10 Hard SAT Math Questions

Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

Question 1 :

a is 540% more than b and b is 0.02% of c. If a is k% of c, then what must k equal to ?

Answer :

Question 2 :

(hx + k)(qx + z) = ax² + bx + 35 For the expression above, h, k, q and z are all integer constants. Which of the following must be an integer?

I. 35/k

II. b

III. -a/q

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

Answer :

Question 3 :

f(x) = πx³ + πx²

The given function f represents the volume, in cubic feet, of a right circular cylinder with a radius of x feet. Which expression represents the height, in feet, of the cylinder?

A) x + 1

B) πx³

C) x

D) x³ + 1

Answer :

Formula for volume of a cyliner = πr²h

Radius of the given right circular cylinder is x feet. So, to get volume of the given right circular cylinder, substitute r = x into the above formula.

Volume of the given cylinder = πx²h

Given : f(x) = πx³ + πx²represents the volume of the cylinder.

Then, we have

πx²h = πx³ + πx²

Factor the expression on the right side.

πx²h = πx²(x + 1)

Divide both sides by πx².

h = x + 1

The correct answer answer choice is (A).

Question 4 :

The expression 8x² – ½y² is equivalent to 8(x – cy)(x + cy), where c is a positive constant. What is the value of c?

A) 1/16

B) 1/8

C) 1/4

D) √2/4

Answer :

Given : 8x² – ½y² is equivalent to 8(x – cy)(x + cy).

8x² – ½y² = 8(x – cy)(x + cy)

Using algebraic identity (a + b)(a - b) = a² - b²,

8x² – ½y² = 8[x² – (cy)²]

8x² – ½y² = 8(x² – c²y²)

8x² – ½y² = 8x² – 8c²y²

Subtract 8x²from both sides.

–½y² = –8c²y²

Divide both sides by –8y².

1/16 = c²

1/4 = c

The correct answer answer choice is (C).

Question 5 :

f(x) = –3x² + bx + c

In the given quadratic function, b and c are constants. The graph of y = f(x) in the xy-plane is a parabola that has a vertex at the point (h, k), where h and k are constants. If f(–4) = f(8), and the quadratic function has x-interceptsat (r, 0) and (s, 0), which of the following must be true?

I. r + s = 4

II. b < 0

III. c < k

A) I and II only

B) II and III only

C) I and III only

D) I, II and III

Answer :

Question 6 :

The function g is defined by g(x) = x(x − 2)(x + 6)². The value of g(7 - w) is 0, where w is a constant. What is the sum of all possible values of w?

Answer :

g(x) = x(x − 2)(x + 6)².

Given : The value of g(7 - w) is 0.

g(7 - w) = 0

(7 - w)(7 - w - 2)(7 - w + 6)²= 0

(7 - w)(5 - w)(13 - w)²= 0

7 - w= 0

-w = -7

w = 7

5 - w = 0

-w = -5

w = 5

(13 - w)²= 0

13 - w= 0

w = 13

Sum of all possible values of w :

= 7 + 5 + 13

= 25

Question 7 :

In the equation above, a, b, c and d are constants. What is the value of a + b + c?

Answer :

Question 8 :

A right rectangular prism has a height of 9 inches. The length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base?

A) V(x) = x(x + 9)(x + 7)

B) V(x) = x(x + 9)(x - 7)

C) V(x) = 9x(x + 7)

D) V(x) = 9x(x - 7)

Answer :

Given : The length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base.

Then, the width of the prism's base is (x - 7) inches.

Given : The height of the prism is 9 inches.

Formula for volume of prism = ℓ ⋅ w ⋅ h

Substitute ℓ = x, w = x - 7 and h = 9 in the above formula to get the volume of the given prsim.

V(x) = x ⋅ (x - 7) ⋅ 9

V(x) = 9x(x - 7)