) f(x) = 13(100)^2x

B) f(x) = 13(1000^2/7)^14x/3

C) f(x) = 13(100000^16/5)^x/4

D) f(x) = 13(10^2/3)^6x

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Question 8 :

A juice mixture has a total volume of 125 liters and is 45% juice by volume. The mixture was created by mixing two different solutions (solution A and solution B). Solution A was 24% juice by volume. Solution B was 64% juice by volume. The volume, in liters, of juice in solution A is equal to a. The volume, in liters, of juice in solution B is equal to b. The numbers a, b and p are all positive constants. If a is p% less than b, what is the value of p?(Round your answer to the nearest hundredth)

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Question 9 :

In triangle DEF, angle F is a right angle, point Q lies on DE, point J lies on EF, and QJ is parallel to DF. If the length of EF is 45 units, the length of FJ is 24 units, and the area of triangle DEF is 630 square units, what is the perimeter of triangle QEJ, in units?