SAT Math Practice Hard Questions

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Question 1 :

The expression 4^18x is equivalent to k^3x, where k is a constant. What is the value of k?

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Question 2 :

Jonas has a saving account that earns 3 percent interest compounded annually. His initial deposit was $800. Which of the following expressions gives the value of the account, in dollars, after 10 years?

A) 800(1.30)¹⁰

B) 800 + 30(10)

C) 800(1.03)(10)

D) 800(1.03)¹⁰

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Question 3 :

The rules and regulations demand that the employer should employ not more than 5 experienced people to 1 fresh one. Which of the following inequalities expresses the above situation, if x be the number of experienced people and y be the number of freshers?

A) y ≥ 5x

B) 5y ≤ x

C) 5x ≥ y

D) x ≤ 5y

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Question 4 :

Consider the quadratic function f(x) = ax² + bx + c. The graph of y = f(x) intersects x-axis at (–7, 0) and (3, 0) and y-axis at (0, 42). What is the value of a + b + c?

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Question 5 :

A piece of iron rod costs $60. If the rod was 2 meters shorter and each meter costs $1 more, the cost would remain unchanged. What is the length of the rod?

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Question 6 :

The sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12. What are the two numbers?

A) 3√2, 2√3

B) 5√2, 3√5

C) 5√3, 2√3

D) 2√2, 5√2

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Question 7 :

A manufacturer produces 80 units of a product at a cost $220,000 and 125 units of the same product at a cost of $287,500. Assume that the cost curve is linear and find the cost of 95 units.

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Question 8 :

A line 3x + 4y = 12 forms a right triangle with the coordinate axes in an xy-plane. Find the length of the perpendicular drawn from the origin to the hypotenuse.

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Question 9 :

Which of the following expressions is equivalent to the expression above?

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Question 10 :

Mean of data set A is 60 and it contains 47 values. Mean of data set B is 55. The combined mean of the two data sets A and B is 57.35. Determine the number of values in data set B.

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Question 11 :

In the figure, parallel lines a and b are intersected by lines c, d, and e. If x = 54, v = 127, and w is greater than x, which statement about y and z must be true?

A) z > y

B) z < y

C) z = y

D) z + y = 90

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Question 12 :

An equilateral triangle has a perimeter of 1200 meters. If the height of the triangle is equal to x√3, what is the value of x?

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Question 13 :

f(x) = (x + a)(x + b)

For the given function f(x), where a and b are integer constants, f(-21) is greater than 0, f(-15) is greater than 0, and f(-18) < 0, what is one possible value of a + b?

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Question 14 :

Which system of linear equations has no solution?

-3x + 7y = -9

3x - 7y = 9

3x - 7y = 5

2x + 8y = 6

4x - 9y = 7

-12x + 27y = -21

-3x + 8y = 20

6x - 16y = 40

Answer :

Question 15 :

Function f is a quadratic function. The graph of y = f(x) in the xy-plane has a vertex at (-7, 14) and passes through the (-4, -31) and has a y-intercept at (0, a). The graph of 3f(x) has a y-intercept at (0, b). What is the positive difference between a and b?

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Question 16 :

Each of the following frequency tables represents a data set. Which of these frequency tables represent the data set with the smallest standard deviation?

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Question 17 :

In the given equation, k is a positive constant. The product of the solutions to the equation is 154. What is the value of k?

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Question 18 :

Two lines intersect at exactly one point, forming two acute angles and two obtuse angles. The measure of one of these angles is (7x - 210)°. Which of the following could NOT be the sum of the measures of any two of these angles?

A) (-14x + 780)°

B) (-14x + 420)

C) 180°

D) (14x - 420)°

Answer :

Question 19 :

The mass of particles A, B and C are a atomic mass units, b atomic mass units, and c atomic mass units, respectively. If the mass of particle A is 4,600% of the mass of particle c, and the mass of particle c is 0.004% of the mass of particle b, which expression represents the value of a + b in terms of c?