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
Question Easy
The graph of a linear equation and the graph of a quadratic equation are shown. What is true about the point \((-1,4)\) ?
A) The point satisfies only the quadratic equation
B) The point satisfies only the linear equation.
C) The point satisfies both equations.
D) The point satisfies neither equation.
▶️Answer/Explanation
Ans:C
For the linear equation represented by the straight line: Let’s call this equation y = mx + b, where m is the slope and b is the y-intercept. The point (-1, 4) is on this line, so if I substitute x = -1 and y = 4, it should satisfy the equation. 4 = m(-1) + b Solving for b using the point’s coordinates gives b = 4 + m
For the quadratic equation represented by the parabola: Let’s call this y = ax^2 + bx + c, where a, b, c are constants. Substituting x = -1 and y = 4, we get:
$4 = a(-1)^2 + b(-1) + c$ $
4 = a + (-b) + c$
Therefore, the point (-1, 4) satisfies both the linear and quadratic equations shown.
Question Easy
A ball is thrown upward from a height of 3 feet above the ground. Assuming no air resistance, the function \(h\) defined by \(h(t)=-16 t^2+36 t+3\) models the ball’s height \(h(t)\), in feet, above the ground \(t\) seconds after it is thrown. Based on the model, what is the meaning of \(h(2)=11\) in this context?
A) The ball hits the ground 2 seconds after it is thrown.
B) The ball hits the ground 11 seconds after it is thrown.
C) The ball is 11 feet above the ground 2 seconds after it is thrown.
D) The ball is 2 feet above the ground 11 seconds after it is thrown.
▶️Answer/Explanation
Ans:C
The function \(h(t) = -16t^2 + 36t + 3\) models the height of the ball above the ground at time \(t\). Substituting \(t = 2\) into the function gives us:
\[
h(2) = -16(2)^2 + 36(2) + 3 = -64 + 72 + 3 = 11
\]
So, \(h(2) = 11\) means that the ball is 11 feet above the ground 2 seconds after it is thrown. Therefore, the correct answer is C) The ball is 11 feet above the ground 2 seconds after it is thrown.
Question Easy
\(x^2 + 2x + 1 = 4\)
What is the positive solution to the given equation?
▶️Answer/Explanation
Ans:1
To solve the equation \(x^2 + 2x + 1 = 4\) for the positive solution:
Rewrite the equation:
\[
x^2 + 2x + 1 – 4 = 0
\]
\[
x^2 + 2x – 3 = 0
\]
Factor the quadratic equation:
\[
(x + 3)(x – 1) = 0
\]
Solve for \(x\):
\[
x + 3 = 0 \quad \text{or} \quad x – 1 = 0
\]
\[
x = -3 \quad \text{or} \quad x = 1
\]
Since we are looking for the positive solution:
\[
x = 1
\]
Question Easy
\(x^{2}-x-12=0\)
What is the sum of the solutions to the given equation?
A. -7
B. -1
C. 1
D. 7
▶️Answer/Explanation
Ans: C
To find the solutions, we can factor the quadratic equation:
\[ x^2 – x – 12 = 0 \]
\[ x^2 – 4x +3x- 12 = 0 \]
\[ x(x – 4)+3(x – 4) = 0 \]
\[ (x-4)(x+3) = 0 \]
So, the solutions are \(x = 4\) and \(x = -3\).
The sum of the solutions is \(4 + (-3) = \boxed{\text{C) } -1}\).
Question Easy
An object is kicked from a platform. The equation \(h = -4.9t^2 + 15t + 5\) represents this situation, where h is the height of the object above ground, in meters, t seconds after it is kicked. Which number represents the height, in meters, of the platform ?
A) 0
B) 4.9
C) 5
D) 15
▶️Answer/Explanation
C) 5
The equation \(h = -4.9t^2 + 15t + 5\) represents the height of an object above the ground in meters, \(t\) seconds after it is kicked. We need to find the height of the platform from which the object is kicked.
1. Identify the height of the platform:
The height of the platform corresponds to the value of \(h\) when \(t = 0\).
2. Substitute \(t = 0\) into the equation:
\[
h = -4.9(0)^2 + 15(0) + 5
\]
\[
h = 5
\]
Thus, the height of the platform is:
\[ \boxed{5} \]