SAT MATH QUESTIONS AND SOLUTION
Question 1 :
P = 215(1.005)t/3
The equation above can be used to model the population, in thousands, of a
certain city t years after 2000. according to the model, the population is
predicted to increase by 0.5% every n months. what is the value of n ?
(A) 3 (B) 4 (C) 12 (D) 36
Answer :
0.5% = 0.5/100 = 0.005
It is given that the population (215) is predicted to increase by 0.5%. To
know the value after increment, 215 has to be multiplied by (1 + 0.005) or
1.005.
In the equation P = 215(1.005)t/3, the value of t/3 has to be equal to 1 for
0.5% increase.
t/3 = 1
t = 3 years
Convert years to months.
n = 3 ⋅ 12 months
n = 36 months
, The correct option is D.
Question 2 :
In the xy-plane, the graph of a linear equation of the form y = mx + b and
the graph of an exponential equation of the form y = ab x both contain points
(1, 3) and (2, 4). If the point (r, s) is on the graph of the linear equation and
the point (r, t) is on the graph of the exponential equation, where 0 < r < 4
and s > t, which of the following must be true?
(A) 0 < r < 1 (B) 1 < r < 2 (C) 2 < r < 3 (D) 3 < r < 4
Answer :
Linear equation y = mx + b contains (1, 3) and (2, 4).
4 = 2m + b ----(1) 3 = m + b ----(2)
Solving (1) and (2), we get
m = 1 and b = 2
Linear equation : y = x + 2.
Exponential equation y = abx contains (1, 3) and (2, 4).
3 = ab1 ----(3) 4 = ab2 ----(4)
Divide (4) by (3).
ab2/ab1 = 4/3
Question 1 :
P = 215(1.005)t/3
The equation above can be used to model the population, in thousands, of a
certain city t years after 2000. according to the model, the population is
predicted to increase by 0.5% every n months. what is the value of n ?
(A) 3 (B) 4 (C) 12 (D) 36
Answer :
0.5% = 0.5/100 = 0.005
It is given that the population (215) is predicted to increase by 0.5%. To
know the value after increment, 215 has to be multiplied by (1 + 0.005) or
1.005.
In the equation P = 215(1.005)t/3, the value of t/3 has to be equal to 1 for
0.5% increase.
t/3 = 1
t = 3 years
Convert years to months.
n = 3 ⋅ 12 months
n = 36 months
, The correct option is D.
Question 2 :
In the xy-plane, the graph of a linear equation of the form y = mx + b and
the graph of an exponential equation of the form y = ab x both contain points
(1, 3) and (2, 4). If the point (r, s) is on the graph of the linear equation and
the point (r, t) is on the graph of the exponential equation, where 0 < r < 4
and s > t, which of the following must be true?
(A) 0 < r < 1 (B) 1 < r < 2 (C) 2 < r < 3 (D) 3 < r < 4
Answer :
Linear equation y = mx + b contains (1, 3) and (2, 4).
4 = 2m + b ----(1) 3 = m + b ----(2)
Solving (1) and (2), we get
m = 1 and b = 2
Linear equation : y = x + 2.
Exponential equation y = abx contains (1, 3) and (2, 4).
3 = ab1 ----(3) 4 = ab2 ----(4)
Divide (4) by (3).
ab2/ab1 = 4/3
