## SAT MAth Practice questions – all topics

**Advanced Math**Weightage: 35% Questions: 13-15- Equivalent expressions
- Nonlinear equations in one variable and systems of equations in two variables
- Nonlinear functions

## SAT MAth and English – full syllabus practice tests

**[Calc]**** ****Question**** Easy**

The graph shown models the number of area codes assigned to phone numbers in Illinois from 1947 through 2009, where \(x\) represents the number of years after 1947. Which equation represents this relationship?

A) \(y=1.02(3.26)^{-x}\)

B) \(y=3.26(1.02)^{-x}\)

C) \(y=1.02(3.26)^x\)

D) \(y=3.26(1.02)^x\)

**▶️Answer/Explanation**

**Ans:D**

Given that the number of area codes is growing over time, the graph suggests an exponential growth pattern. The general form of an exponential growth equation is:

\[

y = a(b)^x

\]

Looking at the given options, the correct form must match this pattern. The options are:

A) \( y = 1.02(3.26)^{-x} \)

B) \( y = 3.26(1.02)^{-x} \)

C) \( y = 1.02(3.26)^x \)

D) \( y = 3.26(1.02)^x \)

Since the graph shows an increasing trend, we are dealing with exponential growth, so the exponent should not have a negative sign, ruling out options A and B.

Next, we look at options C and D:

Option C: \( y = 1.02(3.26)^x \)

Option D: \( y = 3.26(1.02)^x \)

To decide between these, we need to check the initial value and the base of the exponent. The graph starts at a point around 3 area codes when \( x = 0 \).

In option C, the initial value \( a = 1.02 \), which does not match our initial observation.

In option D, the initial value \( a = 3.26 \), which is closer to the starting value seen in the graph.

Therefore, the correct equation representing this relationship is:

D) \( y = 3.26(1.02)^x \)

**[Calc]**** ****Question*** *** Easy**

The graph of the function \(t\) is shown, where \(y=t(x)\). Which of the following types of functions is graphed?

A. Increasing linear

B. Decreasing linear

C. Increasing exponential

D. Decreasing exponential

**▶️Answer/Explanation**

Ans:D

**A. Increasing linear:**

- Straight line sloping upwards from left to right
- Constant rate of change (slope)

**B. Decreasing linear:**

- Straight line sloping downwards from left to right
- Constant negative rate of change (slope)

**C. Increasing exponential:**

- Curve increasing rapidly towards positive infinity as x increases
- y-intercept can be positive or negative

**D. Decreasing exponential:**

- Curve decreasing rapidly towards the x-axis (horizontal asymptote at y=0) as x increases
- y-intercept is positive
- Approaches zero but never touches the x-axis

From this above discussion Option- D is best Fit

**[Calc]**** ****Question** ** Easy**

The graph of the exponential function f is shown.

For what value of x is f (x) = 0 ?

A) -4

B) -3

C) 0

D) 4

**▶️Answer/Explanation**

B) -3

**[No-Calc]**** ****Question** ** Easy**

The graph models the radioactive decay of the sodium-24 in a sample over time. According to the graph, at 5 hours, which of the following is closest to the mass, in milligrams, of the sodium-24 in this sample?

A. 25

B. 31

C. 40

D. 50

**▶️Answer/Explanation**

Ans: C

At 5 hours, 40 is closest to the mass, in milligrams, of the sodium-24 in this sample.

*Question*

What is the graph of the equation \(y=3^x\)

**Answer/Explanation**

Ans: A

*Question*

What is the graph of the equation \(y\)=2(3)^{\(x\) }

**Answer/Explanation**

Ans: A

*Question*

What is the \(y\)-coordinate of the \(y\)-intercept of the graph of \(y\)=3^{\(x\)}+9?

**Answer/Explanation**

Ans: 10

*Question*

What is the graph of \(y\)=4-2(0.5)^{\(x\) }?

**Answer/Explanation**

Ans: C

*Question*

The graph of the exponential function \(f\) is shown. For what value of \(x\) is \(f\)(\(x\))=0?

- -4
- -3
- -2
- -1

**Answer/Explanation**

Ans: C

*Question*

What is the equation of the graph shown?

- \(y\)=3
^{\(x\)} - \(y\)=2(3)
^{\(x\)} - \(y\)=2
^{\(x\)} - \(y\)=3(2)
^{\(x\)}

**Answer/Explanation**

Ans: B

*Question*

The graph of \(y = 2^x – a\) is shown, where \(a\) is a constant. What is the value of \(a\) ?

- 4
- 3
- 2
- 1

**Answer/Explanation**

Ans: A

*Question*

(\(x\)-8)^{3}=0

What is the solution to the given equation?

- -8
- -2
- 2
- 8

**▶️Answer/Explanation**

D

Costs of some steps to publish a manuscript can vary, as shown in the table.

*Question*

A calf, the offspring of a cow, weighed 62 pounds at birth. The calf is expected to gain 2 pounds every day for the first 2 years of its life. For this time period, which of the following types of functions best models the weight of the calf as a function of time?

- Increasing linear
- Decreasing linear
- Increasing exponential
- Decreasing exponential

**▶️Answer/Explanation**

A

*Question*

The function A(t) = 10(1/2)^{t/30} represents the mass A(t) , in grams, of a certain radioactive isotope remaining in a substance after t seconds. Which of the following is the best interpretation of the value 10 in this context?

- The initial mass, in grams, of the radioactive isotope in the substance when t = 0
- The mass, in grams, of the radioactive isotope in the substance after 30 seconds
- The number of seconds it takes for the radioactive isotope in the substance to completely disappear
- The number of seconds it takes for half of the initial mass of radioactive isotope in the substance to disappear

**▶️Answer/Explanation**

A

*Question*

The graph of \(y = f(x)\) is shown in the \(xy\)-plane . What is the value of \(f(0)\)?

- -8
- -4
- -1
- 0
**▶️Answer/Explanation**Ans: A